# Data Sufficiency Tricks & Tips

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## Data sufficiency is different

Simply put, the DS section of the Exam is different. It’s different because you aren’t trying to solve for one answer, like PS. Instead, your goal is to test for sufficiency. That means you’re trying to determine whether or not you’ve been provided enough information to definitively answer the question stem. Take this question stem, for example:

Is X > 9?

(1) X is Positive

(2) X – 2 = 11

To reiterate, you goal isn’t to solve for X, but to determine if the statements provided answer the question stem’s query. In this case, statement 1 is too vague: X could be any number greater than 0. Statement 2, however, tells us that when X is reduced by 2, it produces a number greater than 9. Therefore, statement 2 is sufficient.

Another quirk of DS is that every problem contains the same five answer choices. This should be intuitive: if your goal is proving sufficiency, how many different answers can there be? Something can’t be varying degrees of sufficient, right? Each problem offers two statements used to prove the question stem’s sufficiency. The answer choices mirror this objective:

a) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question asked;

b) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question asked;

c) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.

d) EACH statement ALONE is sufficient to answer the question asked;

e) Statements 1 and 2 TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Because of its unique nature, DS can be a question type that test takers loathe. At its core, however, there are really only two reasons why you’d get a DS question wrong:

- You think you don’t have all of the information you need to prove sufficiency, but you do. Solution: Maximize the information you do have. Use the question stem, the other statement, simplifying with algebra, etc.
- You think you have all of the information you need to prove sufficiency, but you don’t. Solution: Be skeptical of the information you received and play devil’s advocate; if picking numbers, be sure to choose ones on both sides of the statement.

Despite what you might think at first, DS can actually be a refreshing change-of-pace from PS. Because you’re testing for sufficiency, not solving for one answer, DS problems can take less time to complete. Also, because the answer choices are always the same, DS is ripe with strategic opportunities – which we’ll discuss next.

## Exam tips: Basic strategy

If you ever hear an interview with a professional athlete about their superstitions, you’ll probably think they’re insane. Athletes obsess over the smallest of details: which shoe they tie first, what to eat before a game, and even where to sit on the team bus and/or plane. While this doesn’t convince the ‘Sports Gods’ to treat them favorably, it does give the athlete a sense of confidence and calm.

Following superstitions makes the athlete feel like they’re doing everything in their power to perform their best. This shouldn’t sound insane, however. Most people follow superstitions, also known as a routine, every day. Whether it’s eating a certain type of breakfast or remembering to pack an umbrella, routines are part of daily life. Again, while this doesn’t mean you’ll have a better life by doing so; routines do provide us with a sense of confidence and calm.

Eating lunch at a certain time each day might not provide you with any tangible benefits, but when approaching the Exam DS problems, having a routine is extremely important and is the first of my Exam** tips** for DS. Because DS is so strategically focused, more so than PS or the three verbal question types, and each question follows a similar pattern, approaching each problem the same way isn’t only possible, but it’s necessary to achieve a high score in quant.

When a DS problem comes up on the exam, before you even read the question, write down ‘AD / BCE’. This will help you keep track of your answers through the decision tree – which we’ll discuss later. Some guides recommend creating a grid before you begin the quant section.

If that’s your preference, feel free to do so. Otherwise, it can be easier to write ‘AD / BCE’ each time to not only engrain your routine, but so that you don’t have to keep flipping back through your scratch paper to find the grid.

After you’ve written down ‘AD / BCE’, read the question stem and ask yourself if it wants you to find the sufficiency of a specific ‘value’ or a ‘yes/no’ response. Depending on what’s asked, the definition of whether a statement is or isn’t sufficient could change.

- A value question will ask you for the exact value of something. If a statement narrows the possibilities down to exactly one number, not a range, it’s sufficient. Therefore, you’ll need to test at least two different numbers.
- A yes/no question will ask whether the question stem is or isn’t correct. For example, “Is X > 10?” Therefore, you should aim to find a yes and a ‘no’ outcome when testing for sufficiency.

