## Aptitude SimplificationPage 3

17.

 What is the value of (P + Q)/(P - Q), if P/Q = 7. (a)4/3 (b)13/17 (c)7/2 (d)1/17
Answer is: ALet, P + Q/P - Q
= [Q(P/Q) + 1]/[Q(P/Q) - 1]
= [(P/Q) + 1]/[(P/Q) - 1]
= [7 + 1]/[7 - 1]
= 8/6
= 4/3

18.

 If X/Y = 4/5 , then the value of [4/7 + (2Y - X)Ã·(2Y + X)] is ? (a)1 (b)10 (c)2 (d)20
Answer is: Aâ‡’ [4/7 â€“ (2Y - X)Ã·(2Y + X)] = [4/7 â€“ (2 - X/Y)Ã·(2 + X/Y)]
â‡’ 4/7 + (2 - 4/5)Ã·(2 + 4/5) = 4/7 + (6/5)Ã·(14/5)
â‡’4/7 + ( 6/5 x 5/14 )
â‡’ 4/7 + 3/7 = 7/7 = 1

19.

 If a/b = 4/3 , then the value of (6a + 4b)Ã·(6a - 5b) is ? (a)2 (b)4 (c)6 (d)8
Answer is: Bâ‡’ a/b = 4/3
â‡’ (6a + 4b)Ã·(6a - 5b) = [6(a/b)+ 4]Ã·[6 (a/b) - 5]
â‡’(6 x 4/3 + 4)Ã·(6 x 4/3 - 5) = (8 + 4)Ã·(8 - 5 ) = 12/3 = 4

20.

 If a/3 = b/4 = c/7 , then the value of (a + b + c)/c is: (a)2 (b)4 (c)6 (d)8
Answer is: ALet, a/3 = b/4 = c/7 = k (say).
Then, a = 3k, b = 4k and c = 7k.
âˆ´ (a + b + c )/c = (3k + 4k + 7k )/7k = 14k/7k = 2

21.

 The value of 1/(2 + 1/(2 + 1/(2 - 1/2))) is: (a)7 / 19 (b)8 / 19 (c)9 / 19 (d)11 / 19
Answer is: BGiven exp. = 1/(2+1/(2+1/(3/2))) = 1/(2+1/(2 + 2/3))
⇒ 1/(2 + 1/(8/3)) = 1/(2 + 3/8)
⇒ 1/(( 19/8 )) = 8/19

22.

 Simplified : 3/4(1 + 1/3) (1 + 2/3) (1 â€“ 2/5) (1 + 6/7) (1 â€“ 12/13) = ? (a)1/7 (b)1/8 (c)1/9 (d)1/10
Answer is: A⇒ 3/4(1 + 1/3) (1 + 2/3) (1 â€“ 2/5) (1 + 6/7) (1 â€“ 12/13) = ( 3/4 x 4/3 x 5/3 x 3/5 x 13/7 x 1/13 ) = 1/7

23.

 Simplified the product (1 â€“ 1/2) (1 â€“ 1/3) (1 â€“ 1/4)â€¦â€¦â€¦.(1 â€“ 1/n) gives: (a)n (b)n + 1 (c)n - 1 (d)1/n
Answer is: DLet, (1 â€“ 1/2) (1 â€“ 1/3) (1 â€“ 1/4)â€¦â€¦â€¦.(1 â€“ 1/n)
⇒ 1/2 x 2/3 x 3/4 x 4/5 xâ€¦â€¦..x (n â€“ 1)/n = 1/n

24.

 Find the sum : 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/43 + 1/56 + 1/72 + 1/90 + 1/110 +1/132 (a)9/10 (b)10/11 (c)11/12 (d)12/13
Answer is: CGiven = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/43 + 1/56 + 1/72 + 1/90 + 1/110 +1/132
⇒ (1 â€“ 1/2) + (1/2 â€“ 1/3) + (1/3 â€“ 1/4) + â€¦â€¦â€¦+ (1/11 â€“ 1/12)
⇒ (1 â€“ 1/12) = 11/12