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Hi;
Please see this case and please comment on its failure in the situation explained below:

A certain number when successfully divided by 8 and 11 leaves remainders of 3 and 7 respectively. What will be remainder when the number is divided by the product of 8 and 11, viz 88? (1) 3 (2) 21 (3) 59 (4) 68

Correct Answer - (3)

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Solution:

When a number is successfully divided by two divisors d1 and d2 and two remainders r1 and r2 are obtained, the remainder that will be obtained by the product of d1 and d2 is given by the relation

d1r2 + r1.

Where d1 and d2 are in ascending order respectively and r1 and r2 are their respective remainders when they divide the number.

In this case, the d1 = 8 and d2 = 11. And r1 = 3 and r2 = 7
Therefore, d1r2 + r1 = 8*7 + 3 = 59.

Case of failure:
Let the number in question be 147. the divisors be 8 and 11 leaving remainders 3 and 4 respectively. When the number is divided by 8 and 11 i.e. 88, the remainder is 59.

According to the theorem, the remainder is 8*4 +3=35.

Please expalin the anamoly.

Shaji

The error as we realized on the chat is that the word "Successfully" should be replaced with "Successively"

Is the formula d1*r2 + r1 is correct?

or is it getting failed this particular case.. Please let me know asap.

According to me answer can be 51..

I assumed the number as 51- which give remainder 3 wen divided by 8 and remaninder 7 when divided by 11..

but didnt find this option anywhere in the answer choices!!

So what is the solution for this problem??

Anusha,

The number is successively divided.

According to the question,a number is first divided by 8 which gives a remainder 3 and a
quotient which gives a remainder 7 when divided by 11.

To solve this question let us follow bottom to up approach

Steps:
1)x/8 -> remainder = 3,Quotient = y
2)y/11-> remainder = 7

Find out the minimum possible value for y that gives a remainder 7 when divided by 11
which is 11 + 7 = 18.

So x should be 18 * 8 + 3 which is 147

Now divide x which is 147 by 88(8*11) which gives a remainder 59 which is the required answer.