Exercise: Numbers

Questions for: Numbers

If the number 42573 * is exactly divisible by 72, then the minimum value of * is:
A:
4
B:
5
C:
6
D:
7
Answer: C

72 = 9 x8, where 9 and 8 are co-prime.

The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6.

Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.

Required value of * is 6.

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Which natural number is nearest to 8485, which is completely divisible by 75 ?
A:
8475
B:
8500
C:
8550
D:
8525
Answer: A 
On dividing, we get

 75) 8485 (113
     75
     ---
      98
      75
      ----
       235
       225
       ---
        10
       ---
 
 Required number = (8485 - 10) // Because 10 < (75 - 10)
                 = 8475.
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(800 ÷ 64) x (1296 ÷ 36) = ?
A:
420
B:
460
C:
500
D:
540
Answer: E
Given Exp. = 800 x 1296 = 450
64 36
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(51 + 52 + 53 + ... + 100) = ?
A:
2525
B:
2975
C:
3225
D:
3775
Answer: D

Sn = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100) - (1 + 2 + 3 + ... + 50)

    = 100 x (1 + 100) - 50 x (1 + 50)
2 2

    = (50 x 101) - (25 x 51)

    = (5050 - 1275)

    = 3775.

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When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?
A:
339
B:
349
C:
369
D:
Data inadequate
Answer: B

x = 13p + 11 and x = 17q + 9

13p + 11 = 17q + 9

17q - 13p = 2

q = 2 + 13p
17

The least value of p for which q = 2 + 13p is a whole number is p = 26
17

x = (13 x 26 + 11)

   = (338 + 11)

   = 349

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