DS

ukr.net wrote:What is the remainder when the positive integer x is divided by 8?

(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.

from the first statement we have , x = 12a+5 , but with this we cant say what the remainder could be when divided by 8 .. so insufficient

from the 2nd statement we have, x = 18b+11, again we cannot tell what the remainder will be when divided by 8 .. so insufficient

Now, from here onwards it gets a little tricky...

The first number that satisfies both the conditions (the conditions given in statement 1 and 2) is 29 and subsequent numbers will be of the form 36*m+29 (36*m is a number that will be the multiple of the LCM of 12 and 18 ). To get subsequent numbers just substitute values of m as 1,2,3, ....

So, the numbers satisfying the 2 conditions are 29, 65 (36*1+29), 101 (36*2+29), 137(36*3+29) and so on ..

Now if we check the numbers for remainders after division with 8, we get the remainders as 5,1,5,1 .. that is the remainder could be 5 or 1 .. so even after combining the 2 statements we do not get a definite answer .. so the answer is E

gabriel explanation is great!

thanks, gabriel

that takes care of a lot many problems of intigers...thanks man!!brilliant....

any easier method to determine the first no. as 29. i got it by trial and error.