# Free Data Sufficiency - 01 Practice Test - CAT

### Question 1

Find the total amount which Amico spends on printing in the year 2000, if everyday same quantity of material is printed as in 1990. printing cost is volatile but it remains constant for the year in consideration1. In the year 1990, total amount spent on printing was 10 crore2. Printing cost a day in the year 2000 changes by 20% over that in 1990. it is also known that printing cost has an increasing trend over the years till 1995.

#### SOLUTION

Solution :E

Answer = option (e)

Using both statements it is not possible to determine the amount spent in 2000. Statement (2) gives only partial information.

### Question 2

, where x is an integer.

Find the individual values of P,Q,R,S

1. P,Q,R,S are all prime numbers

2. Q=S, P+R=Q

#### SOLUTION

Solution :E

Using statement (1), we can get several prime numbers which satisfy the condition. We cannot arrive at an unique answer

Using statement (2), we can again get many cases. Hence, this statement also does not individually give an unique answer

Using both statements together, we are looking for an integral sum with prime numbers where Q=S and P+R=Q

One such possible case is 2/5 + 3/5 = 1 (where A= 2 or 3 and C=2 or 3). Hence, unique values cannot be obtained. Answer is option (e)

### Question 3

There are 2 APs, each having 3 terms whose common difference differ by 1. find the two APs.

1. Sum of the three consecutive terms is 15

2. P and

#### SOLUTION

Solution :E

Answer=option (e)

If the three terms

AP 1 = a-d,a and a+d

AP 2 = A, A-D and A+D and D= d+1

S= 3a = 3A= 15. a=A=5

Also, P/P1= {a(a

^{2}-d^{2})}/ {(A^{2}-D^{2})} = 7/8It is not possible to get a unique solution, even after using both statements. Answer is

option (e)

### Question 4

Little Bo Peep lost her sheep. She could not remember how many were there. She knew she would have 400 more next year, than the number of sheep she had last year. How many sheep were there?

1. The number of sheep last year was 20% more than the year before that and this rate of increase continues to be the same for the next 10 years.

2. The increase is compounded annually

#### SOLUTION

Solution :D

Option (d)

We need to have both statements to find the number of sheep

### Question 5

If 20 sweets are to be distributed among some boys and girls such that each girl gets 2 sweets and each boy gets 3 sweets, what are the numbers of boys and girls?

1. The number of girls is not more than 5

2. If each girl gets 3 sweets and each boy get 2 sweets, the number of sweets required for the children will still be the same

#### SOLUTION

Solution :B

(b)

Given that 2G+3B=20

Using statement I that number of girls is not more than 5, we have G=1, B=6 and G=4, B=4. since we cannot get a single solution from this statement it is not sufficient to answer the question

If statement II is used, 3B+2G=20, we have G=4 and B=4

Hence, statement II alone is sufficient to answer the question

### Question 6

Two schools decide to send their students to a picnic on the same day. How many students attend the picnic from the first school?

1. 40 students in all attend the picnic

2. If you multiply the number of students from first school with the number of students from the second school, the answer is 300

#### SOLUTION

Solution :E

(e)

While at first glance, you may be tempted to answer (c), since there are two linear equations and two variables, as you try to solve the question you will get two answers 30 and 10. So you can’t say which one of those applies to the first school

### Question 7

Radhesh is a class X student and is practicing for his board exam. He draws a circle of radius 9.6 cm. He also draws a chord, whose length is

1. If you measure the perpendicular distance from the centre of the centre of the circle to the chord, you get 6 cm

2. If you draw a triangle with two end points being the end points of the chord and the third point touching the circle, the 3rd angle is 80 degrees

#### SOLUTION

Solution :C

Statement I allows you get the answer since the perpendicular from the centre of the circle to the chord is going to bisect the chord. Then using Pythagoras theorem, you can calculate the length of the ½ chord

Statement II- if two sides and the included angle is given, then the third side can be found.

