# Free Data Sufficiency - 02 Practice Test - CAT

### Question 1

If x is a positive integer, find the remainder when x is divided by 6

A. When x-1 is divided by 6, the remainder is 1

B. When 3x is divided by 6, the remainder is 0

#### SOLUTION

Solution :A

Option (a)

Statement A alone is sufficient. When x-1 is divided by 6, the remainder is 1. therefore, when x is divided by 6; the remainder will be 2.

Statement B states that 3x is exactly divisible by 6. take 2 cases; say x=8 and in this case 3x= 24 is divisible by 6. but in another case, if x=16; then 3x= 48; which is divisible by 6; but 16 leaves a remainder of 4.

Hence B does not conclusively answer the question

### Question 2

What is the average speed of a Volvo bus traveling a distance of 500 kms between Bangalore and Hyderabad?

A. The bus travels at an average speed of 60 kmph during the first five hours of the journey

B. The bus covers the last 150 kms in 3 hours

#### SOLUTION

Solution :E

Option (e)

From statement A, we know the time taken to cover the first 300 kms. From statement B, we know the time taken to cover the last 150 kms. But neither of the statements provides any information about the time taken to cover the 50 kms in between.

### Question 3

What is the value of the positive integer n?

A. The product of the numbers a, and b, which are respectively three less and two less than n,is 0.

B. n!/2 =(n-2)!

#### SOLUTION

Solution :B

Option (b)

From A

(n - 3) (n - 2) = 0

n = 2 or 3

A alone is not sufficient

From B

Only for n = 2

n!/2 =(n-2)!

B alone is sufficient.

### Question 4

What is the perimeter of the triangle ABC? One of its side is 10√3 units.

A. BC is the hypotenuse of the right angle triangle ABC.

B. The sum of the areas of the semicircles described on the three sides of the triangle ABC is 100 π sq. units.

#### SOLUTION

Solution :D

Option (d)

Given, sum of areas of semi-circles x, y and z is 100π

If BC = a cm, AC = b cm, AB = c cm.

Area of semi-circle x is π/2 x a

^{2}/4 cm2Area of semi circle y is π/2 x c

^{2}/4 cm2Area of semi circlezx is π/2 x b

^{2}/4 cm2½ π/4 (a

^{2}+ b^{2}+c^{2}) =100πa2 + b

^{2}+ c^{2}= 800from Statement 1:We know that in ABC is a right angle triangle.

a

^{2}= b^{2}+c^{2}= 2(b^{2}+c^{2}) = 800b

^{2}+c^{2}= 400b

^{2}+c^{2}= a^{2}= 400 ;a = 20b or c = 10√3 and the sides are 10, 10√3, 20

the perimeter = 30 + 10√3 cm

### Question 5

The cost price of an article is 100. Find the profit made by selling it.

A. Ten percent discount was given on the list price and the profit percentage made is 25 percentage points more than the discount percent.

B. List price is Rs.180 and profit percent is 1/5th of the mark up percentage.

#### SOLUTION

Solution :C

Option (C)

From A profit % is 35% (i.e. 10 +25) => profit = Rs.35

From B Markup% = 80%

profit % = 1/5 x 80 = 16%

profit = Rs.16

Either statement is sufficient

### Question 6

The total capacity of production of two types of bikes in a factory is 25000 units. Using a total of 6000 tones of metal for production of both types of bikes and operating at full capacity, what is the production of type I?

A. 200 kgs of metal is used for Type 1

B. 300 kgs of metal is used for Type II

#### SOLUTION

Solution :D

Option (d)

If x are the number of type 1 bikes produced and y the number of type 2 bikes produced, then we can get two simultaneous equations based on the two statements which need to be solved

x+y=25000 and 200x+300y=6000000.

### Question 7

What is the ratio of radii of the circumcircle and the incircle of a polygon of 12 sides

(A) The polygon is a regular one of side 8 cm.

(B) One angle measures 150°

#### SOLUTION

Solution :A

We can find the answer based on statement 1 alone.

