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# Data Sufficiency Shortcut Tricks & Tips Concept Learn Now

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# Data Sufficiency Tricks & Tips

Data sufficiency is one of the most important as well as most difficult type of question. Questions based on data sufficiency requires deeper knowledge in the subject area. Data sufficiency questions can be from any topic viz Numbers, Arithmetic, Algebra, Geometry, and puzzles. These questions are not only difficult but also confusing. Students generally get confuse with the given information. Some general tips to solve the data sufficiency questions are discussed below.

Tip 1 : 1st and foremost is understanding of options.

Tip 2 : Identify the parent question, means the main question that is asked.

Tip 3 : Look at the statement (i) and information given in that, see whether it is sufficient enough to answer the parent question.

Tip 4 : Look at the statement (ii) and information given in that, most important is that whenyou see statement (ii) then just forget the information given in statement (i) , then seewhether it is sufficient enough to answer the parent question.

Tip 5 : When the given statements are not sufficient then use information given in both the statements.

First, set your timer for 2 minutes and try this problem:

* ” A contractor combined x tons of gravel mixture that contained 10 percent gravel G, by weight, with y tons of a mixture that contained 2 percent gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight. What is the value of x?

“(1) y = 10

“(2) z = 16”

### 1. Did We know WHAT they were trying to test?

It’s testing the concept of average (arithmetic mean) and, more specifically, it’s testing the concept of weighted average. The problem never mentions the word “average” but we figured this out because the problem talks about 2 sub-groups that are combined in some way to make a 3rd overall group, or mixture of the original 2 sub-groups.

– Did we COMPREHEND the symbols, text, questions, statements, and answer choices? Can we comprehend it all now, when we have lots of time to think about it? What do we need to do to make sure that we do comprehend everything here? How am we going to remember whatever we’ve just learned for future?

we noticed that the problem has three variables: x, y, and z. It asks to solve for the value of x. One of the statements gives us the value for y and the other gives us the value for z. We already thinking E is probably not the right answer (think about why before you keep reading – We’ll explain this under the “Other Strategies” question, below).

– Did we understand the actual CONTENT (facts, knowledge) being tested?

What kind of average is this problem discussing? Regular average / mean is characterized by the formula A = S/n, where A is the average of the set, S is the sum of the items in the set, and n is the number of items in the set. Is this problem testing “regular” averages? Let’s see: a “regular” average of 10% gravel and 2% gravel would be (10+2) /2 = 6. But the problem says the resulting mixture is 5% gravel, not 6% gravel – so this isn’t a “regular” average.

That means this problem must be about the more complicated weighted average. In a weighted average, some of the elements are weighed, or counted more heavily, than other elements, so the calculation has to take that into account. (And we have to know how to do that… more on that later.)

### 2. How well did We HANDLE what they were trying to test?

– Did We choose the best APPROACH? Or is there a better way to do the problem? (There’s almost always a better way!) What is that better way? How we are going to remember this better approach the next time we see a similar problem?

Weighted average problems can be solved by using the weighted average formula, which is what we tried to do. we got into trouble with it though – we didn’t set it up properly and so we couldn’t finish it to see whether we could solve.

There’s a shortcut solution method that we could have used, but we forgot about it when we was doing this problem.

– Did w have the SKILLS to follow through? Or did we fall short on anything?

We ended up having to guess because we couldn’t solve the “official math” way and then we forgot to try the easier “shortcut” way. We are going to redo this problem using the easier shortcut, and also going to go find a couple of additional weighted average problems and do those with the easier shortcut way so that we can make sure that (a) We know how to do it this way, and (b) We remember / recognize when we can do it this way.

we should still also learn how to do this using the “official math” weighted average formula, just in case we ever have to use the long way.

– Did we make any careless mistakes? If so, WHY did we make each mistake? What habits could we make or break to minimize the chances of repeating that careless mistake in future?

When we tried to use the “official” formula, we couldn’t remember exactly how to set it up, so we ended up setting it up with too many variables, and then of course we couldn’t solve. It’s data sufficiency, so knowing we can’t solve is sufficient… except that we knew we were doing something wrong because we couldn’t really remember the formula. we need to go and study that formula. we should make a flash card with “weighted average formula” on one side, and the couple of different ways the formula can be written on the other side.

– Do we are comfortable with OTHER STRATEGIES that would have worked, at least partially? How should we have made an educated guess?

We were pretty sure it wasn’t E because it looks like you can set up a three-variable equation, and then we’re supposed to solve for x. Each statement gives us only one of the two remaining variables, so it “looks like” it can’t be done unless you have both of the other variables… which you would for answer choice C. So, at the least, C does work and it’s not E.

We ended up guessing C but, in hindsight, that’s a trap too. we could ask my 14-year-old niece: if you have an equation with three variables and you want to solve for one of those variables, what do you need to know? And she’d say “The other two variables.” (And then she’d probably think, “Duh, Aunt Stacey.”) This test isn’t for my 14-year-old niece, though, it’s for people who have already graduated from college. So that’s too easy. And that’s really interesting, because that means that you most likely CAN actually solve given just one statement. Each statement represents one of the two unknown variables, so if one works, it’s fairly likely that the other one works too… so we probably should have guessed D.

