Question

28. A number when divided by 357 gives a
remainder 37. By dividing the same
number by 17, the remainder would be:
(a) 3
(b) 4
(c) 2
(d) None of these​

Answer 1

Answer:

d)

Explanation:

as we can conclude from the first division i.e when the no. is divided by 357 we get the remainder as 37.Therefore,the no. we are dividing must contain 0 in its unit place to have the remainder containg same unit digit as that of the number's.

So the options didn't have 7 in it.And it was easy to conclude.

Answer 2

Answer:

The remainder is 3 (option a) when the number is divided by 17.

Explanation:

Let the number be X.

Dividing X by 357 gives a remainder 37.

357 is a multiple of 17 (17 × 21 = 357).

So, dividing X by 17 can also reach a point where the remainder is 37. And this 37 is again dividable by 17, and it will stop when the remainder is 3 (37-34).

In other words,

X = 357n + 37 where n is the quotient of X/357

X = 17 × 21n + 37

X = 17 × 21n + (17×2 + 3)

X = 17(21n+2) + 3

X = 17m + 3 where m = 21n+2

This proves that the remainder is 3 when X is divided by 17.

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