Latest Book Aptitude Question SOLUTION: A boy divided the numbers 7654, 8506 and 9997 by a certain largest number and he gets same remainder in each case. What is the common remainder?

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(#M40021149) BOOK question Keep an EYE

A boy divided the numbers 7654, 8506 and 9997 by a certain largest number and he gets same remainder in each case. What is the common remainder?

Asked In Book Abhishek (10 years ago)

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NRIIT  (8 years ago)

Ans: 199

If the remainder is same in each case and remainder is not given, HCF of the differences of the numbers is the required largest number
9997 - 7654 = 2343
9997 - 8506 = 1491
8506 - 7654 = 852
Hence, the greatest number which divides 7654, 8506 and 9997 and leaves same remainder

= HCF of 2343, 1491, 852

= 213
Now we need to find out the common remainder.
Take any of the given numbers from 7654, 8506 and 9997, say 7654

7654 ÷ 213 = 35, remainder = 199

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