Hence, Option (a)

### Question 8

A newspaper boy has 3 TOI, 2 ET and 3 HT in his bag (kept at random). He takes out 2 newspapers at random, without replacement. Does he select at least one ET?

(A) He takes out 5 more newspapers at random of which there is at least one TOI, one ET and one HT

(B) He takes out 5 more newspapers at random and there are 2 TOI and 2 HT among them

#### SOLUTION

Solution :E

Using statement 1, we do not know anything about the initial 2 newspapers removed

Using statement 2, we still do not know anything about the initial 2 papers removed.

Even on combining, no conclusive result can be drawn

Answer is Option (e)

### Question 9

What is the area of the triangle?

(A) Two sides are 41 cm each

(B) The altitude to the third side is 9 cm long.

#### SOLUTION

Solution :D

option (d)

If the altitude to the base of an isosceles triangle is known, the base can be found, and hence the area.

### Question 10

Which of the three bowlers in the series of test matches took most wickets?

(A) The first and the third bowlers took twice as many wickets as the second bowler

(B) The second and the third bowlers took three times as many wickets as the first bowler.

#### SOLUTION

Solution :D

This is the solving of 2 simultaneous equations

A+C=2B

B+C=3A

subtracting the above equations we get B=2A, hence B is greater than A.

Also we get 4C=5B, hence c is greater than B.

So the order will be C>B>A. hence C took the maximum wickets

Option (d)

### Question 11

A fruitseller sells 80% of all his fruits on a particular day, which comprise of only mangoes and apples. He sells an equal number of mangoes and apples. He sells mangoes for Rs 1 each and apples for Rs 3 each. How many fruits were there before the sale?

A. His total revenue from the sale of his fruits was Rs 32

B. Exactly 2 mangoes and 2 apples are remaining after the sale

#### SOLUTION

Solution :C

Answer= option (c)

Using statement (1) we can arrive at an equation x+3x=32. hence, the answer can be

obtained based on statement 1 alone

Using statement (2) we can also arrive at the answer

20% 4 fruits

100% = 400/20 = 20 fruits. Hence, using both statements individually, it is possible to arrive at the solution.

### Question 12

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.

#### SOLUTION

Solution :D

option (d) To make a Venn diagram, we need both statements. Total = 300.

### Question 13

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

A. Jagdish received 2/9 of what Punit and Girish together received.

B. Punit received 3/11 of what Jagdish and Girish together received

#### SOLUTION

Solution :D

Option (d) From first statement we get only J’s share. Only by combining the statements we get the values of each student.

### Question 14

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

A. Deepak Thakur, the Indian striker, scored 3 goals in the last five minutes of the match.

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

#### SOLUTION

Solution :E

option (e)

India was trailing by 2 goals

With Statement A we cannot find if india won the match or not as Koreas score line is not know.

With Statement B alone we dont get Indias Scoreline.

Combining Both statements :

Case A:

Initial Score line can be 0-2

Hence in the last 5 minutes the score line becomes 3-3 hence a draw

CASE B:

the initial score line is 1-3

In the last 5 minutes the score line becomes 4-3 hence a win.

So we cannot determine if india wins even after we combine both the statements

### Question 15

Amrutha makes candles. She follows a particular pattern for the number of candles she makes. She works for more than a day. If Amrutha makes “x” candles on the first day, she makes “x+1” candles on the next day. On the third day she makes as many candles as the sum of the number of candles made in the previous two days. The pattern of the third day is followed for the rest of the days This process can finish any day and “x” is a natural number. How many days does she work for?

1.she makes a total number of candles equal to the highest two digit prime number.

2. she makes 48 candles on the first day

#### SOLUTION

Solution :A

Answer = option (a)

97 is the highest two digit prime number. Since she takes more than one day , she prepares 47 candles on the first day and 48 candles on the second day. This is the only possible combination. Answer can be obtained based on statement (1) alone

Statement (2) does not give us information about the total number of candles made.