Question 108

When 3738, 5659 and 9501 are divided by the greatest possible number x, the remainder in each case is y. What is the sum of x and y?

Solution

From the given numbers 3738, 5659, 9501

5659 - 3738 = 1921 , 9501 - 5659 = 3842 , 9501 - 3738 = 5763

then HCF of 1921,3842 , 5763 is 1921

so $$x = 1921 $$

when we will divide 3738 with 1921 reminder will be 1817 which is same for other two number also

so $$y = 1817 $$

$$x+y = 1921 + 1817 $$ = 3738 Ans

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