– Do we understand every TRAP & TRICK that the writer built into the question, including wrong answers?

See above – we think C and E are both trap answers on this one, and C is especially tempting.

### 3. How well did we or could we RECOGNIZE what was going on?

– Did we make a CONNECTION to previous experience? If so, what problem(s) did this remind me of and what, precisely, was similar? Or did we have to do it all from scratch? If so, see the next bullet.

– Can we make any CONNECTIONS now, while we were analyzing the problem? What have we done in the past that is similar to this one? How are they similar? How could that recognition have helped me to do this problem more efficiently or effectively? (This may involve looking up some past problem and making comparisons between the two!)

Yes, we did make a connection, but we also missed one. we did recognize that this was a weighted average problem even though it didn’t explicitly mention the word “average,” so we are happy about that. we didn’t recognize, however, that we could have used a big shortcut that would have saved us a lot of time and frustration. we need to go study that shortcut, how to recognize it, how to use it, etc – and maybe make a couple of flash cards.

– HOW will we recognize similar problems in the future? What can we do now to maximize the chances that we will remember and be able to use lessons learned from this problem the next time we see a new problem that tests something similar?

we need to do everything we already described in our notes above. we are also going to re-do this problem from scratch– actually make yourself write out the best way to do it, alternate ways to do it, how to make a guess, and so on, so that we really remember the lessons. Then, because our big problem on this one was with recognizing that we could use a shortcut and then actually using it, we are going to find other weighted average problems that we’ve already done in the past and practice: (1) knowing how to recognize that it’s a weighted average and that it qualifies for the “weighted average shortcut,” (2) working through the problem using that shortcut, and (3) thinking about how to make an educated guess. Then we are going to do new weighted average problems as part of a mixed set of problems consisting of things we’ve messed up recently and other random things (so that we don’t know exactly what we were getting for each problem) and see whether we can quickly recognize and apply what we just learned.

And that’s it! Note that, of course, the details above are specific to each individual person – such a write-up would be different for every single one of you, depending upon your particular strengths, weaknesses, and mistakes. Hopefully, though, this gives you a better idea of the way to analyze a problem. This framework also gives you a valuable way to discuss problems with fellow online students or in study groups – this is the kind of discussion that really helps to maximize scores.

We have seen that a majority of aspirants try follow guess work to solve these data sufficiency questions. This is not the right approach. So instead of guessing, we should use certain tips and tricks to solve these questions.

• Don’t  Solve the Question:

The interesting part about DS type questions is that they only ask you whether the question can be solved with the help of information given in the statements. That simply means there is no need to solve that question completely and waste your precious time. So just answer these questions and do not even try to solve them .There are several common tricks.

Do not think in terms of “What will be the exact value?” or “Is it true or false?”

Instead, just focus on only one issue: “Is the information enough o answer the question?”

Example:

Directions:-

• if statement I alone is sufficient to answer the question, Marks A as answer
• if statement II alone is sufficient to answer the question, Marks B as answer
• if statement I and II together are sufficient to answer the question but neither statement aloneis sufficient to answer the question, Marks C as answer
• if either statement I or II aloner is sufficient to answer the question, Marks D as answer
• if statement I and II together are not sufficient to answer the question, Marks E as answer

How much was the cost of Diamond Necklace in January 2000?

(1) In January 2010 the necklace was worth \$10,000.

(2) Over the ten years 2000-2010, the necklace increased in value by 10% each 12 months.

Solution

Statement (1) is insufficient. You don’t know the rate at which value has changed. You immediately know the answer must be B, C or E.

Statement (2) is insufficient. Without a value between 2000 and 2010, you can’t calculate the value.

Using statements (1) and (2) together, you could calculate the value in 2000. Since you need both statements to find the value, the answer is option (C).

The trick: Don’t do the calculation. For most “value” questions, you could calculate the value but calculations are a waste of time. The problem asks if there is enough information to answer the question, not for the actual answer.

• Atempt YES NO type questions first

A number of questions are based on “YES-NO” type data. See the statements and discard them on the basis of yes or no.

Example:

• if statement I alone is sufficient to answer the question, Marks A as answer
• if statement II alone is sufficient to answer the question, Marks B as answer
• if statement I and II together are sufficient to answer the question but neither statement aloneis sufficient to answer the question, Marks C as answer
• if either statement I or II aloner is sufficient to answer the question, Marks D as answer
• if statement I and II together are not sufficient to answer the question, Marks E as answer

Is x divisible by 28?

Statement I: x is divisible by 20

Statement II: x is divisible by 84

Answer. Using statement I – x is divisible by 4 and 5

Using statement II – x is divisible by 3, 4 and 7.

By using both statements we can conclude that x is divisible by 28 (4*7), hence answer is C.

• Treat both the statements separately:

So now you have studied the question and analyzed the information given in, now is the time to analyze the statements given in the question. The key rule here “Read statements independently of each other”. Try to “forget” statement 1 before you move on to statement 2.

