# Top 108 CAT Data Sufficiency Questions With Video Solutions

Data Sufficiency questions are designed to test a candidate's ability to analyze data and determine whether the given information is sufficient to answer the question or not. Since 2009, the questions from this topic are not appearing the CAT exam. One can check out the questions that appeared in the previous CAT question papers with detailed video solutions. Click on the link below to download the CAT Data sufficiency questions with video solutions PDF.

## CAT 2008 Data Sufficiency questions

Instruction for set 1:

In a single elimination tournament, any a player is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules :

(a) If the number of players, say n, in any round is even, then the players are grouped into n/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round.

(b) If the number of players, say n, in any round is odd, then one of them is given a bye, that is he automatically moves on to the next round. The remaining (n–1) players are grouped into (n–1)/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round. No player gets more than one bye in the entire tournament.

Thus, if n is even, then n/2 players move on to the next round while if n is odd, then (n+1)/2 players move on to the next round. The process is continued till the final round, which obviously is played between two players. The winner in the final round is the champion of the tournament.

#### Question 1

What is the number of Matches played by the champion?

A. The entry list for the tournament consists of 83 players?

B. The champion received one bye.

Instruction for set 1:

In a single elimination tournament, any a player is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules :

(a) If the number of players, say n, in any round is even, then the players are grouped into n/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round.

(b) If the number of players, say n, in any round is odd, then one of them is given a bye, that is he automatically moves on to the next round. The remaining (n–1) players are grouped into (n–1)/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round. No player gets more than one bye in the entire tournament.

Thus, if n is even, then n/2 players move on to the next round while if n is odd, then (n+1)/2 players move on to the next round. The process is continued till the final round, which obviously is played between two players. The winner in the final round is the champion of the tournament.

#### Question 2

If the number of players, say n, in the first round was between 65 and 128, then what is the exact value of n?

A. Exactly one player received a bye in the entire tournament.

B. One player received a bye while moving on to the fourth round from the third round.

## CAT 2007 Data Sufficiency questions

Instruction for set 1:

Directions for the following four questions:

Each question is followed by two statements, A and B. Answer each question using the following instructions:

#### Question 1

In a particular school, sixty students were athletes. Ten among them were also among the top academic performers. How many top academic performers were in the school?

A. Sixty per cent of the top academic performers were not athletes.

B. All the top academic performers were not necessarily athletes.

Instruction for set 1:

Directions for the following four questions:

Each question is followed by two statements, A and B. Answer each question using the following instructions:

#### Question 2

Five students Atul, Bala, Chetan, Dev and Ernesto were the only ones who participated in a quiz contest. They were ranked based on their scores in the contest. Dev got a higher rank as compared to Ernesto, while Bala got a higher rank as compared to Chetan. Chetan’s rank was lower than the median. Who among the five got the highest rank?

A. Atul was the last rank holder.

B. Bala was not among the top two rank holders.

Instruction for set 1:

Directions for the following four questions:

Each question is followed by two statements, A and B. Answer each question using the following instructions:

#### Question 3

Thirty per cent of the employees of a call centre are males. Ten per cent of the female employees have an engineering background. What is the percentage of male employees with engineering background?

A. Twenty five per cent of the employees have engineering background.

B. Number of male employees having an engineering background is 20% more than the number of female employees having an engineering background

Instruction for set 1:

Directions for the following four questions:

Each question is followed by two statements, A and B. Answer each question using the following instructions:

#### Question 4

In a football match, at the half-time, Mahindra and Mahindra Club was trailing by three goals. Did it win the match?

A. In the second-half Mahindra and Mahindra Club scored four goals.

B. The opponent scored four goals in the match.

Instruction for set 2:

Directions for the following four questions: Each question is followed by two statements A and B. Indicate your responses based on data sufficiency

#### Question 5

The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II, each with 50 students. The average weight, $$W_I$$ , of Section I is smaller than the average weight, $$W_{II}$$ , of Section II. If the heaviest student, say Deepak, of Section II is moved to Section I, and the lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the two sections are switched, i.e., the average weight of Section I becomes $$W_{II}$$ and that of Section II becomes $$W_I$$ . What is the weight of Poonam?

