DS

[ukr.net]

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.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient

ANS is C, why???

[gabriel]

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

[cjiang16]

gabriel explanation is great!

[gmattakers]

thanks, gabriel

[its time]

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

[sashi.dr]

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