Don’t carry over any info from statement 1 when you read statement 2.

Example:

How many adults eat pizza in city X if all adults in city X either eat Pizza or Pasta?

(1) 75% of the 100,000 adults in city X eat Pasta.

(2) 75,000 adults in city X eat Pasta.

Solution

Statement (1) is sufficient. Taking a percent of a total population allows you to calculate the adults that eat pizza. (NO need to do the calculation.) You immediately know the answer is A or D.

Statement (2) is insufficient. Without the total population or other information, you can’t calculate the number of adults eating pasta.

Since first statement alone is sufficient, the correct answer is option (A).

The trick: Keep the information from first statement and second statement as separate. Either the percentage or total population from first statement can make second statement sufficient.

When you read second statement, forget what you read in first statement so you can evaluate second statement alone.

The only time to combine the statements is when each of them is insufficient alone

• Eliminate wrong options:

This will help you to eliminate the statements quickly if you have something to compare with the information given.

Do this step with a focused mind.

If first statement is sufficient, eliminate B, C, and E.

You will now be left with only two options ie A and D.

In the same way If second statement is sufficient, eliminate A, C, and E.

You will now be left with only two options ie B and D.

Conversely if first statement is NOT sufficient, eliminate A and D

In the same if second statement is NOT sufficient, eliminate B and D.

In this way you can eliminate a number of options.

### Sample Question #1

A certain group of car dealerships agreed to donate x dollars to a Red Cross chapter for each card sold during a 30-day period. What was the total amount that was expected to be donated?

1. A total of 500 cars were expected to be sold.
2. 60 more cars were sold than expected, so that the total amount actually donated was \$28,000.
1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
3. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
4. EACH statement ALONE is sufficient
5. Statements (1) and (2) TOGETHER are NOT sufficient

#### SAMPLE QUESTION #1 EXPLANATION

The best way to approach data sufficiency questions is to take each statement individually first, before having to consider them together. To that end, let’s start with statement 1.

Statement 1: The question asks us to determine how much money will be donated to the Red Cross based on the number of cars sold at the dealership. With data sufficiency questions, we always want to start with what we know.

We know that 500 cars are expected to be sold, as it tell us that in statement 1. Now, we need to decide if we can figure out how much money will be donated.

The question tells us that x dollars will be donated for each car sold, so the equation 500x represents the total amount of the expected donation.

However, we don’t know the value of x, and we have no way of determining it from the information given. So, we cannot solve the equation 500x, meaning that statement 1 is NOT sufficient for us to solve this problem.

Statement 2: Just as we took statement 1 by itself, let’s take statement 2 by itself first.

Statement 2 tells us that 60 more cars were sold than expected. If we know that x represents the amount of money donated to the Red Cross for each car, then we know that 60x represents the amount donated beyond the expected amount, because 60 cars were sold and x dollars were donated for each car.

If the total amount of the donation was \$28,000, then the total amount that was expected can be found using the equation \$28,000 – 60x, with 60x representing the unexpected amount we found before. Since we don’t know what x represents, we can’t find the total amount of the expected donation using Statement 2 alone.

Now that we’ve evaluated both statements individually, it’s time to evaluate them together. The first thing I notice when I look at both statements is that both statements have x in them. That means that I can combine the statements and solve for x.

Combining the two statements yields me the equation 500x = 28000 – 60x. From there, I can determine the total amount of the expected donation since I can combine like terms and solve for x.

Notice that I don’t actually have to solve this equation. All I need to do is know that I can solve it. Since I can solve with the statements together, but not alone, my correct answer is C.

### Sample Question #2

A certain wooded lot contains 56 oak trees. How many pine trees does the lot contain?

1. The ratio of the number of oak trees to the number of pine trees in the lot is 8 to 5.
2. If the number of oak trees was increased by 4 and the number of pine trees remained unchanged, the ratio of the number of oak trees to the number of pine trees in the lot would be 12 to 7.
1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
3. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
4. EACH statement ALONE is sufficient
5. Statements (1) and (2) TOGETHER are NOT sufficient

The first step in this question is to figure out what you’re trying to solve for. The question asks you how many pine trees the lot contains. Let’s use p as our variable to represent the number of pine trees the lot contains. You’re trying to solve for p in this equation.

Statement 1: Remember, we always want to start out by evaluating each statement individually. Statement 1 says that the ratio of oak trees to pine trees is 8 to 5. The ratio 8 to 5 can also be represented as 8/5. We can also say that the number of oak trees to pine trees is 56 to p, or 56/p, based on the information in the question.

Now, we can set the equations equal to each other because they both represent the same thing (ratio of oak to pine trees). Setting the equations equal to each other yields the equation 8/5 = 56/p. Because there is only one variable in this equation, I will be able to solve for p with no extra information. Statement 1 is therefore sufficient to answer the question.

Statement 2: Even though we already know that Statement 1 is sufficient, we’re still going to solve evaluate Statement 2 by itself first. Statement 2 says that the number of oak trees increased by 4. The question tells us that the original number of oak trees was 56, so 56 + 4 = 60. 60 is the new number of oak trees.

