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(Statement1): x is divisible by 8. --> x could be 24 (96 is divisible by 24--YES) --> x could be 40 (96 is not divisible by 40--NO) Insufficient
(Statement2): x is divisible by 12.
--> x could be 24 (96 is divisible by 24--YES) --> x could be 60 (96 is not divisible by 60--NO) Insufficient
Taken together 1&2, LCM(8,12)=24 --> 96 is divisible by 24 (YES) --> 96 is divisible by 48 (YES) --> but if x=72, 96 is not divisible by 72 Insufficient
96 = 2^5*3 #1 x is divisible by 8 so x has to be at least 2^3 ; in that case yes 2^5*3 will be divisible by 2^3 ; sufficient and x can be 200 5^2*2^3 ; 96 will not be divisible by 5^2*2^3 ; insufficient #2 x is divisible by 12 12= 2^2*3 x has to be at least 2^2*3 ; so 2^5*3 will be divisible by 2^2*3 x=108 2^2^3^3 so no. 2^5*3 not divisible insufficient from 1 &2 LCM of 2^3 and 2^2*3= 2^3*3; 24 yes 96 is divisible by 24,48 and no when x=72 IMO E
96=2^5 * 3 1. x is divisible by 8 Not sufficient because x can be 16 which is divisible by 8 and 96 is divisible by 16. x can also be 40 which is divisible by 8 but 96 is not divisible by 40.
2. x is divisible by 12 Not sufficient because x can be 24 which is divisible by 12 and 96 is divisible by 24. However, when x=60 which is divisible by 12 but 96 is not divisible by 60.
1+2 we have x=24 which is divisible by both 8 and 12, and 96 is divisible by 24. However when x=120, which is divisible by 8 and 12 but 96 is not divisible by 120. Both statements taken together are still not sufficient.
(1) x is divisible by 8. x = 16; 96 is divisible by x(16). x = 64; 96 is not divisible by x(64) NOT SUFFICIENT
(2) x is divisible by 12. x = 12; 96 is divisible by x(12) x = 36; 96 is not divisible by x(36) NOT SUFFICIENT
(1) + (2) (1) x is divisible by 8. (2) x is divisible by 12. x is divisible by LCM(8,12) = 24 x = 24; 96 is divisible by x(24) x = 72; 96 is not divisible by x(72) NOT SUFFICIENT
IMO E
gmatclubot
Re: Is 96 divisible by integer x?
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28 Oct 2019, 21:29
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63% (01:19) correct 