A: $$W_{II} - W_I = 1.0$$

B: Moving Deepak from Section II to I (without any move from I to II) makes the average weights of the two sections equal.

Instruction for set 2:

Directions for the following four questions: Each question is followed by two statements A and B. Indicate your responses based on data sufficiency

#### Question 6

ABC Corporation is required to maintain at least 400 Kilolitres of water at all times in its factory, in order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the tank capacity adequate to meet ABC’s requirements?

A: The inner diameter of the tank is at least 8 meters.

B: The tank weighs 30,000 kg when empty, and is made of a material with density of 3 gm/cc.

Instruction for set 2:

Directions for the following four questions: Each question is followed by two statements A and B. Indicate your responses based on data sufficiency

#### Question 7

Consider integers x, y and z. What is the minimum possible value of $$x^2 + y^2 + z^2$$?

A: x + y + z = 89

B: Among x, y, z two are equal.

Instruction for set 2:

Directions for the following four questions: Each question is followed by two statements A and B. Indicate your responses based on data sufficiency

#### Question 8

Rahim plans to draw a square JKLM with a point O on the side JK but is not successful. Why is Rahim unable to draw the square?

A: The length of OM is twice that of OL.

B: The length of OM is 4 cm

## CAT 2004 Data Sufficiency questions

#### Question 1

Zakib spends 30% of his income on his children's education, 20% on recreation and 10% on healthcare. The corresponding percentage for Supriyo are 40%, 25%, and 13%. Who spends more on children's education?

A. Zakib spends more on recreation than Supriyo.

B. Supriyo spends more on healthcare than Zakib.

#### Question 2

Four candidates for an award obtain distinct scores in a test. Each of the four casts a vote to choose the winner of the award. The candidate who gets the largest number of votes wins the award. In case of a tie in the voting process, the candidate with the highest score wins the award. Who wins the award?

A. The candidates with top three scores each vote for the top score amongst the other three.

B. The candidate with the lowest score votes for the player with the second highest score.

#### Question 3

In a class of 30 students, Rashmi secured the third rank among the girls, while her brother Kumar studying in the same class secured the sixth rank in the whole class. Between the two, who had a better overall rank?

A. Kumar was among the top 25% of the boys merit list in the class in which 60% were boys.

B. There were three boys among the top five rank holders, and three girls among the top ten rank holders.

#### Question 4

Tarak is standing 2 steps to the left of a red mark and 3 steps to the right of a blue mark. He tosses a coin. If it comes up heads, he moves one step to the right; otherwise he moves one step to the left. He keeps doing this until he reaches one of the two marks, and then he stops.

At which mark does he stop?

A. He stops after 21 coin tosses.

B. He obtains three more tails than heads.

#### Question 5

Ravi spent less than Rs. 75 to buy one kilogram each of potato, onion, and gourd. Which one of the three vegetables bought was the costliest?

A. 2 kg potato and 1 kg gourd cost less than 1 kg potato and 2 kg gourd.

B. 1 kg potato and 2 kg onion together cost the same as 1 kg onion and 2 kg gourd.

#### Question 6

Nandini paid for an article using currency notes of denominations Re. 1, Rs. 2, Rs. 5, and Rs. 10 using at least one note of each denomination. The total number of five and ten rupee notes used was one more than the total number of one and two rupee notes used. What was the price of the article?

A. Nandini used a total of 13 currency notes.

B. The price of the article was a multiple of Rs. 10.

## CAT 2003 Data Sufficiency questions

#### Question 1

F and M are father and mother of S, respectively. S has four uncles and three aunts. F has two siblings. The siblings of F and M are unmarried. How many brothers does M have?

