Practice MCQ Questions and Answer on Number System
61.
The greatest whole number, by which the expression n4 + 6n3 + 11n2 + 6n + 24 is divisible for every natural number n , is -
(A) 6
(B) 24
(C) 12
(D) 48
Solution:
62.
One-third of a tower is painted black, th of the remaining part is painted red and the rest is painted white. If the white part measures 60 ft.,the total height of the tower is-
(A) 100 ft.
(B) 154 ft.
(C) 165 ft.
(D) 110 ft.
Solution:
Let the tower height will be x ft. ∴ Black part will be = Remaining part = ∴ Red part will be = White part will be = i.e. = 60 x = 165 ft.
63.
The smallest five digit number which is divisible by 12, 18 and 21 is:
(A) 10080
(B) 30256
(C) 10224
(D) 50321
Solution:
We know, smallest five digit number is = 10000 LCM of 12, 18, 21 = 252 Difference = 252 - 172 = 80 Then number is = 10000 + 80 = 10080
64.
If n is an integer, how many values of n will give an integral value of ÃÂÃÂ ?
(A) 2
(B) 3
(C) 4
(D) None of these
Solution: For to be an integer, we may have n = 1 or n = 2 or n = 3 or n = 6 Hence, 4 value of n will give the desired result.
65.
If a and b are two numbers such that ab = 0, then -
(A) a = 0 and b = 0
(B) a = 0 or b = 0 or both
(C) a = 0 and b 0
(D) b = 0 and a 0
Solution:
ab = 0 ⇒ a = 0 or b = 0 or both are zero
66.
A heap of pebbles when made up into group of 32, 40, 72, leaves the remainder 10, 18 and 50 respectively. Find least number of pebbles in the heaps.
(A) 1440
(B) 1420
(C) 1418
(D) 1422
Solution:
In this type of problem we find the difference of divisors and their remainders. Here difference, 32 - 10 = 22 40 - 18 = 22 72 - 50 = 22 Here, in each case difference is same i.e. 22 Then required number of pebbles is given by [(LCM of 32, 40, 72) -22] 32 = 2 × 2 × 2 × 2 × 2 40 = 2 × 2 × 2 × 5 72 = 2 × 2 × 2 × 3 × 3 Hence, LCM = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 = 1440 Thus, Required number of pebbles, = 1440 - 22 = 1418
67.
Two positive whole numbers are such that the sum of the first and twice the second number is 8 and their difference is 2. The numbers are:
(A) 7, 5
(B) 3, 5
(C) 6, 4
(D) 4, 2
Solution:
In such type of question always go through option to save your valuable time. By option D: 4, 2 4 + 2 × 2 = 8 4 - 2 = 2 (Satisfied)
68.
If n is an integer, how many values of n will give an integral value of ÃÂÃÂ ?
(A) 2
(B) 3
(C) 4
(D) None of these
Solution: For to be an integer, we may have n = 1 or n = 2 or n = 3 or n = 6 Hence, 4 value of n will give the desired result.
69.
If a + b + c = 0, (a + b) (b + c) (c + a) equals
(A) ab (a + b)
(B) (a + b + c)2
(C) - abc
(D) a2 + b2 + c2
Solution:
a + b + c = 0⇒ (a + b) = - c (b + c) = - a and (c + a) = - b ⇒ (a + b) (b + c) (c + a) = (- c) × (- a) × (- b) = - (abc)
70.
Three-fifth of a number is equal to 70% of another number. What is the ratio between the first number and second number ?