Next, the statement tells us that the ratio of oak trees to pine trees is now 12 to 7. We can also write the ratio of 12 to 7 as 12/7. We can also say that the number of oak trees to pine trees is 60 to p or 60/p. Just as we did with Statement 1, we can set the equations equal to each other, yielding the equation 60/p = 12/7.

Remember, we don’t need to solve for p, we just need to know that we can. Based on the information in Statement 2, we can also solve for p.

Statements 1 and 2 both contain enough information for us to answer the question, so the correct answer is D.

### Sample Question #3

Does 2m – 3n = 0?

1. m ≠ 0
2. 6m = 9n
1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
3. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
4. EACH statement ALONE is sufficient
5. Statements (1) and (2) TOGETHER are NOT sufficient

Let’s start off by examining the question. We always want to make sure we understand what the question is asking us. We also want to make sure that we simplify the question, if possible,because simplifying the question will give us easier and clear equations to use as we solve the problem. In this case, we can simplify the question. The question “Does 2m – 3n = 0” is equivalent to the simpler question “Does 2m = 3n?”

Statement 1: If you’ve read the explanations for the previous two questions, I probably sound like a broken record by now, but I’ll repeat myself again. Remember, we always want to evaluate each statement individually, before looking at them together.

Let’s look at Statement 1 by itself. Statement 1 says that m doesn’t equal 0. That doesn’t give us a lot of information. Let’s go back to the original equation and see what we can learn there.

In the original, we see that 2m = 3n. In that equation, we also don’t have a lot of information. Statement 1 leaves an infinite range of possible values for m, and, since neither Statement 1 nor the original equation address possible values for n, we have no way to figure out the relationship between m and n. Therefore, Statement 1 is not sufficient.

Statement 2Even though we know Statement 1 isn’t sufficient, we’re going to try to figure out Statement 2 by itself first. Statement 2 says that 6m = 9n. Right away, I notice that both 6 and 9 are multiples of 3, so the equation can be simplified by dividing each term by 3.

When I divide each term by 3, I get 6m/3 = 9n/3. If I simplify that, I get 2m = 3n. Remember, 2m = 3n is the original equation I’m looking for, so Statement 2 is sufficient and the correct answer is B.

### Sample Question #4

If n is a member of the set {33, 36, 38, 39, 41, 42}, what is the value of n?

1. n is even.
2. n is a multiple of 3.
1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
3. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
4. EACH statement ALONE is sufficient
5. Statements (1) and (2) TOGETHER are NOT sufficient

Let’s start out by understanding what the question’s asking us. It’s asking us to determine the value of n, which is a member of the set {33, 36, 38, 39, 41, 42}. So, for our statements to be sufficient, they need to help us decide which of those six numbers n is.

Statement 1: Look at Statement 1 alone first. Statement 1 says that n is even. That implies that n can be either 36, 38, or 42, because those are the even numbers of that six number set. However, there’s no other information in the statement that can help us narrow down which one of those three numbers n is. So, Statement 1 is not sufficient.

Statement 2: Statement 2 says that n is a multiple of 3. This implies that n could be 33, 36, 39, or 42. However, there’s no further distinction in Statement 2 to determine which of those four numbers n is. So, Statement 2 is not sufficient.

If we combine Statements 1 and 2 together, n is even and a multiple of three. That leaves us with n equaling either 36 or 42, with no way to determine which of those n is. Therefore, the statements are insufficient alone and together, so the correct answer is E.

PATTERN OF QUESTION

Directions : Each of the following questions is followed by two statements. Mark

(a) if statement I alone is sufficient to answer the question.
(b) if statement II alone is sufficient to answer the question.
(c) if both statement I and II together are necessary to answer the question.
(d) if both statements I and II together are not sufficient to answer the question

Directions: In each of the following questions, a question is followed by two or three statement. Read all the statements and find that which statements are required to answer the question and answer accordingly.

Who is the tallest among A, B, C, D and E?
I. D is the tallest among C, A and E.
II. B is not shorter than at most A and E.

(a) if statement I alone is sufficient to answer the question.
(b) if statement II alone is sufficient to answer the question.
(c) if both statement I and II together are necessary to answer the question.
(d) if both statements I and II together are not sufficient to answer the question

Solution: From I, we get that

D > C, A, E.

From II, B is the third or 4th tallest or the shortest person.

On combining, we get that D is the tallest person.
Hence, option c.

Directions: In each of the following questions, a question is followed by two or three statement. Read all the statements and find that which statements are required to answer the question and answer accordingly.

Who is the tallest among A, B, C, D and E?
I. D is the tallest among C, A and E.
II. B is not shorter than at most A and E.

(a) if statement I alone is sufficient to answer the question.
(b) if statement II alone is sufficient to answer the question.
(c) if both statement I and II together are necessary to answer the question.
(d) if both statements I and II together are not sufficient to answer the question

Among four friends A, B, C and D, who is the heaviest ?