A. F has two brothers.

B. M has five siblings.

#### Question 2

A game consists of tossing a coin successively. There is an entry fee of Rs. 10 and an additional fee of Re. 1 for each toss of coin. The game is considered to have ended normally when the coin turns heads on two consecutive throws. In this case the player is paid Rs. 100. Alternatively, the player can choose to terminate the game prematurely after any of the tosses. Ram has incurred a loss of Rs. 50 by playing this game. How many times did he toss the coin?

A. The game ended normally.

B. The total number of tails obtained in the game was 138.

#### Question 3

Each packet of SOAP costs Rs. 10. Inside each packet is a gift coupon labelled with one of the letters S, O, A and P. If a customer submits four such coupons that make up the word SOAP, the customer gets a free SOAP packets. Ms. X kept buying packet after packet of SOAP till she could get one set of coupons that formed the word SOAP. How many coupons with label P did she get in the above process?

A. The last label obtained by her was S and the total amount spent was Rs. 210.

B. The total number of vowels obtained was 18.

#### Question 4

If A and B run a race, then A wins by 60 seconds. If B and C run the same race, then B wins by 30 seconds. Assuming that C maintains a uniform speed what is the time taken by C to finish the race?

A. A and C run the same race and A wins by 375 metres.

B. The length of the race is 1 km.

#### Question 5

Is $$a^{44} < b^{11}$$, given that a = 2 and b is an integer?

A. b is even

B. b is greater than 16

#### Question 6

What are the unique values of b and c in the equation $$4x^2 + bx + c = 0$$ if one of the roots of the equation is (-1/2)?

A. The second root is 1/2.

B. The ratio of c and b is 1.

#### Question 7

AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches the minor arc AB at E. What is the radius of the circle?

A. AB is not a diameter of the circle.

B. The distance between AB and the tangent at E is 5 cm.

#### Question 8

Is $$(1/a^2 + 1/a^4 + 1/a^6 +...) > (1/a + 1/a^3 + 1/a^5 +...)$$?

A. $$0< a \leq 1$$

B. One of the roots of the equation $$4x^2-4x+1 = 0$$ is a

#### Question 9

D, E, F are the mid points of the sides AB, BC and CA of triangle ABC respectively. What is the area of DEF in square centimeters?

A. AD = 1 cm, DF = 1 cm and perimeter of DEF = 3 cm

B. Perimeter of ABC = 6 cm, AB = 2 cm, and AC = 2 cm.

## CAT 2002 Data Sufficiency questions

#### Question 1

A sum of Rs. 38,500 was divided among Jagdish, Punit and Girish. Who received the minimum amount?

#### Question 2

In a hockey match, the Indian team was behind by 2 goals with 5 min remaining. Did they win the match?

A. Deepak Thakur, the Indian striker, scored 3 goals in the last 5 min of the match.

B. Korea scored a total of 3 goals in the match.

#### Question 3

Four students were added to a dance class. Would the teacher be able to divide her students evenly into a dance team (or teams) of 8?

A. If 12 students were added, the teacher could put everyone in teams of 8 without any leftovers.

B. The number of students in the class earlier was not divisible by 8.

#### Question 4

Is $$x = y$$?

A. $$(x+y)(1/x + 1/y) = 4$$

B. $$(x-50)^2 = (y-50)^2$$

#### Question 5

A dress was initially listed at a price that would have given the store a profit of 20% of the wholesale cost. What was the wholesale cost of the dress?

A. After reducing the listed price by 10%, the dress sold for a net profit of $10. B. The dress is sold for$50.

#### Question 6

Is 500 the average (arithmetic mean) score in the GMAT?

A. Half of the people who take the GMAT score above 500 and half of the people score below 500.

B. The highest GMAT score is 800 and the lowest score is 200.

Is |x - 2| < 1?

A. |x| < 1

B. |x - 1| < 2

#### Question 8

People in a club either speak French or Russian or both. Find the number of people in a club who speak only French.

