Quantitative Aptitude MCQ - Numbers and Algebra

21 If x+y+z=0,then x²/yx + y²/zx + z²/xy equal

x²/yx + y²/zx + z²/xy
...(since, x+y+z=0 x³+y³+z³=3xyz)
(x³+y³+z³) / xyz = 3xyz / xyz = 3.

22 Average age of a committee of seven trustees is the same as it was five years ago, a younger man having been substituted for one of them. How much younger was he then trustee whose place he took?

Increase after 5 years should have been 7 x 5 = 35 years. But since average remains same, diference in their age is 35 years.

23 What is the least number which must be subtracted from 1936 so that the remainder when divided by 9, 10, 15 will leave in each case the same remainder 7?

L.C.M. of 9, 10 and 15 = 90 ∴ 1936 = 90 x 21 + 46 (Remainder). But a part of this remainder is 7. 39 should be subtracted from 1936.

24 What is the maximum sum of the series 60, 58, 56, 54, 52, ?

Since d = -2, maximum sum of the series will be sum of all the positive terms.
Least positive term of the series is 2 or 0 (both giving equal sum)
Let, 2 be the n^th term
2 = 60 + (n 1) - 2
=> n = 30
Required sum = 30/2 (60 + 2) = 930

25 What is the least number which on being divided by 12, 21 and 35 will leave in each case the same remainder 6?

L.C.M. of 12, 21 and 35 = 420
∴ Number required = 420 + 6 = 426

Quantitative Aptitude MCQ - Numbers and Algebra

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