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# 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

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

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)

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

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

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

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

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

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

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

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

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

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

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