I. B is heavier than A, but lighter than D.
II. C is lighter than B.

Solution:
From I, we have A < B < D.
From II, we have C < B.
Combining (i) and (ii), we can conclude that D is the heaviest. So, both the statements are needed

# Problems Based On Data Sufficency

Directions: In each of the following questions, a question is followed by two or three statement. Read all the statements and find that which statements are required to answer the question and answer accordingly.

1. How much time will Train P take to cross Train Q (from the moment they meet) running in opposite directions (towards each other) ?
statement I: The respective ratio of speeds of Train P and Train Q is 3 : 4. The sum of the lengths of Train P and Train Q is 700 metre.
statement II: Train P can cross a signal pole in 12 seconds. It can cross 600  metre long station in 25 seconds.
A) Only I
B) Both I and II
C) Only II
D) Either I or II
E) Neither I nor II
Option E
Solution:
From statement I:

Relative speed = 3x + 4x = 7x units
Sum of Length of trains = 700 m
Required time = 700/7x = no result
From statement II:
speed of train P = x/12 = (x + 600)/25
=> 25x = 12x + 7200
=> 13x = 7200
=> x = 7200/13

• What is the area the isosceles triangle A ?
statement I: The length of the side opposite the single largest angle in the triangle is 8cm.
statement II: The perimeter of triangle X is 20cm.
A) Only II
B) Only I
C) Neither I nor II
D) Both I and II
E) Either I or II

Option  D
Solution:
In a triangle, the side opposite the largest angle will be the longest. Correspondingly, the side opposite the smallest angle will be the shortest.

• What is the ratio between the two numbers a and b ?
statement I: 50% of a is 25% of 80.
statement II: 20% of b is 10% of 100.
A) Both I and II
B) Only I
C)Only II
D) Either I or II
E) Neither I nor II
Option A
Solution:
Both I and II required together.

• What is the age of R, in a group of P,Q, R,S and T whose average age is 45 years?
statement I: Average of the age of S and T is 47 years?
statement II: Average of the age of P and Q is 53 years?
A)  Only II
B) Only I
C) Both I and II
D) Neither I nor II
E) Either I or II

Option C
Solution:
From statement I and II:

P + Q + R + S + T = 5 * 45 = 225 years ———-(1)
P + Q = 106 years ————–(2)
S + T = 94 years —————(3)
From (1), (2) and (3), we get
We get the age of  R .

• How many people are there in the aeroplane ?
statement I: There are 45 females in the aeroplane.
statement II: 30% of passengers are males and 10% are children.
A) Either I or II
B) Only II
C) Only I
D) Neither I nor II
E) Both I and II

Option E
Solution:
From statements I and II:

Number of female passengers = 45
There are  60% of the female in the aeroplane.
Total no. of passengers = 45 *(100/60) = 75

•  The ratio between the present ages of the Rohit and Rina is 1 : 3. Find the present age of the Rina.
statement I: Difference between the present ages of the Pooja and Rohit is 22 years.
statement II:The present age of Pooja is 4 years less than thrice the present age of Rohit.
statement III:Difference between the present ages of the Rina and Rohit is 26 years.
A) Only III
B) Either I and II together or III alone.
C) All are together
D) Only I and II
E) None of the statements

Option B
Solution:
From statement III: Age of Rina = 26/2 *13 = 39 years

From statement I and II:
Rina = 3Rohit , Pooja – Rohit = 22 and 3Rohit – Pooja = 4
On solving, we get  Rina = 39 years

• What are the marks obtained by Sushil in Physics?
statement I: Marks obtained in Biology is as much more than that in Chemistry as the marks obtained in Chemistry is more than that in Physics.
statement II:The average marks obtained by Sushil in Physics, Biology and Chemistry are 65.
statement III: Marks obtained by Sushil in Biology is 6 more than that obtained in Physics.
A) None of  these
B) Only I and II
C) All statements together
D) Only II and III
E)  Only I

Option C
Solution:
From statement I: Biology – Chemistry = Chemistry – Physics

From statement II: Physics + Chemistry + Biology = 3*65 = 195
From statement III: Biology = Physics + 6
From all the above equations , Physics  = 62

• What is the area of the hall?
statement I: Total cost of flooring the hall is Rs. 14,500.
statement II: Labour cost of flooring the hall is Rs. 3000.
statement III: Material cost of flooring per sq. metre is Rs. 150.
A) All statements together
B) Only II and III
C)Only I and II
D) None of these
E) Only III

Option A
Solution:
Let the area of the hall be x m^2.

Then , total material cost  = Rs. 150x
Labour cost = Rs. 3000
Therefore,Total cost = 150x + 3000 = 14500
From this we get the value of x.
Hence , all the three statements are required.

• A,B,C,D and E are five friends. Their mean age is 18. What is the age of C ?
Statement I : A’s age is 18
Statement II : B’s age is 2 years less than E and E’s age is 6 years less than D.
Statement III : C’s age is 6 years more than B’s age and 4 years more than E’s age.
A) Only III
B) Neither I and II nor III
C) Only I and III
D) All statements together
E) Either I and III or II alone

Option D
Solution:
A+B+C+D+E = 90

From statement I : B+C+D+E = 72
From statement II: B = E – 2 and E = D – 6
so, D = E + 6
From statement III: D = B + 6 and D = E + 4
Combining all three statements, we get the age of C.

