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Aptitude - Numbers

Exercise : Numbers - General Questions
71.
397 x 397 + 104 x 104 + 2 x 397 x 104 = ?
250001
251001
260101
261001
Answer: Option
Explanation:
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
72.
(35423 + 7164 + 41720) - (317 x 89) = ?
28213
84307
50694
56094
None of these
Answer: Option
Explanation:
  35423         317 x 89 = 317 x (90 -1 )
+  7164                  = (317 x 90 - 317)
+ 41720                  = (28530 - 317)
  -----                  = 28213
  84307
- 28213
  -----
  56094
  -----
73.
(xn - an) is completely divisible by (x - a), when
n is any natural number
n is an even natural number
n is and odd natural number
n is prime
Answer: Option
Explanation:

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

74.
Which one of the following numbers is completely divisible by 45?
181560
331145
202860
2033555
None of these
Answer: Option
Explanation:

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.

75.
Which of the following numbers will completely divide (325 + 326 + 327 + 328) ?
11
16
25
30
Answer: Option
Explanation:

(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.

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