Aptitude - Simplification
21.
11 x 2 x 3 + 12 x 3 x 4 + 13 x 4 x 5 + 14 x 5 x 6 = ?
Answer
Given expression = 4 x 5 x 6 + 5 x 6 + 2 x 6 + 61 x 2 x 3 x 4 x 5 x 6 = 120 + 30 + 12 + 61 x 2 x 3 x 4 x 5 x 6
= 1682 x 3 x 4 x 5 x 6 = 730
Answer :
Option BExplanation :
Given expression = 4 x 5 x 6 + 5 x 6 + 2 x 6 + 61 x 2 x 3 x 4 x 5 x 6 = 120 + 30 + 12 + 61 x 2 x 3 x 4 x 5 x 6
= 1682 x 3 x 4 x 5 x 6 = 730
22.
a3 = b4 = c7, then a + b + cc = ?
Answer
Let a3 = b4 = c7 = k. Then, a = 3k, b = 4k, c = 7k
∴ a + b + cc = 3k + 4k + 7k7k = 14k7k = 2
Answer :
Option CExplanation :
Let a3 = b4 = c7 = k. Then, a = 3k, b = 4k, c = 7k
∴ a + b + cc = 3k + 4k + 7k7k = 14k7k = 2
23.
2.75 + 3.78 = ?
Answer
2.75 + 3.78 = −2 + 0.75 − 3 + 0.78 = − 5 + 1.53 = − 4 + 0.53 = 4.53
Answer :
Option CExplanation :
2.75 + 3.78 = −2 + 0.75 − 3 + 0.78 = − 5 + 1.53 = − 4 + 0.53 = 4.53
24.
The number whose square is equal to the difference of the squares of 75.15 and 60.12 is
Answer
x2 = (75.15)2 − (60.12)2 = (75.15 + 60.12)(75.15 − 60.12)
⇒ x2 = 135.27 x 15.03 = 9 x 15.03 x 15.03
⇒ x = √9 x 15.03 x 15.03 = (3 x 15.03) = 45.09.
Answer :
Option AExplanation :
x2 = (75.15)2 − (60.12)2 = (75.15 + 60.12)(75.15 − 60.12)
⇒ x2 = 135.27 x 15.03 = 9 x 15.03 x 15.03
⇒ x = √9 x 15.03 x 15.03 = (3 x 15.03) = 45.09.
25.
1 litre of water weighs 1 kg. How many cubic millimetres of water will weigh 0.1 gm ?
Answer
1000 gm is the weight of 1000 cu. cm of water.
1 gm is the weight of 1 cu. cm = 1000 cu. mm
0.1 gm is the weight of (1000 x 0.1) cu. mm = 100 cu. mm.
Answer :
Option AExplanation :
1000 gm is the weight of 1000 cu. cm of water.
1 gm is the weight of 1 cu. cm = 1000 cu. mm
0.1 gm is the weight of (1000 x 0.1) cu. mm = 100 cu. mm.
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