Aptitude - Simplification
16.
99917 + 99927 + 99937 + 99947 + 99957 + 99967 =
Answer
Given expression = (999 x 6) +
17 + 27 + 37 + 47 + 57 + 67 
= 5994 + (1 + 2 + 3 + 4 + 5 + 6)7 = 5994 + 217 = 5994 + 3 = 5997
Answer :
Option CExplanation :
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
x + y + z = 0 ⇒ (x + y) = −z
⇒ (x + y)2 = z2 ⇒ x2 + y2 + 2xy = z2
⇒ x2 + y2 + xy = z2 − xy = z2 − x(− x − z) [ x + y + z = 0 ⇒ (−x − z) = −y]
⇒ x2 + y2 + xy = z2 + zx + z2
Answer :
Option DExplanation :
x + y + z = 0 ⇒ (x + y) = −z
⇒ (x + y)2 = z2 ⇒ x2 + y2 + 2xy = z2
⇒ x2 + y2 + xy = z2 − xy = z2 − x(− x − z) [ x + y + z = 0 ⇒ (−x − z) = −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
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
Answer :
Option DExplanation :
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 a − b = 1, then (a3 − b3 − 3ab) =
Answer
a − b = 1 ⇒ (a − b)3 = 1 ⇒ a3 − b3 −3ab(a − b) = 1
⇒ a3 − b3 −3ab x 1 = 1
⇒ a3 − b3 − 3ab = 1
Answer :
Option CExplanation :
a − b = 1 ⇒ (a − b)3 = 1 ⇒ a3 − b3 −3ab(a − b) = 1
⇒ a3 − b3 −3ab x 1 = 1
⇒ a3 − b3 − 3ab = 1
20.
If PQ = 7, then P + QP − Q = ?
Answer
P + QP − Q = P/Q + 1P/Q − 1 = 7 + 17 − 1 = 86 = 43
Answer :
Option DExplanation :
P + QP − Q = P/Q + 1P/Q − 1 = 7 + 17 − 1 = 86 = 43
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