A. There are 300 people in the club and the number of people who speak both French and Russian is 196.

B. The number of people who speak only Russian is 58.

## CAT 2001 Data Sufficiency questions

#### Question 1

What are the values of m and n?

I. n is an even integer, m is an odd integer, and m is greater than n.

II. Product of m and n is 30.

#### Question 2

Is Country X’s GDP higher than country Y’s GDP?

I. GDPs of the countries X and Y have grown over the past 5 years at compounded annual rate of 5% and 6% respectively.

II. Five years ago, GDP of country X was higher than that of country Y.

#### Question 3

What is the value of X?

I. X and Y are unequal positive even integers, less than 10, and $$\frac{X}{Y}$$ is an odd integer.

II. X and Y are positive even integers, each less than 10, and product of X and Y is 12.

#### Question 4

On a given day a boat ferried 1,500 passengers across the river in 12 hr. How many round trips did it make?

I. The boat can carry 200 passengers at any time.

II. It takes 40 min each way and 20 min of waiting time at each terminal.

#### Question 5

I. Transfer rate is 6 kilobytes per second.

II. The size of the software is 4.5 megabytes.

#### Question 6

A square is inscribed in a circle. What is the difference between the area of the circle and that of the square?

I. The diameter of the circle is $$25 \sqrt{2}$$ cm.

II. The side of the square is $$25$$ cm.

#### Question 7

Two friends, Ram and Gopal, bought apples from a wholesale dealer. How many apples did they buy?

I. Ram bought one-half the number of apples that Gopal bought.

II. The wholesale dealer had a stock of 500 apples.

## CAT 2000 Data Sufficiency questions

#### Question 1

Consider three real numbers, X, Y, and Z. Is Z the smallest of these numbers?

A. X is greater than at least one of Y and Z.
B. Y is greater than at least one of X and Z.

#### Question 2

Let X be a real number. Is the modulus of X necessarily less than 3?

A. X(X+3)<0

B. X(X-3)>0

#### Question 3

Triangle PQR has angle PRQ equal to 90 degrees. What is the value of PR + RQ?

A. Diameter of the inscribed circle of the triangle PQR is equal to 10 cm.
B. Diameter of the circumscribed circle of the triangle PQR is equal to 18 cm

#### Question 4

Harshad bought shares of a company on a certain day, and sold them the next day. While buying and selling he had to pay to the broker one percent of the transaction value of the shares as brokerage. What was the profit earned by him per rupee spent on buying the shares?

A.The sales price per share was 1.05 times that of its purchase price.
B. The number of shares purchased was 100.

#### Question 5

For any two real numbers:

a + b = 1 if both a and b are positive or both a and b are negative.
a + b = -1 if one of the two numbers a and b is positive and the other negative.

What is (2 + 0) + (-5 + -6)?
A. a + b is zero if a is zero
B. a + b = b + a

#### Question 6

There are two straight lines in the x-y plane with equations:

ax + by = c

dx + ey = f

Do the two straight lines intersect?

A. a, b, c, d, e and f are distinct real numbers.

B. c and f are non-zero.

#### Question 7

O is the centre of two concentric circles. AE is a chord of the outer circle and it intersects the inner circle at points B and D. C is a point on the chord in between B and D. What is the value of AC/CE?

A. BC/CD=1
B. A third circle intersects the inner circle at B and D and the point C is on the line joining the centres of the third circle and the inner circle.

#### Question 8

How many people are watching TV programme P?

A. Number of people watching TV programme Q is 1000 and number of  people watching both the programmes, P and Q, is 100.

B. Number of people watching either P or Q or both is 1500.

#### Question 9

Ghosh Babu has decided to take a non-stop flight from Mumbai to No-man’s-land in South America. He is scheduled to leave Mumbai at 5 am, Indian Standard Time on December 10, 2000. What is the local time at No-man's-land when he reaches there?

A. The average speed of the plane is 700 kilometres per hour.

B. The flight distance is 10,500 kilometres.

#### Question 10

What are the ages of two individuals, X and Y?

