Quantitative Aptitude - Numbers and Algebra
- Option : D
- Explanation : 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
- Option : D
- Explanation : 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?
19. Which of the following is true?
- Option : B
- Explanation :
(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
- Option : B
- Explanation : 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
