Tuesday, 19 June 2012

Quantitative Aptitude 102

Numbers1.  Which one of the following is not a prime number?
A. 31B. 61
C. 71D. 91
Answer: Option D
Explanation:
91 is divisible by 7. So, it is not a prime number.

2.  (112 x 54) = ?
A. 67000B. 70000
C. 76500D. 77200
Answer: Option B
Explanation:

(112 x 54) = 112 x 10 4 = 112 x 104 = 1120000 = 70000
2 24 16

3.  It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
A. (216 + 1)B. (216 - 1)
C. (7 x 223)D. (296 + 1)
Answer: Option D
Explanation:

Let 232 = x. Then, (232 + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.

4.  What least number must be added to 1056, so that the sum is completely divisible by 23 ?
A. 2B. 3
C. 18D. 21
E. None of these
Answer: Option A
Explanation:

 23) 1056 (45
      92
      ---
      136
      115
      ---
       21
      ---
     
 Required number = (23 - 21)    
                 = 2.   

5.  1397 x 1397 = ?
A. 1951609B. 1981709
C. 18362619D. 2031719
E. None of these
Answer: Option A
Explanation:

1397 x 1397 = (1397)2

= (1400 - 3)2

= (1400)2 + (3)2 - (2 x 1400 x 3)

= 1960000 + 9 - 8400

= 1960009 - 8400

= 1951609.

6.  How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
A. 4B. 5
C. 6D. 7
Answer: Option A
Explanation:

132 = 4 x 3 x 11
So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.
264 11,3,4 (/)
396 11,3,4 (/)
462 11,3 (X)
792 11,3,4 (/)
968 11,4 (X)
2178 11,3 (X)
5184 3,4 (X)
6336 11,3,4 (/)
Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.

7.  (935421 x 625) = ?
A. 575648125B. 584638125
C. 584649125D. 585628125
Answer: Option B
Explanation:


935421 x 625 = 935421 x 54 = 935421 x 10 4
2


= 935421 x 104 = 9354210000
24 16

= 584638125

8.  The largest 4 digit number exactly divisible by 88 is:
A. 9944B. 9768
C. 9988D. 8888
E. None of these
Answer: Option A
Explanation:

Largest 4-digit number = 9999

 88) 9999 (113
     88
     ----
     1199
      88
     ----
      319
      264
      ---
       55
      ---
       
 Required number = (9999 - 55)
                 = 9944.        


9.  Which of the following is a prime number ?
A. 33B. 81
C. 93D. 97
Answer: Option D
Explanation:
Clearly, 97 is a prime number.


10 What is the unit digit in {(6374)1793 x (625)317 x (341491)}?
A. B. 2
C. 3D. 5
Answer: Option A
Explanation:

Unit digit in (6374)1793 = Unit digit in (4)1793
    = Unit digit in [(42)896 x 4]
    = Unit digit in (6 x 4) = 4
Unit digit in (625)317 = Unit digit in (5)317 = 5
Unit digit in (341)491 = Unit digit in (1)491 = 1
Required digit = Unit digit in (4 x 5 x 1) = 0.

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