• What is the area of the right angled triangle ?
statement I: The perimeter of the triangle is 5 times of the base.
statement II: The one of the angles of the triangle is 60deg.
statement III: The length of hypotenuse is 4 cm.
A) Neither I and III nor II
B) Either I and II or III
C) All statements together
D) Only II and III
E) Only I and III

Option D
Solution:
From statement II and III are sufficient to answer the question.

Directions (1-10): In each of the following questions, a question is followed by two statements numbered I and II. Read both the statements and answer accordingly.

1. What is Bhavna’s rank in a class of 44 students?
Statement I: Kartik whose rank is 17th in the class, is ahead of Preet by 6 ranks, Preet being 7 ranks ahead of Bhavna.
Statement II: Suman is 26 ranks ahead of Bhavna and Priya is 6 ranks behind Bhavna while Savita stands  exactly in the middle of Suman and Priya in ranks, her rank being 17.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option C

2. Who is paternal uncle of P?
Statement I: P is brother of  L, who is daughter of Q, who is sister of N, who is brother of S.
Statement II: M is brother of K, who is husband of L, who is mother of G, who is sister of P.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option B
Solution:
In statement 1, only the maternal relationships are given.

In statement 2, M is paternal uncle of P

3. Who amongst P, Q, R, S, T and U is the tallest?
Statement I: P is taller than R and T but not as tall as U, who is taller than Q and S.
Statement II: R is third in height in ascending order and not as tall as U, P and Q, Q being taller than P but not the tallest.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option C
Solution:
From statement 1, U is tallest

From statement 2 also U is tallest: Order in ascending order is –  S/T, S/T, R P Q U

4. Do A, B, and C stand in a straight line?
Statement I: F is 2 km towards the south of E. K is 5 km towards the west of F. A is 2 km towards the north of F. B is 3 km towards the east of E and C is 4 km towards the east of B.
Statement II: A is 2 km towards the north of L. K is 4 km towards the west of L. S is 1 km towards the south of K. M is 2 km towards the west of S. B is 3 km towards the north of M and C is 2 km towards the north of W.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option A
Solution:
From statement I,  A, B, C stand in stand in a straight line

From statement II, Point C cannot be connected to the figure formed in which points A and B exists. So cannot be said about point C that it lies straight to A and B or not.

5. Which direction is Preeti facing?
Statement I:  If Gagan, who is currently facing east, turns 90 degree towards his right, he would face a direction exactly opposite to the direction Preeti is facing.
Statement II: If Priya, who is currently facing south, turns left, walks 1 km and then takes a left turn again, she would face the same direction as Preeti.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option C

6. How is ‘party’ coded in the language?
Statement I: ‘going to a party’ is coded as ‘la fa qu tu’ and ‘for a party’ is coded as ‘fa me tu’.
Statement II: ‘start the party’ is coded as ‘tu co ra’ and ‘going to start’ is coded as ‘qu co la’
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option E
Solution:
From both: party – tu

7. How is E related to F?
Statement I: D is son of E. C is father of B. F is daughter of A. G is only brother of A. B is sister-in-law of G and sister of D.
Statement II: A is father of F. D is sister of F. G is brother of A. K is mother of H. H is sister of G. C is only sister-in-law of H. E is father-in-law of C.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option B
Solution:
From I, B can be wife of A or can be sister of G’s wife.

From II, E is grandfather of F.

8. 7 persons are sitting in a line facing north. Who is sitting second to left of D?
Statement I: H is sitting immediate left of A. Two persons are sitting between A and B. 2 persons are sitting between E and D. D and F are immediate neighbors. E is somewhere left of B.
Statement II: A is sitting second to left of C. F is third to right of C. A is exactly between H and E such that one of them is at extreme end. B and C are immediate neighbors.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option B
Solution:
From I, All people cannot be fitted in line

From II, arrangement from left to right is H/E… A…H/E…C…B…D….F

9. A is in which direction with respect to B?
Statement I: A walks 1 km towards north-east from point P and then before walking 2 km towards south, walks 2 km towards east. Before walking 3 km towards west, B walks 4 km towards north from point P.
Statement II:  B walks 2 km towards south from point P and then before moving 8 km towards north, walks 3 km towards west.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option A

10. How is ‘he is smart’ written in the code language?
Statement I: In the same code language ‘I want to be smart’ is written as ‘jai gai pa mai ka’, ‘he needs money’ is written as ‘tik si sa’ and ‘she needs sweets’ is written as ‘ko sa ja’
Statement II: In the same code language ‘what she want to be’ is written as ‘jai ka aaj gai ko’, ‘I want sweets what he needs’ is written as ‘ja sa pa ka aaj tik’ and ‘smart are gentle’ is written as ‘bo mai ali’.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option D
Solution:
From both statements also, code for ‘is’ is not known

Directions(1-10): In each of the following questions, a question is followed by two  statements . Read all the statements and find that which statements are required to answer the question and answer accordingly.

