How to find the divisor in this question?

2018-02-20 7:55 pm

Two numbers when divided by a certain divisor give remainders 35 and 20 respectively and when their sum is divided by the same divisor the remainder is 15. Find the divisor.

I tried solving this by assuming the two numbers as "a" and "b". I took the divisor as "d" and tried to find a general answers. It just got more complicated.

Can someone help me. Thanks in advance

回答 (1)

胡雪8°

2018-02-20 8:47 pm

✔ 最佳答案

Let a and b be the two numbers respectively, and d be the divisor.

When a is divided by d, the remainder is 35 :
(a - 35) is a multiple of d. …… [1]
and d > 35

When b is divided by d, the remainder is 20 :
(b - 20) is a multiple of d. …… [2]

[1] + [2] :
(a + b - 55) is a multiple of d. …… [3]

When (a + b) is divided by d, the remainder is 15 :
(a + b - 15) is a multiple of d. …… [4]

[4] - [3] :
40 is a multiple of d.
But d > 35
Hence, d = 40

The divisor = 40

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