A. The age difference between them is 6 years.
B. The product of their ages is divisible by 6.

## CAT 1999 Data Sufficiency questions

Instruction for set 1:

Each question is followed by two statements, A and B. Choose the option based on the given statements and questions

#### Question 1

The average weight of students in a class is 50 kg. What is the number of students in the class?

A. The heaviest and the lightest members of the class weigh 60 kg and 40 kg respectively.

B. Exclusion of the heaviest and the lightest members from the class does not change the average weight of the students.

Instruction for set 1:

Each question is followed by two statements, A and B. Choose the option based on the given statements and questions

#### Question 2

A small storage tank is spherical in shape. What is the storage volume of the tank?

A. The wall thickness of the tank is 1 cm.

B. When the empty spherical tank is immersed in a large tank filled with water,20 litres of water overflow from the large tank.

Instruction for set 1:

Each question is followed by two statements, A and B. Choose the option based on the given statements and questions

#### Question 3

Mr. X starts walking northwards along the boundary of a field, from point A on the boundary, and after walking for 150 metres reaches B, and then walks westwards, again along the boundary, for another 100 metres when he reaches C. What is the maximum distance between any pair of points on the boundary of the field?

A.The field is rectangular in shape.

B.The field is a polygon, with C as one of its vertices and A the mid point of a side.

Instruction for set 1:

Each question is followed by two statements, A and B. Choose the option based on the given statements and questions

#### Question 4

A line graph on a graph sheet shows the revenue for each year from 1990 through 1998 by points and joins the successive points by straight line segments. The point for revenue of 1990 is labelled A, that for 1991 as B, and that for 1992 as C. What is the ratio of growth in revenue between 91-92 and 90-91?

A.The angle between AB and X-axis when measured with a protractor is 40 degrees, and the angle between CB and X-axis is 80 degrees.

B.The scale of Y-axis is 1 cm = 1000 Rs.

Instruction for set 1:

Each question is followed by two statements, A and B. Choose the option based on the given statements and questions

#### Question 5

There is a circle with centre C at the origin and radius r cm. Two tangents are drawn from an external point D at a distance d cm from the centre. What are the angles between each tangent and the X-axis?

A.The coordinates of D are given

B.The X-axis bisects one of the tangents.

Instruction for set 1:

Each question is followed by two statements, A and B. Choose the option based on the given statements and questions

#### Question 6

Find a pair of real numbers x and y that satisfy the following two equations simultaneously. It is known that the values of a, b, c, d, e and f are non-zero. ax + by = c dx + ey = f

A. a = kd and b = ke, c = kf, k is not equal to 0

B. a = b = 1, d = e = 2, f is not equal to 2c

Instruction for set 1:

Each question is followed by two statements, A and B. Choose the option based on the given statements and questions

#### Question 7

Three professors A, B and C are separately given three sets of numbers to add. They were expected to find the answers to 1+1, 1+1+2, and 1+1 respectively. Their respective answers were 3, 3, and b How many of the professors are mathematicians?

A. A mathematician can never add two numbers correctly, but can always add three numbers correctly.

B. When a mathematician makes a mistake in a sum, the error is + I or -1.

Instruction for set 1:

Each question is followed by two statements, A and B. Choose the option based on the given statements and questions

#### Question 8

How many among the four students A, B, C and D have passed the exam'?

A.The following is a true statement: A and B passed the exam.

B.The following is a false statement: At least one among C and D has passed the exam.

Instruction for set 1:

Each question is followed by two statements, A and B. Choose the option based on the given statements and questions

#### Question 9

What is the distance x between two cities A and B in integral number of Kms?

A.x satisfies the equation $$\log_2 x = \sqrt{x}$$

B. x less than or equal to 10 Kms

Instruction for set 1:

Each question is followed by two statements, A and B. Choose the option based on the given statements and questions

#### Question 10

Mr. Mendel grew one hundred flowering plants from black seeds and white seeds, each seed giving rise to one plant. A plant gives flowers of only one colour. From a black seed comes a plant giving red or blue flowers. From a white seed comes a plant giving red or white flowers. How many black seeds were used by Mr. Mendel?