1. There are two cylindrical rollers – bigger and smaller. How many rotations will the bigger roller take to flatten a stretch of land(X)?
The respective ratio of the radii of the bigger and the smaller roller is 7:3. Both the rollers are of the same length.
II. The smaller takes 63 rotations to flatten the stretch of land(X).
A) Either I or II
B) Neither I nor II
C) Only II
D) Only I
E) Both are required

Option E
Solution:
From both the statements,

Radius of the larger roller = 7x units
Radius of the smaller roller = 3x units
Area flattened by smaller roller in 63 rotations = 2*pi * 3x * l * 63
Therefore, 6 * 63*pi*r*l = 2*pi * 7x * l * n
=> n = 27

2. What was the total compound interest on a sum after three years?
I. The interest after one year was Rs. 100 and the sum was Rs. 1000.
II. The difference between simple interest and compound interest on a sum of Rs. 1000 at the end of two years was Rs. 10.
A) Only II
B) Only I
C) Either I or II
D) Neither I nor II
E) Both I and II

Option  C
Solution:
From statement I: r = (100*100)/1000 = 10%

P = Rs. 1000 , r = 10%, t = 3 years
Hence, CI can be described.
From statement II: SI = (1000*r*2)/100 = 20r
CI = 1000[(1+(r/100)^2) – 1] Therefore, CI – SI = 1000[(1+(r/100)^2) – 1] – 20r
=> r = 10
Hence , CI can be determined.

3. What is the marked price of the pen ?
I. The marked price of the pen is 20% above the cost price of the pen.
II. When a discount of 25% is given on the marked price of the pen, the loss incurred is 10%. The cost price of the pen is Rs.300.
A) Both I and II
B) Only I
C) Neither I nor II
D) Only II
E) Either I or II

Option D
Solution:
From statement I: no result comes.

From statement II: x*(75/100) = (300*90)/100
=> x = 27000/75

4. In how many days, men A , B and C together can finish the same piece of work
I. A and B can together finish the same piece of work  in 6 days. B and C together can finish the same piece of work in 12 days. C and A can finish the same piece of work in 10 days .
II. The time taken by A alone to finish the same piece of work is 24 days less than time taken by C alone to finish the same piece of work.
A) Only I
B) Either I or II
C) Neither I nor II
D) Only II
E) Both I and II

Option A
Solution:
From statement I: 2(A+B+C) = (1/6) + (1/12) + (1/10)

From this we can find  (A + B + C) ‘s one day’s of work .
From statement II: No such result can be concluded.

5. In a  certain village is losing 12% of its water supply each day because of a burst water pipe, then what is the loss in rupees per day?
I. The cost to the village for every 24000 gallons of water lost is Rs. 25.
II. The daily water to the village is 700 m gallon.
A) Neither I nor II
B) Either I or II
C) Only II
D)Both I and II
E) None of these

Option D
Solution:
From statement I: We can find the loss in rupees .

From statement II:  Loss of water supply = 700 million gallon * 12%
Both the statements are required to answer the question.

6. Rohan and Mohan start walking towards each other simultaneously. What is the distance between them when they start?
I. 30 minutes after  crossing each other they were 1200 m apart.
II. After crossing each other, Rohan reaches the starting point of Mohan in twice as much time as Mohan takes to reach the starting point of Rohan.
A) Both I and II
B) Only I
C) Only  II
D) Either I or II
E) Neither I nor II

Option E
Solution:
Both the statements are not sufficient to  answer the question.

7. What is the area of the circular field?
I. The area of the largest square that can be inscribed in the given circular field is 3000 sq. cm.
II. The area of the smallest square in which the given circular field can be inscribed is 3600 sq. cm.
A) Only II
B) Either I or II
C)Neither I nor II
D) Both I and II
E) Only I

Option B
Solution:
Diagonal of the square = Diameter of the circular field

From statement I: side of square = √3000 cm
diagonal of square = √2 * √3000 cm
Area of the circular field = 22/7 * (diagonal/2)^2
From statement II: side of a square = √3600
= 60cm = diameter of circle
Area of circular field = (22/7)* 30*30

8. Find the average of five consecutive odd numbers .
I. The sum of the first two numbers is 5 more than the seventh number.
II. The difference of fifth number and the first number is 10.
A) Only I and II
B) Only I
C)Either I nor II
D)Neither I nor II
E) Both I and II

Option D
Solution:
From both the statements, the values are hidden .

9. What is the present age of  Tina ?
I. Tina is 5 years older than her brother .
II. The ratio of the present ages of her brother and Tina  is 4:5 resp.
A)  Only I
B) Only II
C) Both I and II
D) Either I or II
E) Neither I nor II

Option C
Solution:
From both the statements:

=> 5x – 4x = 5
=> x = 5
Present age of Tina = 25 years.

