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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.

**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 ?

# 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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