Once you’ve determined what type of question you’re tasked with, your next step, and the next of my Exam tips, is to simplify the question stem and statements. Doing so will make testing for sufficiency, either by algebra or by picking numbers, a much easier process. For example:

Is X >0?

(1) X2 = 9x

(2) X < Y

Focusing on statement 1, x2 = 9x can be simplified into X(X – 9) = 0. Therefore, X = 0, 9. Since there are two possible answers for X, statement 1 doesn’t sufficiently answer the question stem.

Assuming you understand the aim of the question stem and the provided information is simplified, your next step is to test for sufficiency, following the decision tree. The decision tree is, as follows, and begins with statement 1:

For the non-visual learner, your first test of sufficiency is statement 1. Depending on whether or not it’s sufficient, you test statement 2 individually and then the two statements together. Because these tests relate to each other, once you find out an individual statement’s sufficiency, you can immediately eliminate other answer choices.

Remember that AD / BCE grid? If statement 1 is sufficient, you can immediately cross off answer choices B, C, and E. You only have to test statement 2 to see if it’s also sufficient. If it is, the answer is D: both statements are individually sufficient. If not, then A is your answer: statement 1 alone is sufficient.

That’s your DS routine. In the next sections we’ll discuss how to test statements for sufficiency and some advanced strategy. To summarize:

1. Write down ‘AD / BCE’

2. Read the question stem

3. Simplify the question stem and statements 1 and 2

4. Follow the decision tree:

- Test statement 1
- Test statement 2
- Test both statements together (if applicable)

5. Choose answer and move to the next question

## Testing for sufficiency

You have three main options to test statements for sufficiency:

- Algebra
- Picking numbers
- Informed guess

Algebra

Breaking down each statement algebraically is the best way to test a statement for sufficiency. Solving algebraically does require a higher understanding of math, but limits careless mistakes one can make using a strategy like picking numbers. The test makers build traps into DS problems and unless you dissect the question stem and statements with algebra, you might fall into one.

Picking numbers

Time is a factor, however, and so if you’re unable to use algebra, picking numbers is an excellent substitute. As explained Earlier, picking numbers is a type of strategy where the test taker assigns values to the variable(s) listed in the question stem and statements. By doing so, you’re essentially guessing at what might be a solution. You shouldn’t just pick any number, however. Pick ‘smart’ numbers, meaning ones that could prove both sides of the statement. A commonly used set is every half-number from negative two to positive two:

- {-2, -3/2, -1, -1/2, 0, 1/2, 1, 3/2, 2}

When picking numbers, make sure you cast a wide net. To do so, you’ll need to select at least two sets of options. For example, a question stem with two variables might be tested with {-1, 0} and then {1/2, 2}. To those without a strong command of algebra, fear not. A mix of algebra and picking numbers can still be a successful plan of attack.

Informed guess

Even if you apply the right strategy, avoid traps set by the test makers, and follow the above Exam tips, you still might not feel confident enough to answer the question. In that situation, you’ll have to make an informed guess. The key to guessing in DS, and the Exam as a whole, is to try to increase your odds of answering correctly: it’s far better to guess between two answers than five.

To improve your odds, try to evaluate at least one of the statements in the decision tree. This way you’ll eliminate at least two answer choices through ‘AD / BCE’. Try to resist the urge to guess E. In general, complicated or hard-to-evaluate statements are more likely to be sufficient than insufficient. If you think E is correct, however, to be safe, make sure to prove it out algebraically.

## Advanced Strategy

As discussed in the above Exam tips, a quirk of DS is that you don’t necessarily need to solve the entire problem to know the correct answer. You only need to determine if the statement answers the question stem or not. In some case, this means you can complete DS problems at a faster rate than PS. With speed comes careless mistakes, however, so here are a few of the most common tricks the test makers use:

