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ANALYTICAL APTITUDE QUESTION - HARD


1.  If a = 5 + 2 √6, the value of √a - 1/√a is —
 
(A)  2 √2    (Ans)
(B)  2 √3
(C)  3 - √2
(D)  1 + √5

Explanation :  
a = 5 + 2 √6
         = (√3)2 + 2 (√3) * (√2) + (√2)2
         = (√3 + √2)2
∴ √a  = √3 + √2
∴ √a - 1/√a   = (√3 + √2) -  (1/√3 + √2)
 = (√3 + √2)2 - 1 / (√3 + √2) =  5 + 2 √6 - 1  / √3 + √2
 =  4 + 2 √6  / √3 + √2  = 2 √2 (√2 + √3) / √3 + √2
= 2 √2



2.  Simplify —

√[(12.1)2 - (8.1)2 ÷ [(0.25)2 + (0.25) (19.95)]

(A)  1
(B)  2
(C)  3
(D)  4    (Ans)

Explanation :  
√[(12.1)2 - (8.1)2 ÷ [(0.25)2 + (0.25) (19.95)]
= √[(12.1 + 8.1) (12.1 - 8.1)] ÷ [0.25 (0.25 + 19.95)]
= √(20.2 * 4) ÷ (0.25 * 20.2)
= √20.2 *  4 / 0.25 * 20.2  = √16 = 4




3.   Simplify —

(2.3)3 - 0.027 / (2.3)2 + 0.69 + 0.09

(A)  0
(B)  1.6
(C)  2   (Ans)
(D)  3.4




4.  On simplification of —

1/30  +  1/42  +  1/56  +  1/72  +  1/90  +  1/100  we get —

(A)  2/27
(B)  1/9
(C)  5/27
(D)  6/55   (Ans)




5.  If 0 < a < 1, then the value of a + 1/a is —

(A)  Greater than 2   (Ans)
(B)  Less than 2
(C)  Greater than 4
(D)  Less than 4

Explanation : 
 a + 1/a - 2  = (√a - 1/√a)2 = positive
∴  a + 1/a > 2


6.  The simplification of
2.002 + 7.9 {2.8 - 6.3 (3.6 - 1.5) + 15.6} yields —

(A)  2.002
(B)  4.2845
(C)  40.843
(D)  42.845   (Ans)




7.  The arrangement of rational numbers -7/10, 5/-8, 2/-3 in ascending order is  —

(A)  -7/10, 5/-8, 2/-3
(B)  -7/10, 2/-3, 5/-8     (Ans)
(C)  2/-3, 5/-8, -7/10
(D)  5/-8, -7/10, 2/-3

Explanation :  
-7/10 = -0.7
-5/8 = - 0.625
and 2/-3 = - 0.667
On writing these numbers in ascending order, we get
 -7/10, 2/-3, and -5/8




8.  Given that log10 2 = 0.3010, then log2 10 is equal to —

(A)  0.3010
(B)  0.6990
(C)  1000/301     (Ans)
(D)  699/301

Explanation :   log2 10 =  1/log10 2
= 1/0.3010 = 1000/301
 



     _          _
9
.    3.9  +  5.7 is equal to  —

     

      _
(A)  9.6

      _
(B)  8.6 

      _
(C)  7.6      (Ans)

      _
(D)  1.6

                            _       _  Explanation :    3.9 + 5.7 = - 3 + .9 - 5 + .7
                          _
 =  - 8 + 1.6 = 7.6





10.  If 1/6.198 = 0.16134, then the value of 1/0.0006198 is  —
(A)  16134
(B)  1613.4     (Ans)
(C)  0.16134
(D)  0.016134
Explanation :   1/6.198 = 0.16134
∴    1/0.0006198  = 1/6.198 * 10-4
= 1 * 104 / 6.198 = 1/6.198 * 10,000
= 0.16134 * 10,000
= 1613.4





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