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Arithmetic Aptitude | Numbers V - with Explanation


1. 
Which one of the following is a prime number ?
A.161
B.221
C.373
D.437
E.None of these
Answer: Option C
Explanation:
437 > 22
All prime numbers less than 22 are : 2, 3, 5, 7, 11, 13, 17, 19.
161 is divisible by 7, and 221 is divisible by 13.
373 is not divisible by any of the above prime numbers.
373 is prime.

2. 
The smallest 6 digit number exactly divisible by 111 is:
A.111111
B.110011
C.100011
D.110101
E.None of these
Answer: Option C
Explanation:
The smallest 6-digit number 100000.

 111) 100000 (900
      999
      -----
        100
        ---

 Required number = 100000 + (111 - 100)
                 = 100011.       

3. 
The largest 5 digit number exactly divisible by 91 is:
A.99921
B.99918
C.99981
D.99971
E.None of these
Answer: Option B
Explanation:
Largest 5-digit number = 99999

 91) 99999 (1098
     91
     ---
     899
     819
     ----
      809
      728
      ---
       81
      ---
 
 Required number = (99999 - 81)
                 = 99918.      

4. 
768 x 768 x 768 + 232 x 232 x 232= ?
768 x 768 - 768 x 232 + 232 x 232
A.1000
B.536
C.500
D.268
E.None of these
Answer: Option A
Explanation:
Given Exp. =(a3 + b3)= (a + b) = (768 + 232) = 1000
(a2 - ab + b2)


5. 
The smallest 5 digit number exactly divisible by 41 is:
A.1004
B.10004
C.10045
D.10025
E.None of these
Answer: Option B
Explanation:
The smallest 5-digit number = 10000.

 41) 10000 (243
     82
     ---
     180
     164
     ----
      160
      123
      ---
       37
      --- 

 Required number = 10000 + (41 - 37)
                 = 10004.      

6. 
How many terms are there in the G.P. 3, 6, 12, 24, ... , 384 ?
A.8
B.9
C.10
D.11
E.7
Answer: Option A
Explanation:
Here a = 3 and r =6= 2. Let the number of terms be n.
3
Then, tn = 384     arn-1 = 384
 3 x 2n - 1 = 384
 2n-1 = 128 = 27
 n - 1 = 7
 n = 8
 Number of terms = 8.

7. 
If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?
A.4x + 6y
B.x + y + 4
C.9x + 4y
D.4x - 9y
Answer: Option D
Explanation:
By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.
 (4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;
(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;
(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;
(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11



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