Exercise: Numbers

Questions for: Numbers

Which of the following numbers will completely divide (325 + 326 + 327 + 328) ?
A:
11
B:
16
C:
25
D:
30
Answer: D

(325 + 326 + 327 + 328) = 325 x (1 + 3 + 32 + 33) = 325 x 40

     = 324 x 3 x 4 x 10

     = (324 x 4 x 30), which is divisible by30.

Which one of the following numbers is completely divisible by 45?
A:
181560
B:
331145
C:
202860
D:
2033555
Answer: C

45 = 5 x 9, where 5 and 9 are co-primes.

Unit digit must be 0 or 5 and sum of digits must be divisible by 9.

Among given numbers, such number is 202860.

(xn - an) is completely divisible by (x - a), when
A:
n is any natural number
B:
n is an even natural number
C:
n is and odd natural number
D:
n is prime
Answer: A

For every natural number n, (xn - an) is completely divisible by (x - a).

(35423 + 7164 + 41720) - (317 x 89) = ?
A:
28213
B:
84307
C:
50694
D:
56094
Answer: D
  35423         317 x 89 = 317 x (90 -1 )
+  7164                  = (317 x 90 - 317)
+ 41720                  = (28530 - 317)
  -----                  = 28213
  84307
- 28213
  -----
  56094
  -----
397 x 397 + 104 x 104 + 2 x 397 x 104 = ?
A:
250001
B:
251001
C:
260101
D:
261001
Answer: B
Given Exp. = (397)2 + (104)2 + 2 x 397 x 104
= (397 + 104)2
= (501)2 = (500 + 1)2
= (5002) + (1)2 + (2 x 500 x 1)
= 250000 + 1 + 1000
= 251001
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