Practice MCQ Questions and Answer on Number System

31.

The sum of the digits of a two digit number is $\frac{1}{7}$ of the number. The units digit is 4 less than the tens digit. If the number obtained on reversing its digits is divided by 7, the remainder will be:

(A) 4
(B) 6
(C) 1
(D) 5

Solution: $\begin{aligned} x + y = \frac{1}{7} (10 x + y) \\ 7 x + 7 y = 10 x + y \\ 3 x = 6 y \\ x : y = 2 : 1 \\ 1 unit \to 4 \\ Number will be = 84 \\ \frac{48}{7} R \to 6 \end{aligned}$

32.

A and B are positive integers. If A + B + AB = 65, then what is the difference between A and B (A, B ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ¤ 15)?

(A) 3
(B) 4
(C) 5
(D) 6

33.

A six digit number is formed by repeating a three digit number : For example, 256, 256 or 678, 678 etc. Any number of this form is always exactly divisible by -

(A) 7 only
(B) 11 only
(C) 13 only
(D) 1001 only

34.

Each member of a club contributes as much rupees and as much paise as the number of members of the club. If the total contribution is Rs. 2525, then the number of members of the club is:

(A) 60
(B) 45
(C) 55
(D) 50

Solution: Let the total member be x. x member contribute is Rs. x and each member also contributes x paise. So total rupees is x member Rs. x = Rs. x2 x member Rs. x paise $= \frac{x . x}{100}$ Total rupees is $\begin{aligned} x^{2} + \frac{x^{2}}{100} = 2525 \\ 101 x^{2} = 2525 \times 100 \\ 101 x^{2} = 101 \times 25 \times 100 \\ x = 50 \end{aligned}$

35.

7 is added to a certain number; the sum is multiplied by 5 ; the product is divided by 9 and 3 is subtracted from the quotient. Thus, if the remainder left is 12, what was the original number ?

(A) 20
(B) 30
(C) 40
(D) 60

Solution: Let the original number be x. Then, $\frac{(x + 7) \times 5}{9}$ - 3 = 12 ⇒ $\frac{5 x + 35}{9}$ = 15 ⇒ 5x + 35 = 135 ⇒ 5x = 100 ⇒ x = 20

36.

Prof. Suman takes a number of quizzes for a course. All the quizzes are out of 100. A student can get an A grade in the course if the average of her scores is more than or equal to 90. Grade B is awarded to a student if the average of her scores is between 87 and 89 (both included). If the average is below 87, the student gets a C grade. Ramesh is preparing for his last quiz and he realizes that he must score a minimum of 97 to get an A grade. After the quiz, he realizes that he will score 70, and he will just manage a B. how many quizzes did Prof. Suman take?

(A) 6
(B) 7
(C) 8
(D) 9

37.

Number 2, 4, 6, 8, 10.....196, 198, 200 are multiplied together. The number of zeros at the end of the product on the right will be equal to -

(A) 21
(B) 22
(C) 24
(D) 25

Solution: $\begin{aligned} 2, 4, 6, 8, 10 . . . . . . 198, 200 \\ 2^{100} (1 \times 2 \times 3 \times . . . . . \times 99 \times 100) \end{aligned}$ $\begin{aligned} \underset{―}{5 | 100} \\ \underset{―}{5 | 20} = 24 zero's (20 + 4) \\ | 4 \end{aligned}$ When we multiply the series of 1 × 2 × 3 ×..... × 100 then we find 24 zero at the end of the product

38.

If A381 is divisible by 11, find the value of the smallest natural number A?

(A) 5
(B) 6
(C) 7
(D) 9

39.

Of the three numbers, the sum of the first two is 55, sum of the second and third is 65, and sum of third with thrice of the first is 110. The third number is -

(A) 25
(B) 30
(C) 35
(D) 28

Solution: $\begin{aligned} Let the 3 numbers be x, y, & z \\ According to question \\ x + y = 55 \to y = 55 - x \\ y + z = 65 \to 55 - x + z = 65 \\ z - x = 10. . . . . (i) \\ z + 3 x = 110. . . . . (i i) \\ Solve (i) and (ii) \\ z = 35, \\ x = 25, \\ y = 30 \end{aligned}$

40.

What will be the unit digit in the 7¹⁰⁵ ?

(A) 5
(B) 7
(C) 9
(D) 1

Solution: $\begin{aligned} 7^{105} \Rightarrow \\ 7^{1} \to 7 \to 7 \\ 7^{2} \to 49 \to 9 \\ 7^{3} \to 343 \to 3 \\ 7^{4} \to 2401 \to 1 \\ Divided power of 7 by 4 \\ \frac{105}{4} \to remainder = 1 \\ \Rightarrow 7^{1} is left unit digit = 1 \times 7 = 7 \end{aligned}$

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Practice MCQ Questions and Answer on Number System

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