- Assumption – Assuming something about a statement or question stem. If it isn’t disclosed, don’t assume. For example, don’t assume that a value must be an integer or must be a positive number.
- Contradiction – Statements 1 & 2 must come to the same conclusion. If they don’t, you messed up the math. That means if statement 1 says X = 2 and statement 2 says X = 4, you need to start over. That simply isn’t possible.
- The N rule – If you have N unique variables, you need N distinct equations to solve for them. Knowing this property can help you answer more difficult DS problems.
- Identical equations – Equations that simplify into themselves. You may think that X = 2 and 2X = 4 are different equations, but they simplify into themselves. Be careful to not misinterpret them and select the wrong answer. If this is the case, you know that the correct answer is only D or E. Either each statement is sufficient, or they’re both insufficient.
- Beware of 0 – Don’t forget that 0 is an integer, and when you’re picking numbers, it can be a smart choice. Further, whenever dividing a small number by a bigger one, remember that the quotient is always 0 and the remainder is the divisor.
- No is yes – While rare, if a statement consistently answers the question stem as ‘no’, then that statement is sufficient. Don’t get confused by the fact that the yes/no objective is fulfilled by no. No can answer the question stem.
- The C trap – The test makers know you’d prefer to have more information, so if C is clearly sufficient and A & B don’t seem to be individually sufficient, reexamine. Chances are it’s a trap. Try to prove out C before selecting it.
- Be skeptical – Always be skeptical of the test makers. If an answer seems too easy, it probably is. If it was that easy, the question would be in the 20th percentile. Since you are testing way above that range, don’t fall for the trap.

To build off the ‘C trap’ and ‘be skeptical’ points, if one statement is obviously sufficient, then the other must be included for a reason. Either it will give you context for the first statement, or it will show you something you overlooked. While you need to test each statement individually, you don’t need to do it in a vacuum. Use all of the clues available. For example:

How many trees are pine in a grove of 30 pine, oak, and maple trees?

(1) The ratio of oak to maple trees is 14:9

(2) The ratio of oak to pine trees is 2:1

At first glance you might think this is an easy question in which you can find the answer through both statements – choice C. And while that’s true, both statements aren’t necessary to answer this question correctly. In fact, the right answer is A. If there are 30 trees total and the ratio of oak to maple is 14:9, there can only be room for seven more trees: Statement 1 is sufficient.

## Putting it all together

Let’s illustrate our routine and the strategies discussed above with a practice question:

What is the tens digit of positive integer X?

(1) X divided by 100 has a remainder of 30

(2) X divided by 110 has a remainder of 30

At first glance, what does this question tell us? A quick observation is that:

- This is a ‘value’ question
- X is a positive integer
- It deals with number properties
- It’s a ‘remainder’ problem

Knowing that X is a positive integer is particularly helpful when picking numbers. Also, knowing the equation for remainders will allow us to solve this question quickly. Specifically, that equation states: any number X is the sum of the dividend multiplied by the divisor plus the remainder.

Translating math to English, the equation for statements 1 and 2 would be:

- X = 100*D + 30
- X = 110*D + 30

The goal of this question is to find the tens digit of X. Let’s pick some numbers and see if we can see a pattern in statement 1:

Clearly, statement 1 is sufficient. The tens digit, regardless of the divisor, is always 3. From here we can eliminate B, C, and E. The only other possible answer choice is D – that is, if statement 2 is also sufficient. Let’s find out:

As you can see, the tens digit changes with each different divisor. This is a ‘value’ question, so only one answer can possibly make the question prompt sufficient. Since that isn’t the case in statement 2, it’s insufficient; the correct answer is A.

***

## Data Sufficiency Tips & Tricks

- You should attempt Data Sufficiency questions for those topics in which you have conceptual clarity.
- You should never assume anything on your own. For example, if it is given that the product of two numbers is 10, it does not imply the numbers could be only 10 & 1 or 5 & 2. The statement does not state that the numbers are natural or integers; these numbers could be fractions also. This is why you cannot make assumptions in this question type.
- Be careful while marking the answer for an affirmative question. So many times, when you get the answer of the question prompt as ‘No’, you tend to mark the answer as Data Insufficient. Remember, even ‘no’ is an answer in some cases and this might mean that the data is sufficient.
- Carefully read the directions given for marking an answer in Data Sufficiency questions. The examiners can change the order of directions at any given time

### Approach for Data Sufficiency Questions

**(i) Understanding the question**

**(ii) Consider each statement individually**

If neither statement by itself is sufficient to answer the question, go on to the third stage as follows:

