Exercise: Numbers

Questions for: Numbers

How many terms are there in the G.P. 3, 6, 12, 24, ... , 384 ?
A:
8
B:
9
C:
10
D:
11
Answer: A

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.

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The smallest 5 digit number exactly divisible by 41 is:
A:
1004
B:
10004
C:
10045
D:
10025
Answer: B 
The smallest 5-digit number = 10000.

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

 Required number = 10000 + (41 - 37)
                 = 10004.
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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
Answer: A
Given Exp. = (a3 + b3) = (a + b) = (768 + 232) = 1000
(a2 - ab + b2)
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The largest 5 digit number exactly divisible by 91 is:
A:
99921
B:
99918
C:
99981
D:
99971
Answer: B 
Largest 5-digit number = 99999

 91) 99999 (1098
     91
     ---
     899
     819
     ----
      809
      728
      ---
       81
      ---
 
 Required number = (99999 - 81)
                 = 99918.
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The smallest 6 digit number exactly divisible by 111 is:
A:
111111
B:
110011
C:
100011
D:
110101
Answer: C 
The smallest 6-digit number 100000.

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

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