Practice MCQ Questions and Answer on Number System
11.
The sum of three numbers is 252. If the first number is thrice the second and third number is two-third of the first, then the second number is :
(A) 41
(B) 21
(C) 42
(D) 84
Solution:
Let the number is a, b, c a = 3b $$\frac{a}{b}$$ = $$\frac{3}{1}$$ c = $$\frac{2}{3}$$a $$\frac{c}{a}$$ = $$\frac{2}{3}$$ c a b 2 3 3 1 c : a : b = 2 : 3 : 1 So, (2 + 3 + 1) = 252 units 6 units → 252 1 unit → 42 3 units → 42 × 3 So, second number is = 42
12.
There are 576 boys and 448 girls in a school that are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed?
(A) 24
(B) 32
(C) 16
(D) 20
Solution:
576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 448 = 2 × 2 × 2 × 2 × 2 × 2 × 7 HCF = 2 × 2 × 2 × 2 × 2 × 2 = 64 Hence, number of classes required $$\frac{{576}}{{64}} + \frac{{448}}{{64}}$$ = 9 + 7 = 16 Shortcut: The numbers (3 × 3) and 7 are not a part of HCF. And sum of multiplication of these number is the required answer.
13.
If (px3 - 8x2 - qx + 1), the expression is completely divisible by the expression (3x2 - 4x + 1). Then what will be the value of p and q respectively?
Which one of the following numbers is divisible by 15 ?
(A) 17325
(B) 23755
(C) 29515
(D) 30560
Solution:
Consider the number is 17325 Its unit digit is 5, so it is divisible by 5 Sum of its digits = (5 + 2 + 3 + 7 + 1) = 18, which is divisible by 3 So, the given number is divisible by 3 And since 5 and 3 are co-primes, So the given number is divisible by (5 × 3), i.e., 15
15.
A number consists of two digits. If the number formed by interchange the digits is added to the original number, the resulting number (i.e., the sum) must be divisible by -
(A) 11
(B) 9
(C) 5
(D) 3
Solution:
Let the unit digit of the number be x And ten's place number be y Number = 10y + x Interchange digit's = 10x + y Adding result = 10y + x + 10x + y = 11x + 11y = 11(x + y) So number is divisible by 11
16.
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)
17.
If $$13 = \frac{{13w}}{{\left( {1 - w} \right)}}$$ ÃÂÃÂ , then (2w)2 = ?