Practice MCQ Questions and Answer on Number System
21.
76n - 66n, where n is an integer > 0, is divisible by :
(A) 13
(B) 127
(C) 559
(D) All the above
Solution:
When n is even, (xn - an) is divisible by both (x - a) as well as (x + a). Now, (76n - 66n) = [(73)2n - (63)2n] = [(343)2n - (216)2n] ∴ (76n - 66n) is divisible by both (7 - 6) and (7 + 6) (76n - 66n) is divisible by 13 And, [(343)2n - (216)2n] is divisible by both (343 - 216) and (343 + 216) ⇒ (76n - 66n) is divisible by both 127 and 559
22.
A number when divided by three consecutive numbers 9, 11, 13 leaves the remainders 8, 9 and 8 respectively. If the order of divisors is reversed, the remainders will be :
(A) 10, 8, 9
(B) 10, 1, 6
(C) 8, 9, 8
(D) 9, 8, 8
Solution:
z = 13 × 1 + 8 = 21 y = 11 × z + 9 = 11 × 21 + 9 = 240 x = 9 × y + 8 = 9 × 240 + 8 = 2168 Now, when order of divisor is reversed, we have : ∴ Respective remainders are 10, 1 and 6
23.
If the sum of two numbers is 14 and their difference is 10, find the product of these two numbers.
(A) 18
(B) 20
(C) 24
(D) 22
Solution:
Let the two numbers be are a and b ∴ a + b = 14.....(i) a - b = 10.....(ii) By adding equation (i) and (ii) we get 2a = 24 ∴ a = 12 and b = 2 ∴ Product of these two numbers= 12 × 2 = 24
24.
The numbers 2, 4, 6, 8 ..... 98, 100 are multiplied together. The number of zeros at the end of the product must be :
(A) 10
(B) 11
(C) 12
(D) 13
Solution:
N = 2 × 4 × 6 × 8 × ..... × 98 × 100 = 250 (1 × 2 × 3 × ..... × 49 × 50) = 250 × 50! Clearly, the highest power of 2 in N is much higher than that of 5 ∴ Number of zeros in N = Highest power of 5 in N = = 10 + 2 = 12
25.
If ÃÂÃÂ , then the value of ÃÂÃÂ is :
(A) 0.12
(B) 0.012
(C) 0.0012
(D) 1.2
Solution:
Given :
26.
If a (0.4)2 , b = 0.04 and c = , then the correct relationship among the three is :
(A) b > a > c
(B) a > b > c
(C) a > c > d
(D) c > a > b
Solution:
a = (0.4)2 = 0.16 b = 0.04 c = 0.4 c > a > b
27.
The number 89715938* is divisible by 4. The unknown non-zero digit marked as * will be :
(A) 2
(B) 3
(C) 4
(D) 6
Solution:
Let the missing digit be x. Then, (80 + x) must be divisible by 4. Hence, x = 4
28.
What is the least value of x such that 517x324 is divisible by 12?
(A) 3
(B) 1
(C) 0
(D) 2
Solution:
Divisibility rule of 3 : The sum of all digit should be divide by 3
29.
ÃÂÃÂ ÃÂÃÂ ÃÂÃÂ is equal to :
(A) 2
(B) 2.5
(C) 3
(D) 3.5
Solution:
30.
The largest natural number, which exactly divides the product of any four consecutive natural numbers, is :
(A) 6
(B) 12
(C) 24
(D) 120
Solution:
Let P = n (n + 1) (n + 2) (n + 3)Then, n = 1 gives P = (1 × 2 × 3 × 4) = 24 Hence, the required number is 24