**(iii) Combine the two statements**

### Solved Examples:

**Example 1:**Is the product of two numbers greater than 400?

A. The sum of the two numbers is greater than 100.

B. Each of the numbers is greater than 20.

**Solution:**Statement A alone is not sufficient to answer the question and this can be proved with the help of examples. If the two numbers are 50 and 51, their sum is greater than 100 and their product is greater than 400; but if the two numbers are 100 and 1- though their sum is greater than 100, their product is only 100, which is less than 400. Statement B is sufficient. If both of the numbers are greater than 20, then their product must be greater than 20 x 20, or greater than 400.

Hence, only the second statement is sufficient to solve the question.

**Example 2:**Is x a prime number?

A. 114 < x < 126

B. x is a factor of 169

**Solution:**Here, the first statement is sufficient to answer the question as we see that there is no prime number between 114 <x< 126. Hence, ‘x’ is not a prime number.

What do we learn from this question? Remember, even if a question has an answer as ‘no’, even then it is a valid answer. In second statement, the factors of 169 are 1, 13 and 169. Here, 1 and 169 are not prime numbers whereas 13 is a prime number. Hence in this case ‘x’ may or may not be a prime number.

Hence, only the first statement is sufficient to solve the question.

**Example 3:**Is x = – 11?

A. x

^{2}= 144

B. x is a natural number.

**Solution:**Here, the question directly asks whether x is equal to – 11 or not. From statement A, we have x = 12 or – 12. In both the cases, x is not equal to – 11. Hence, the first statement is sufficient to get the answer.

Statement B says that x is a natural number. Since x is a natural number, it cannot be negative. Hence, it is not equal to – 11. So, the second statement is also sufficient to solve the question.

Hence, both statements are independently sufficient to answer the question.

**Example 4:**What is the value of ‘x’?

A. x<10

B. x>8

**Solution:**By combining both statements, we can say that x lies between 8 and 10. The only integer between 8 and 10 is 9. So our answer should be Option E. But this approach is actually incorrect.

Remember, nowhere in the question is it mentioned that x is an integer / natural number. Until and unless that is specified, we cannot uniquely determine the value of ‘x’. It can take any value from 8 to 10 {e.g.: 8.1, 8.2, 9.999, etc.}

So, the correct answer is option D i.e. the answer cannot be determined even with the help of both the statements.

__Tips to Solve Data Sufficiency Questions__

- These type of questions consists of problems on any reasoning topics like blood relation, coding-decoding, direction test, ranking, seating arrangement, etc. followed by statements containing clues to solve the question
- The candidates are supposed to find out which of the given statements is or are sufficient to solve the given question
- This section tests the candidate’s efficiency to determine the information necessary to solve the given problem
- We have to make sure whether the question can be solved with the help of information provided in the 1
^{st}statement or 2^{nd}statement or together in the 1^{st}and the 2^{nd}statement - We are not supposed to assume anything beyond the information given in the question and the following statements

__EXAMPLE:__

DIRECTIONS:

** Answer (1)**if the data in statement I alone is sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

** Answer (2)**if the data in statement II alone is sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

** Answer (3)**if the data either in statement I alone or in statement II alone are sufficient to answer the question.

** Answer (4)**if the data even in statement I and II together are not sufficient to answer the question.

** Answer (5)**if the data in both statement I and II together are necessary to answer the question.

__QUESTION 1__

On which date in May was Arun’s birthday?

__Statement:__

- Arun’s mother correctly remember that Arun’s birthday was before 14
^{th}but after 12^{th}May - Arun’s brother correctly remembers that Arun’s birthday was after 10
^{th}but before 15^{th}May

__Solution__

- From statement I alone we can deduce that Arun’s birthday was on 13
^{th}May as it was correctly remembered by his mother to be between 12^{th}and 14^{th}May i.e.,**13**^{th}May. - From statement II alone we can’t find Arun’s birth date as it can be any day between 10
^{th}and 15^{th}may. - Therefore, statement I alone is sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

Hence**Answer: (1)**

__QUESTION 2__

What is the color of the fresh grass?

