# CSEET Quantitative aptitude - MCQ part 1

**1) Every rational number is a -**

a) Whole number

b) Real number

c) Natural number

d) None of the above

Answer: (b) Real number

Explanation: The numbers which can be found on the number line and include both rational and irrational numbers are known as real numbers, e.g., -1.5,√2,0,1,2,3,π.Almost any number which you can imagine is a real number.

**2) Between any two numbers, there are -**

a. Two rational numbers

b. No rational number

c. Infinite rational numbers

d. None of the above

Answer: (c) Infinite rational numbers

Explanation: There are infinite rational numbers in between any two numbers.

**3) What will be the value of x3 + y3 + z3, if x + y + z = 0?**

a) 3xyz

b) 2xyz

c) xyz

d) xyz(xy + yz + zx)

Answer: (a) 3xyz

Explanation: It is given that

x + y + z = 0

On cubing both sides, we will get

(x + y + z)3 = 0

x3 + y3 + z3 - 3xyz = 0

So, the value of x3 + y3 + z3 = 3xyz

**4) Digit 1 is occurring 136 times on writing all of the page numbers of a book. What will be the number of pages in the book?**

a. 194

b. 195

c. 200

d. 295

Answer: (b) 195

Explanation: From 1 - 99, the digit 1 occurs 20 times, and from 100 - 199, the digit 1 occurs 120 times.

So, from 1 to 199, the digit 1 occurs -

20 + 120 = 140 times

According to question 1 is occurring only 136 times, which means we need to remove 196, 197, 198, and 199. So, the required number of pages will be 195.

**5) Which of the following is the unit digit in the product of 853 x 452 x 226 x 1346?**

a) 2

b) 5

c) 6

d) 7

Answer: (c) 6

Explanation: Pick up the unit digit of each number and multiply them;

a. 3 in 853

b. 2 in 452

c. 6 in 226

d. 6 in 1346

∴ 3 x 6 x 2 x 6 = 216 (consider the unit digit in the product)

So, the unit digit in the product of 853 * 1346 * 452 * 226 is 6.

**6) The sum of odd numbers upto 240 is -**

A. 11400

B. 12400

C. 13400

D. 14400

Answer: (d) 14400

Explanation: Number of odd numbers up to 240 = 240/2 = 120

Sum of first n odd numbers = n2

n = 120

Required sum = 1202 = 14400

**7) Which of the following number is divisible by 9?**

a) 56785

b) 45678

c) 65889

d) 67578

Answer: (c) 65889

Explanation: A number is divisible by 9 if the sum of its digits is divisible by 9.

The Sum of the digits of the given numbers are;

6+7+5+7+8= 33

5+6+7+8+5= 31

4+5+6+7+8= 30

6+5+8+8+9= 36

The sum of the digits of the number 65889 is 36, which is divisible by 9, so the correct answer is 65889.

**8) What smallest number should be subtracted from 9805 so that it is divisible by 8?**

A. 6

B. 7

C. 5

D. 8

Answer: (c) 5

Explanation: On dividing 9805 by 8, the remainder is 5. So, 5 is the smallest number which should be subtracted from 9805 to make it divisible by 8.

**9) Which of the following is the unit digit in the product of {(341)491 x (625)317 x (6374)1793}?**

a) 3

b) 7

c) 0

d) 8

Answer: (c) 0

Explanation: Pick up the unit digit of each number and multiply them;

Unit digit in (341)491

= Unit digit in (1)491 = 1

Unit digit in (625)317

= Unit digit in (5)317 = 5

Unit digit in (6374)1793

= (4)1793

= unit digit in [(42)896 x 4]

= unit digit in 6 x 4 = 4

So, on multiplying the unit digits, we will get -

1 x 5 x 4 = 20 (consider the unit digit in the product)

So, the unit digit in the product of {(341)491 x (625)317 x (6374)1793} is 0.

**10) Which of the following is completely divisible by 45?**

a. 331145

b. 306990

c. 181660

d. None of the above

Answer: (b) 306990

Explanation: A number that can be divisible by 3, 5, and 9 is also divisible by 45.

So, we check the divisibility of given numbers by the following rules -

A number is divisible by 3 if the sum of its entire digits is divisible by 3.

The number which ends with 0 or 5 is divisible by 5.

A number is divisible by 9 if the sum of its entire digits is divisible by 9.

The number 306990 fulfills all the requirements, so the answer is 306990.

**11) 7X2 is a three-digit number in which X is a missing digit. If the number is divisible by 6, the missing digit is -**

a) 4

b) 3

c) 7

d) 5

**12) Which is the largest 4-digit number that can be exactly divisible by 66?**

A. 9987

B. 9912

C. 9913

D. 9966

**13) Which is the largest 4-digit number that can be exactly divisible by 66?**

9987

9912

9913

9966

Answer: (d) 9966

Explanation: The largest four-digit number is = 9999, and on dividing it with 66, we will get 33 as the remainder.

So, the largest 4-digit number divided by 66 = 9999 - 33 = 9966

**14) What will be the remainder when 636 is divided by 215?**

a) 3

b) 2

c) 1

d) None of the above

Answer: (c) 1

Explanation: We can write 636/215 as

(63)12/215

Or, we can say 21612/215

We will always get remainder 1 on dividing 216 by 215

= 112/215

So, the remainder will be 1.

**15) Which of the following is the least number which will leave the remainder 5, when divided by 8, 12, 16, and 20?**

a. 245

b. 255

c. 265

d. None of the above

Answer: (a) 245

Explanation: First we need to find the least number, so we have to find out the LCM of 8, 12, 16, and 20.

8 = 2 x 2 x 2

12 = 2 x 2 x 3

16 = 2 x 2 x 2 x 2

20 = 2 x 2 x 5

LCM = 2 x 2 x 2 x 2 x 3 x 5 = 240

240 is the least number that is exactly divisible by 8, 12, 16, and 20.

So, the required number that will leave remainder 5 is -

240 + 5 = 245