Aptitude - Simplification
6.
1 − [1 − {1 − (1 − 1 − 1 )}] = ?
Answer
Given expression = 1 − [1 − {1 − (1 − 0)}] = 1 − [1 − {1 − 1}]
= 1 − [1 − 0] = 1 − 1 = 0
Answer :
Option AExplanation :
Given expression = 1 − [1 − {1 − (1 − 0)}] = 1 − [1 − {1 − 1}]
= 1 − [1 − 0] = 1 − 1 = 0
7.
53 + 31 − 23 = ?
Answer
Given expression =
53 + 3 13 = 53 + 9 = 512
Answer :
Option CExplanation :
Given expression =
53 + 3 13 = 53 + 9 = 512
8.
If (a − b) = 3 and (a2 + b2) = 29, then ab = ?
Answer
2ab = (a2 + b2) − (a − b)2 = 29 − (3)2 = 29 − 9 = 20
⇒ ab = 10
Answer :
Option DExplanation :
2ab = (a2 + b2) − (a − b)2 = 29 − (3)2 = 29 − 9 = 20
⇒ ab = 10
9.
5852 ÷ 28 x y − 1653 = 1064
Answer
5852 ÷ 28 x y − 1653 = 1064
Then, 5852 x 128 x y = 1653 + 1064 = 2717
⇒ 209y = 2717 ⇒ y = 2717209 = 13
Answer :
Option BExplanation :
5852 ÷ 28 x y − 1653 = 1064
Then, 5852 x 128 x y = 1653 + 1064 = 2717
⇒ 209y = 2717 ⇒ y = 2717209 = 13
10.
{(1998)2 − (1997)2 + (1996)2 − (1995)2 + (1994)2 − (1993)2} =
Answer
Given expression :
(1998 + 1997)(1998 − 1997) + (1996 + 1995)(1996 − 1995) + (1994 + 1993)(1994 − 1993)
= (3995 x 1) + (3991 x 1) + (3987 x 1) = (3995 + 3991 + 3987) = 11973
Answer :
Option DExplanation :
Given expression :
(1998 + 1997)(1998 − 1997) + (1996 + 1995)(1996 − 1995) + (1994 + 1993)(1994 − 1993)
= (3995 x 1) + (3991 x 1) + (3987 x 1) = (3995 + 3991 + 3987) = 11973
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