A. The number of plants with white flowers was 10.

B. The number of plants with red flowers was 70.

## CAT 1998 Data Sufficiency questions

#### Question 1

Find the length of AB if $$\angle YBC = \angle CAX = \angle YOX = 90$$.

I. Radius of the arc is given.

II. OA = 5

#### Question 2

Is n odd?

I. n is divisible by 3, 5, 7 and 9.

II. 0 < n < 400

#### Question 3

Find $$2 \circledast 3$$, where $$2\circledast 3$$ need not be equal to $$3\circledast2$$

I. $$1 \circledast 2$$=3

II. $$a \circledast b=\frac{a+b}{a}$$, where a and b are positive.

#### Question 4

Radha and Rani appeared in an examination. What was the total number of questions?

I. Radha and Rani together solved 20% of the paper.

II. Radha alone solved 5/3 rd of the paper solved by Rani.

#### Question 5

What is the price of tea?

I. Price of coffee is Rs. 5 more than that of tea.

II. Price of coffee was Rs. 5 less than the price of a cold drink which cost three times the price of tea.

#### Question 6

What is the value of ‘a’?

I. Ratio of a and b is 3 : 5, where b is positive.

II. Ratio of 2a and b is 10 12 , where a is positive.

#### Question 7

In a group of 150 students, find the number of girls.

I. Each girl was given 50 paise, while each boy was given 25 paise to purchase goods totaling Rs. 49.

II. Girls and boys were given 30 paise each to buy goods totalling Rs. 45.

#### Question 8

There are four envelopes — E1, E2, E3 and E4 — in which one was supposed to put letters L1, L2, L3 and L4 meant for persons C1, C2, C3 and C4 respectively, but by mistake the letters got jumbled up and went in wrong envelopes. Now if C2 is allowed to open an envelope at random, then how will he identify the envelope containing the letter for him?

I. L2 has been put in E1.

II. The letter belonging to C3 has gone in the correct envelope.

#### Question 9

There are four racks numbered 1, 2, 3, 4 and four books numbered 1, 2, 3, 4. If an even rack has to contain an odd-numbered book and an odd rack contains an even-numbered book, then what is the position of book 4?

I. Second book has been put in third rack.

II. Third book has been put in second rack.

#### Question 10

Find the value of X in terms of ‘a’.

I. Arithmetic mean of X and Y is ’a’ while the geometric mean is also ‘a’.

II. Y X = R; X - Y = D.

#### Question 11

There are two concentric circles C1 and C2 with radii r1 and r2. The circles are such that C1 fully encloses C2. Then what is the radius of C1?

I. The difference of their circumference is k cm.

II. The difference of their areas is m sq. cm.

## CAT 1997 Data Sufficiency questions

#### Question 1

What is the value of $$a^3 + b^3$$ ?
I. $$a^2 + b^2 = 22$$
II. $$ab = 3$$

#### Question 2

Is the number completely divisible by 99?
I. The number is divisible by 9 and 11 simultaneously.
II. If the digits of the number are reversed, the number is divisible by 9 and 11.

#### Question 3

A person is walking from Mali to Pali, which lies to its north-east. What is the distance between Mali and Pali?

I. When the person has covered $$\frac{1}{3}$$ the distance, he is 3 km east and 1 km north of Mali.

II. When the person has covered $$\frac{2}{3}$$ the distance, he is 6 km east and 2 km north of Mali.

#### Question 4

What is the value of x and y?
I. 3x + 2y = 45
II. 10.5x + 7y = 157.5

#### Question 5

Three friends P, Q and R are wearing hats, either black or white. Each person can see the hats of the other two persons. What is the colour of P's hat? I. P says that he can see one black hat and one white hat. II. Q says that he can see one white hat and one black hat.

#### Question 6

What is the speed of the car?