__Statement:__

- Blue is Green, Red is Orange and orange is yellow
- Yellow is white, white is black, green is brown and brown is purple

__Solution__

- The color of fresh grass is Green.
- From statement I alone we cannot deduce the code for green.
- From statement II alone we can determine the code for Green i.e.,
(Green is Brown).**brown** - Therefore, statement II alone is sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

Hence**Answer: (2)**

__QUESTION 3__

How is A related to B?

__Statement:__

- B and C are children of D who is wife of A
- E’s brother A is married to B’s mother

__Solution__

- From statement I alone we can deduce that B is the child of D who is the wife of A. Therefore,
**A is B’s Father.** - From statement II alone we can determine that A is married to B’s mother that shows that
**A is B’s father.** - Therefore, statement I alone or in statement II alone are sufficient to answer the question.

Hence**Answer: (3)**

__QUESTION 4__

How is ‘never’ written in a code language?

__Statement:__

- ‘never ever come here’ is written as ‘ jo na hi da’ in a certain language
- ‘come here and go back’ is written as ‘ ho ma si no di’ in that language

__Solution__

- From statement I ‘never’ cannot be determined it can be either one of jo, na, hi or da
- From statement II there is no ‘never’ in the statement and even considering both the statements there is no common term using which the code for ‘never’ can be determined
- Therefore, data even in statement I and II together are not sufficient to answer the question

Hence**Answer: (4)**

__QUESTION 5__

How many children are there between P and Q in a row of children?

__Statement:__

- P is 15
^{th}from the left in the row - Q is exactly in the middle and there are 10 children towards his right

__Solution__

- From statement I alone we can deduce that the position of
**P is 15**^{th}from the left - From statement II alone we can understand that
and having 10 children to his right means there will be 10 children to his left too. So position of**Q being in the middle****Q is 11**^{th}from the left - Now considering statements I and II together, we can conclude that there are
between Q (11**3 persons**^{th}) and P (15^{th}) - Here answer cannot be found using one statement alone.
- Therefore, data in both statements I and II together are necessary to answer the question

Hence**Answer: (5)**

## Tips for Solving Data Sufficiency Problems

## Data Sufficiency Tip #1: memorize the answer choices

The five answer choices are always the same. Know them cold. If someone breaks into your residence at night, wakes you with a bucket of ice water, and demands that you recite the five DS answer choices, you should be able to rattle them off with no problem.

Here are those five answer choices (exact wording).

**Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.****Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.****Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.****Each statement alone is sufficient to answer the question.****Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.**

## Data Sufficiency Tip #2: use elimination and guessing to your advantage

On a Problem Solving question, if you eliminate one answer, the other four are still there. While guessing the answer from among four choices is slightly better odds than guessing from among five, this is not much of a gain.

Fortunately, you can often eliminate answers two or three at a time on the Data Sufficiency. Suppose you can make a sensible decision about one of the two statements, and the other statement is completely incomprehensible to you. Here’s what you can do:

**Case One**: Statement #1 is sufficient on its own, Statement #2 is incomprehensible

Eliminate: B, C, E

Only possible answers: A, D

**Case Two**: Statement #1 is not sufficient on its own, Statement #2 is incomprehensible

Eliminate: A, D

Only possible answers: B, C, E

**Case Three**: Statement #1 is incomprehensible, Statement #2 is sufficient on its own

Eliminate: A, C, E

Only possible answers: B, D

**Case Four**: Statement #1 is incomprehensible, Statement #2 is not sufficient on its own

Eliminate: B, D

Only possible answers: A, C, E

In all four cases, you can eliminate at least two answers, so even if you guess randomly from the remaining answers, the odds are very much in your favor.

## Data Sufficiency Tip #3: focus on the sufficiency question

On Problem Solving questions and in most traditional math, the focus is: *find the answer*. That’s ** not** the focus in Data Sufficiency. The focus in DS is:

*could you find the answer*? In other words,

*do you have enough information to be able to find the answer*? That’s the sufficiency question, and which answer choices you choose or eliminate depends on answers you find to the sufficiency questions for each statement.

