Quantitative Aptitude MCQ - Numbers and Algebra

16 Sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is

x + (x + 36) + y = 100
⇒2x + y = 64
Therefore y must be even prime which is 2
2x + 2 = 64
⇒x = 31.
∴ Third prime number = x + 36 = 31+ 36 = 67

17 A school has 5 divisions in a class IX having 60, 50, 55, 62 and 58 students. Mean marks obtained in a History test were 56, 64, 72, 63 and 50 by each division respectively. What is overall average of the marks per students?

Average = (60x56+50x64+55x72+62x63+58x50)/ (60+50+55+60+58 ) = (3360+3200+3960+3906+2900)/285 = 60.8

18 What is the smallest number which when increased by 3 is divisible by 27, 35, 25 and 21?

L.C.M. of 27, 35, 25 and 21 = 4725

∴ Number = 4725-3 = 4722.

19 Which of the following is true?

(A) Four consecutive even numbers can be written as 2n, 2n + 2, 2n + 4 and 2n + 6,where n is any natural number.
Sum = 2n +(2n + 2) + (2n + 4) + (2n +6) = 8n + 12
= 4(2n + 3) not always divisible by 8.
Thus, (A) is not true.
(B) Four consecutive odd numbers can be written as 2n-1, 2n+ 1, 2n + 3, 2n + 5 where n is a natural number
Sum = (2n-1) + (2n + 1) + (2n + 3) + (2n + 5)
= 8n + 8 = 8(n + 1) divisible by 8
Thus, (B) is true
(C) In product of n consecutive natural numbers atleast one is divisible by n, atleast one by n - 1 ... till 1.
Thus product is atleast divisible by
n * (n - 1) * (n - 2) *1 = n!.
Thus, (C) is not true.
(D) Take four consecutive odd numbers as 7 x 9 x 11 x 13 which is not divisible by 15.
Thus, (D) is not true.

20 Sum of all odd numbers up to 100 is

Given numbers are 1, 3, 5.....99.
This is an A.P with a = 1, d = 2
Let it contain n terms
∴ 1 +(n-1)2 = 99
=> n = 50
Hence required sum = n/2 (first term +last term)
= 50/2(1 + 99) = 2500