I. The speed of a car is 10 (km/hr) more than that of a motorcycle.
II. The motorcycle takes 2 hr more than the car to cover 100 km.

#### Question 7

What is the ratio of the volume of the given right circular cone to the one obtained from it?
I. The smaller cone is obtained by passing a plane parallel to the base and dividing the original height in the ratio 1 : 2.
II. The height and the base of the new cone are one-third those of the original cone.

#### Question 8

What is the area bounded by the two lines and the coordinate axes in the first quadrant?
I. The lines intersect at a point which also lies on the lines 3x - 4y = 1 and 7x - 8y = 5.
II. The lines are perpendicular, and one of them intersects the Y-axis at an intercept of 4.

#### Question 9

What is the cost price of the chair?
I. The chair and the table are sold at profits of 15% and 20% respectively.
II. If the cost price of the chair is increased by 10% and that of the table is increased by 20%, the profit reduces by Rs. 20.

#### Question 10

After what time will the two persons Tez and Gati meet while moving around the circular track? Both of them start at the same point and at the same time.

I. Tez moves at a constant speed of 5 m/s, while Gati starts at a speed of 2 m/s and increases his speed by 0.5 m/s at the end of every second thereafter.

II. Gati can complete one entire lap in exactly 10 s.

## CAT 1996 Data Sufficiency questions

#### Question 1

What is the number of type-2 widgets produced, if the total number of widgets produced is 20,000? The company produces only two types of widgets.
I. If the production of type-1 widgets increases by 10% and that of type-2 decreases by 6%, the total production remains the same.
II. The ratio in which type-1 and type-2 widgets are produced is 2 : 1.

Instruction for set 1:

Each question is followed by two statements, I and II. Mark the answer

#### Question 2

A tractor travelled a distance 5 m. What is the radius of the rear wheel?
I. The front wheel rotates ‘N’ times more than the rear wheel over this distance.
II. The circumference of the rear wheel is ‘t’ times that of the front wheel.

Instruction for set 1:

Each question is followed by two statements, I and II. Mark the answer

#### Question 3

What is the ratio of the two liquids A and B in the mixture finally, if these two liquids kept in three vessels are mixed together? (The containers are of equal volume.)
I. The ratio of liquid A to liquid B in the first and second vessel is 3 : 5, 2 : 3 respectively.
II. The ratio of liquid A to liquid B in vessel 3 is 4:3.

Instruction for set 1:

Each question is followed by two statements, I and II. Mark the answer

#### Question 4

If a,b and c areintegers,is(a-b+c)>(a+b-c)?
I. b is negative.
II. c is positive.

Instruction for set 1:

Each question is followed by two statements, I and II. Mark the answer

#### Question 5

If α and β are the roots of the equation $$(ax^2+bx+c=0)$$, then what is the value of $$(α^2 +β^2)$$?
I.$$α+β=\frac{-b}{a}$$
II.$$αβ =\frac{c}{a}$$

Instruction for set 1:

Each question is followed by two statements, I and II. Mark the answer

#### Question 6

What is the cost price of the article?
I. After selling the article, a loss of 25% on cost price is incurred.
II. The selling price is three-fourths of the cost price.

Instruction for set 1:

Each question is followed by two statements, I and II. Mark the answer

#### Question 7

What is the selling price of the article?
I. The profit on sales is 20%.
II. The profit on each unit is 25% and the cost price is Rs. 250.

Instruction for set 1:

Each question is followed by two statements, I and II. Mark the answer

#### Question 8

How many different triangles can be formed?
I. There are 16 coplanar, straight lines.
II. No two lines are parallel.

Instruction for set 1:

Each question is followed by two statements, I and II. Mark the answer

#### Question 9

What is the total worth of Lakhiram's assets?
I. A compound interest at 10% on his assets, followed by a tax of 4% on the interest, fetches him Rs. 1,500 this year.
II. The interest is compounded once every four months.

