Practice MCQ Questions and Answer on Number System

31.

12345679 ÃÂÃÂÃÂÃÂÃÂÃÂ 72 is equal to :

(A) 88888888
(B) 888888888
(C) 898989898
(D) 999999998

32.

10531 + 4813 - 728 = ? ÃÂÃÂÃÂÃÂÃÂÃÂ 87

(A) 168
(B) 172
(C) 186
(D) 212

Solution: Let 10531 + 4813 - 728 = x × 87 Then, (15344 - 728) = 87 × x x = $\frac{14616}{87}$ = 168

33.

Which of the following numbers are completely divisible by 7 ?
I. 195195
II. 181181
III. 120120
IV. 891891

(A) Only I and II
(B) Only II and III
(C) Only I and IV
(D) Only II and IV

34.

Recently, a small village, in Tamilnadu where only male shepherd reside with four sheep each, was devastated by Tsunami waves. Therefore 8 persons and 47 sheep were found to be dead and the person who luckily survived, left the village with one sheep each since 21 sheep were too injured to move so have left on their on luck, in the village. The number of sheep which were earlier in the village was :

(A) 84 sheep
(B) 120 sheep
(C) 80 sheep
(D) 90 sheep

35.

If the arithmetic mean of 3a and 4b is greater than 50, and a is twice b, then the smallest possible integer value of a is:

(A) 20
(B) 21
(C) 18
(D) 19

Solution: $\begin{aligned} According to the question, \\ \frac{3 a + 4 b}{2} > 50 \\ 3 a + 4 b > 100 \\ a = 2 b (Given) \\ 6 b + 4 b > 100 \\ 10 b > 100 \\ b > 10 \\ If b = 10.1 \\ ∴ a = 2 \times 10.1 \\ a = 20.2 \\ ∴ a = 21 (Approx) \end{aligned}$

36.

The unit digit in the product 7 ÃÂÃÂÃÂÃÂÃÂÃÂ 6 ÃÂÃÂÃÂÃÂÃÂÃÂ 3 = ?716365

(A) 1
(B) 2
(C) 3
(D) 4

37.

$\frac{768 \times 768 \times 768 + 232 \times 232 \times 232}{768 \times 768 - 768 \times 232 + 232 \times 232} = ?$

(A) 1000
(B) 536
(C) 500
(D) 268

Solution: Given expression, $= \frac{(a^{3} + b^{3})}{(a^{2} - a b + b^{2})}$ (where a = 768 and b = 232) $\begin{aligned} = (a + b) \\ = (768 + 232) \\ = 1000 \end{aligned}$

38.

The sum of all three digit numbers, each of which on divide by 5 leaves remainder 3, is -

(A) 180
(B) 1550
(C) 6995
(D) 99090

Solution: $\begin{aligned} S e r i e s : \\ 103 + 108 + . . . . . . . . + 998 \\ a = 103 \\ d = 5 \\ Last term = 998 \\ Number of term \\ = \frac{998 - 103}{5} + 1 \\ = \frac{895}{5} + 1 \\ = 180 \\ Sum of n terms \\ = \frac{n}{2} [2 a + (n - 1) d] \\ = \frac{180}{2} [2 \times 103 + (180 - 1) 5] \\ = 99090 \end{aligned}$

39.

It is being given that (2³² + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

(A) (216 + 1)
(B) (216 - 1)
(C) (7 x 223)
(D) (296 + 1)

40.

The digit in unit's place of the number (1570)² + (1571)² + (1572)² + (1573)² is :

(A) 4
(B) 1
(C) 2
(D) 3

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Practice MCQ Questions and Answer on Number System

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