SSC Aptitude-Analytical Contributed by Keerthy updated on Sep 2019

SSC Combined Graduate Level Examination. Staff Selection Commission SSC CGL examinations sample placement papers questions with detailed explanations.  SSC previous years solved question papers SSC previous years solved question papers of aptitude,anlytical,reasoning verbal ability and others

SSC CGL Model Test Paper - Aptitude, analytical reasoning

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

11.  Square root of 0.081/0.0064 * 0.484/6.25 * 2.5/12.1 is  
(A)  0.45    (Ans)
(B)  0.75
(C)  0.95
(D)  0.99

Explanation :   ?0.081/0.0064 * 0.484/6.25 * 2.5/12.1
= ?810/64 * 484/6250 * 25/121
= ?81/64 * 484/625 * 25/121
= 9/8 * 22/25 * 5/11 = 0.45

12.  If xy = yx, then (x/y)x/y is equal to 
(A)  xx/y
(B)  xx/y -1    (Ans)
(C)  xy/x
(D)  xy/x -1

Explanation :    xy = yx
or     xy/x = y
?   x/y = x/xy/x = x1-y/x  = xx-y/x
?   (x/y)x/y = (xx-y/x)x/y = xx-y/y = xx/y-1

13.  Which is the greatest out of the following ?
(i)  3?1.728
(ii) ?3 - 1 / ?3 + 1
(iii) (1/2)-2
(iv) 17/8

(A)  (i)
(B)  (ii)
(C)  (iii)    (Ans)
(D)  (iv)

Explanation :  (i)   3?1.728 = 1.2
(ii) ?3 - 1 / ?3 + 1  =  (?3 - 1)(?3 + 1)
(?3 + 1)(?3 - 1)

=  3 + 1 - 2 ?3
3 - 1

=  2 - ?3  = 0.26

(iii)   (1/2)-2   =  (2/1)2 = 4
(iv)   17/8  =  2.125
?   (iii) is the greatest.

14.  If (a + b = 3), then what is the value of  (a3 + b3 + 9ab) ?
(A)  18
(B)  27    (Ans)
(C)  81
(D)  Cannot be determined due to insufficient data

Explanation :  Given,a + b = 3
?   a3  + b3  = (a + b) (a2 + b2 - ab)
= (a + b) [(a + b)2 - 3ab]
= 3 [9 - 3ab]
= 27 - 9ab
?   a3  + b3 + 9ab  =  27 - 9ab + 9ab = 27

15.  A vertical stick 10 cm long casts a shadow 8 cm long.  At the same time a tower casts a shadow 30 m long. What is the height of the tower ?
(A)  37.5 m     (Ans)
(B)  36 m
(C)  32.5 m
(D)  32 m

Explanation :  Let the height of the tower = h metre and angle of elevation of sun = ?

tan ? =  10/8  = h/30
?  h = 10 * 30/8  = 75/2  = 37.5 metres