Instruction for set 1:

Each question is followed by two statements, I and II. Mark the answer

#### Question 10

How old is Sachin in 1997?
I. Sachin is 11 years younger than Anil whose age will be a prime number in 1998.
II. Anil's age was a prime number in 1996.

## CAT 1991 Data Sufficiency questions

#### Question 1

What is the time difference between New York and London?
I. The departure time at New York is exactly 9.00 a.m local time and the arrival time at London is at 10.00 a.m. local time.
II. The flight time is 5 hours.

#### Question 2

Mr. Murthy takes the morning train to his office from station A to station B, and his colleague Mr.Rahman joins him on the way. There are three stations C, D and E on the way not necessarily in that sequence. What is the sequence of stations?
I. Mr. Rahman boards the train at D.
II. Mr. Thomas, who travels between C & D has two segments of journey in common with Mr. Murthy but none with Mr. Rahman.

#### Question 3

Is it more profitable for Company M to produce Q?
I. Product R sells at a price four times that of Q
II. One unit of Q requires 2 units of labour, while one unit of R requires 5 units of labour. There is a no other constraint on production.

#### Question 4

A train started from Station A, developed engine trouble and reached Station B, 40 minutes late. What is the distance between Stations A and B?
I. The engine trouble developed after travelling 40 km from Station A and the speed reduced to 1/4th of the original speed.
II. The engine trouble developed after travelling 40 km from station A in two hours and the speed reduced to 1/4th of the original speed.

#### Question 5

What is the value of prime number x?
I. $$x^2 + x$$ is a two-digit number greater than 50
II. $$x^3$$ is a three digit number.

#### Question 6

The average of three unequal quotations for a particular share is Rs.110. If all are quoted in integral values of rupee, does the highest quotation exceed Rs. 129?
I. The lowest quotation Rs. 100.
II. One of the quotations is Rs. 115.

#### Question 7

How many people ( from the group surveyed ) read both Indian Express and Times of India?

#### Question 8

X says to Y, 'I am 3 times as old as you were 3 years ago'. How old is X?
I. Y's age 17 years from now is same as X.s present age.
II. X's age nine years from now is 3 times Y.s present age.

#### Question 9

What is the radius of the circle?
I. Ratio of its area to circumference is > 7.
II. Diameter of the circle is <=32.

## CAT 1990 Data Sufficiency questions

#### Question 1

If R is an integer between 1 & 9, P - R = 2370, what is the value of R?
I. P is divisible by 4.
II. P is divisible by 9.

#### Question 2

A man distributed 43 chocolates to his children. How many of his children are more than five years old?
I. A child older than five years gets 5 chocolates.
II. A child 5 years or younger in age gets 6 chocolates.

#### Question 3

Ramu went by car from Calcutta to Trivandrum via Madras, without any stoppages. The average speeds for the entire journey was 40 kmph. What was the average speed from Madras to Trivandrum?
I. The distance from Madras to Trivandrum is 0.30 times the distance from Calcutta to Madras.
II. The average speed from Madras to Trivandrum was twice that of the average speed from Calcutta to Madras.

#### Question 4

x, y, and z are three positive odd integers, Is x+z divisible by 4?
I. y - x = 2
II. z - y = 2

#### Question 5

The unit price of product P1 is non-increasing and that of product P2 is decreasing. Which product will be costlier 5 years hence?
I. Current unit price of P1 is twice that of P2.
II. 5 years ago, unit price of P2 was twice that of P1.

#### Question 6

X is older than Y, Z is younger than W and V is as old as Y. Is Z younger than X?
I. W may not be older than V
II. W is not older than V

#### Question 7

How long did Mr. X take to cover 5000 km. journey with 10 stopovers?
I. The $$i^{th}$$ stopover lasted $$i^2$$ minutes.
II. The average speed between any two stopovers was 66 kmph.

#### Question 8

Is $$[(x^{-1} - y^{-1} )/(x^{-2} -y^{-2}]>1$$?
I. x + y > 0
II. x and y are positive integers and each is greater than 2.