A. x can not be divisble by 24

ex of x are 4,5,7,8, etc wid 4 remainder = 0
5 remainder=4
7 remainder=3 so not sufficient

so A and D are out left wid BCE

B. posible value of x 3,5,7,9 etc

wid 3 remainder = 0
5 remainder= 4
7 remainder = 3 hence not sufficient B is out
combining A and B we get possible values as 5 and 7 but both give different remainders so Not sufficient
Hence E

what is oa?

ern5231 wrote:What is the remainder when X is divided by 24?
A: X can not be divisible by 3
B: X-1 can be divisible by 2

What's the source? In mathematics, a can/cannot be divisible by b is understood as a is/isn't divisible by b, there's no possibility otherwise. Moreover, ideally A and B are not used as statements in GMAT DS, they use 1 & 2 or I & II rather.

(1) A number not divisible by 3, if divided by 24, will surely leave some non zero remainder with 16 different possibilities to answer, 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, and 23. Insufficient

(2) If 1 less than a number is divisible by 2, the number, X here, is odd, and when an odd number is divided by 24, the remainder is odd and this will surely have 12 different possibilities to answer, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, and 23. Insufficient

Take them one now

This would get us the common of all the possible remainders to answer, that is the intersection of the two sets, {1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23} and {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23}, which is {1, 5, 7, 11, 13, 17, 19, 23}, [spoiler]not unique. Insufficient

E[/spoiler]