Angle BCD is 160 as angle BAC is given as 80.

### Question 8

If x, y are natural numbers, is the value of x+y an even number?

1. L.C.M of x^{2} and y is 12

2. H.C.F of y^{2} and x is 2

#### SOLUTION

Solution :B

(b)

Statement A implies (x, y) = {(2, 3), (2, 6), (1, 12), (2, 12)}

This implies x+y may be even or odd.

Statement (A) alone is not sufficient

Statement B: x, y = {(2, 2), (2, 6), (2, 8)...} i.e. X and y are both even numbers.

Statement B alone is sufficient.

### Question 9

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

1. Amit spends more on recreation than Deepa.

2. Deepa spends more on healthcare than Amit.

#### SOLUTION

Solution :B

option (b)

Statement A: 20% of A > 25% of D

With this we cannot say. As we are comparing 30% of A and 40% of B

Statement B: 13% of D > 10% of A

39% of D > 30% of A. So 40% of D must be greater than 30% of A.

Hence statement B is sufficient to answer.

### Question 10

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?

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

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

#### SOLUTION

Solution :A

option (a)

Assume A, B, C, D get scores 10, 8, 6, 4 respectively

A B C D

10 8 6 4

Statement A:

With the conditions A will give vote to B

With the conditions B will give vote to A

With the conditions C will give vote to A

Even if D gives to A/B/C — 2 situations arise.

Either A will win or there will a tie when D gives vote to B.

Even then A will win.

So we are getting the answer.

Statement B: Can conclude anything.

### Question 11

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

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

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

#### SOLUTION

Solution :B

option (b)

Statement A: Cannot say anything.

Statement B: Because amongst the Top 5 → 3 are boys, 2 are girls. And Reshma is third

among the girls and Kishor is 6th.

We can conclude.

Answer (b) statement II is sufficient.

### Question 12

Tahir 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?

1. He stops after 21 coin tosses.

2. He obtains three more tails than heads.

#### SOLUTION

Solution :C

option (c)

Statement A: We can find, there are 12 Tails and 9 Heads.

After tosses he will reach at blue point. So statement A is sufficient.

Statement B: 3 more Tails greater than Heads. So he will reach at blue point after tosses.

So statement B is also sufficient.

### Question 13

Anita 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?

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

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

#### SOLUTION

Solution :D

option (d)

Statement A: 2 kg potato cost + 1 kg gourd cost < 1 kg potato cost + 1 kg gourd cost

Which means that 1 kg potato cost < 1 kg gourd cost.

So statement A is not sufficient.

Statement B: 1 kg potato cost + 2 kg onion cost = 1 kg onion cost + 2 kg gourd cost = 1 kg

potato cost + 1 kg onion cost = 2 kg gourd cost.

So statement B is also not sufficient.

Combining both statements we get

1 kg potato cost < 1 kg gourd cost …(i)

1 kg potato cost + 1 kg onion cost = 2 kg gourd cost …(ii)

So the onion is costliest.

### Question 14

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?

1. Nandini used a total of 13 currency notes.

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

#### SOLUTION

Solution :E

option (e)

Statement A: 13 currency notes will give diff. Values.

Statement B: Multiple of 10, there is no unique value

Even if you combine the statement, we can have various values.

### Question 15

My telephone number is a six digit number. What is it?

1) The number is divisible by 22, and three digits of the number are the same

2) Sum of the digits at odd places is equal to 27 and sum of digits at even places is equal to 5. the 100^{th} and units place of the number is zero

#### SOLUTION

Solution :B

option (b)

let the 6 digit telephone number be A B C D E F

from statement (1) no useful information can be obtained to obtain a unique phone number

from statement (2), if the sum of 3 digits = 27 A+C+E=27, the the only possibility is that A=C=E=9. Also given that D=F=0 and B=5. hence the number is 959090. answer can be obtained based on statement (2) alone