The prompt for a Data Sufficiency problem is always a question, either “find the value of blah blah blah” or “is x blah blah blah”, either a “value” question or a “yes-no” question. Especially if the prompt is a “yes-no” question, do not confuse the answer to the promptquestion with the answer to the sufficiency question.

Let’s consider a very easy example to demonstrate this difference.

1. Is x > 5?

Statement #1: blah blah blah

Statement #2: x = 3

This question is way too easy to appear on the Exams, but let’s consider it. Statement #2 tells us, definitively, that x = 3. Therefore, we can give a clear and resounding “no” answer to the prompt question. But that is **NOT** the answer to the *sufficiency* question. If we are in a position to give a clear and definitive answer to the prompt question — any answer, as long as it’s clear and certain — then the information must be sufficient. Therefore the answer to the sufficiency question is “yes”, regardless of whether the definitive answer to the prompt question is “yes” or “no.” By contrast, a “no” answer to the sufficiency question means something very different — it always means we were *not*able to determine anything definitive at all about the prompt. That is, you *can’t* get any clear answer to the prompt question. If you *can* get an answer to the prompt, then the sufficiency answer is “yes.”

## Data Sufficiency Tip #4: don’t calculate an exact answer if you don’t have to

This is a continuation of the previous tip. Data Sufficiency is all about — “*could you* find the answer?” Suppose the prompt is “What is the value of x?”, a standard DS problem. Suppose, in the course of solving this problem, you get to a step like 23x + 144 = 5670. The benighted student with poor managerial instincts will dutifully work through the several steps necessary for finding the actual value of x — without a calculator. The skilled Exams test taker would realize: “From the step 23x + 144 = 5670, I *could* solve for x. That, in and of itself, answers the sufficiency question right there, and in answering the sufficiency question, I am done. The actual value of x is irrelevant to answering the question.”

By the way — this idea has some profound applications in Euclidean geometry.

## Data Sufficiency Tip #5: consider the statements separately first

On the Data Sufficiency, you have to first consider each statement separately —- consider whether each statement, *by itself,* is sufficient. Only if both statements are not sufficient separately would you consider the sufficiency of the information in the combined statements.

One of the biggest mistakes folks make in the Data Sufficiency format is to read Statement #1, do some calculations or deduction, and then carry all that information with them when they consider Statement #2. This is particular tempting if Statement #1 contains all kinds of juicy information with fascinating logical implications. People get wrapped up in the “what if Statement #1 is true” world, and they have trouble leaving that world behind when it comes time to pay attention to statement #2 *alone*.

One helpful strategy: consider whichever statement is simplest first. The Exams loves making Statement #1 a huge, complicated, juicy statement and Statement #2 something incredibly brief. If that’s the case, consider Statement #2 first. You have to consider the two statements separately, but there’s no law saying in which order you need to consider them. Choose the simpler one first.

## Data Sufficiency Tip #6: be smart about picking number

Many people, before studying for the Exams, haven’t thought about math for a while. For these folks, it’s often the case that if the problem uses the word “number”, their minds default to a very limited set. Often, that set consists of only the natural numbers, a.k.a the counting numbers —- {1, 2, 3, 4, …}. People forget that a “number” could be positive or negative or zero, could be a fraction, could be a square root, could be pi or some other decimal, etc. etc. The possibilities are literally infinite.

The Exams loves to test number properties, and one of the principle reasons why is that people without number sense make all kinds of predictable mistakes. The statement might say, for example, x > 7, and people will read that and assume in hordes that x must be 8 or more, totally forgetting that there is an entire continuous infinity of decimals between 7 and 8. When picking numbers for variables, people predictably pick positive whole numbers and predictably forget negative integers, positive fractions, negative fractions, etc. etc. Be smart about picking numbers on Data Sufficiency. Always have absolutely every kind of number in mind when you are analyzing a Data Sufficiency question.

# 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.**** **

- 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 - 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 - 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 - 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 - 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

**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- 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 - 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 - 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 - 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

**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.**

- 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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.

**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.

- 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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

**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.**

- 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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.

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