10. Every student  in a school was given one ticket for a function. The school was charged a total of \$6000 for these tickets, all of which were of equal value. What was the price of one ticket?
I. If the price of each ticket had been \$2 more , the total bill would have increased by 40%.
II. If the price of each ticket had been \$1 less, the total cost would have been 1,200 less.
A)  Only I
B) Either I or II
C)Only II
D) Both I and II
E) Neither I nor II

Option B
Solution:
If the price of the one ticket is p , and the total number of tickets is n , then from the statement , (6000/n) = p

From statement I : 8400/n = p + 2
From statement II : (6000 –  1200)/n = p – 1

Directions (1-10): In each of the following questions, a question is followed by two statements numbered I and II. Read both the statements and answer accordingly.

1. What is the direction of point A with respect to point K?
Statement I: Point A is 6 m to the west of point B. Point C is 6 m to the south of point B. Point E is 4 m to the south of point D. Point C is 8 m to the west of point D. Point E is 10 m to the east of point F.
Statement II: Point I is 7 m to the north of point H. Point I is 3 n to the west of point J. Point H is 6 m to the west if point G. Point F is 4 m to the north of point G. Point K is 2 m to the south of point J.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option E
Solution:
Point A in statement I and K in statement II. Point F in both statement s joins them to tell the direction.

2. What is the distance between the final positions of Arun and Amit?
Statement I: Arun starts from a point in north direction. After walking for 6 m he turns to right and walks 8 m to reach point B. Next he takes a right turn again and walks 5 m before turning to left. Next he walks 7 m and turns right. Leaks for 5 m and stops finally.
Statement II: Amit starts walking in south direction form point B. Walks for 8 m and takes a left turn. Next walks for 10 M and turns to right, walks for and finally stops.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option D
Solution:
Since we do not know the final distance of Amit we cannot know the actual stopping point of Amit so cannot be determined from any of the statement or both together.

3. How is B related to A?
Statement I: K is brother of B. A is father of E. A is son of C. G is son of D. H is sister of G.
Statement II: F is niece of G and sister of A. B is sister in law of G. D has only 3 children one of them being girl
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option D
Solution:
From both statements C and D are not linked in any way. If c and d are a couple then only B is wife of A.

4. How is ‘may’ written in code language?
Statement I: In that code language, ‘she he we’ is written as ‘ip ap de’ and ‘they we may’ is written as ‘ip pu od’.
Statement II: ‘she could we’ is written as ‘ap su ip’ and ‘we he should’ is written as ‘en de ip’.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option D
Solution:
Codes for they and may both are unknown, so can’t be find for ‘may’.

5. Who is tallest among – A, B , C, D, E and F?
Statement I:  C is taller than B and shorter than D. D is not the tallest. B is taller than E. F is taller than C and also A.
Statement II: F is taller than C and B both. D is taller than B. E is shorter than B. A is shorter than D.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option A
Solution:
From I F is tallest.

From II F or D is tallest.

6. How is A related to F?
Statement I: M is sister of F. B is mother of M. D is father of L. L is brother-in-law of A. C is married to D and has only 2 children one of them being B. Only one of the children of D is married.
Statement II: H is niece of G who is brother of A. K is father of A. B is only daughter-in-law of J. G is son of J. F is sister of H.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option A
Solution:
From I: D and C have 2 children – B and L. Only 1 is married. B has children, so only B is married. L is not married so A can only be husband of B so father of F.

From II: B is only daughter-in-law, can be wife of A, G or any other son of K and J. so A can be father or uncle of F.

7. How is C related to A?
Statement I: C is married to D. F is sister of A. H who is not married is son of D. F is sister-in-law of B. A is married to B.
Statement II: A is husband of B. G is daughter of B. F is sister of A. D is father of H. C is mother of F
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option B
Solution:
From I, gender of A and B is not known, so A can be son or daughter of C. So C mother/father of A

From II, C is mother of A

8. What is the direction of point A with respect to point G?
Statement I: Point A is 5 m north of point B. Point B is 7 m to west of point C. Point E is 4 m west of point D. Point G is somewhere south of point E. Point C is 2 m north of point D.
Statement II: Point A is 6 m west of point B. Point C is 3 m to south of point B. Point D is 2m north of point E. Point E 6 m west of point G. Point D is 8 m to west of point C.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option C
Solution:
From I, A is north-west of G

From II also, A is north-west of G

9. Who is sitting opposite E in a circle in which 6 people are sitting facing centre.
Statement I: E is sitting to immediate left of A. There are 2 people in between A and C. F is immediate neighbor of C. D is sitting opposite B.
Statement II:  B and E are sitting together. A is sitting opposite A. F and D are sitting together. A and B are not sitting together.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option A
Solution:
From I, F is sitting opposite E.

From II, many arrangements are possible.

10. Who is sitting second to the left of B in a line in which all people are facing north? (B is not sitting at any extreme end)
Statement I: C is sitting to immediate left of E. There are 2 people between A and E. D and A are immediate neighbors. There are 2 people between B and F. B and E are not sitting together.
Statement II: D is sitting to immediate left of A. There are 2 people between A and E. C is sitting second to left of F
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.

Option C
Solution:
From I, arrangement is D A B C E F

From II also, arrangement is D A B C E F

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