Aptitude - Simplification

16.

99917 + 99927 + 99937 + 99947 + 99957 + 99967 =

Answer

Answer :

Option C

Explanation :


Given expression = (999 x 6) + 17 + 27 + 37 + 47 + 57 + 67
= 5994 + (1 + 2 + 3 + 4 + 5 + 6)7 = 5994 + 217 = 5994 + 3 = 5997
17.

If x + y + z = 0, then (x2 + xy + x2) =

Answer

Answer :

Option D

Explanation :


x + y + z = 0 (x + y) = −z
(x + y)2 = z2 x2 + y2 + 2xy = z2
x2 + y2 + xy = z2xy = z2x(− xz) [ x + y + z = 0 (−xz) = −y]
x2 + y2 + xy = z2 + zx + z2
18.

38 x 38 x 38 + 34 x 34 x 34 + 28 x 28 x 28 − 38 x 34 x 84 38 x 38 + 34 x 34 + 28 x 28 − 38 x 34 − 34 x 28 − 38 x 28 =

Answer

Answer :

Option D

Explanation :


Given expression = a3 + b3 + c3 − 3abc a2 + b2 + c2 − (ab + bc + ca) = (a + b + c) where a = 38, b = 34, c = 28
= (38 + 34 + 28) = 100
19.

If ab = 1, then (a3b3 − 3ab) =

Answer

Answer :

Option C

Explanation :


ab = 1 (ab)3 = 1 a3b3 −3ab(ab) = 1
a3b3 −3ab x 1 = 1
a3b3 − 3ab = 1
20.

If PQ = 7, then P + QP − Q = ?

Answer

Answer :

Option D

Explanation :


P + QP − Q = P/Q + 1P/Q − 1 = 7 + 17 − 1 = 86 = 43
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