GCD prob

[beat_gmat_09]

What is the Greatest Common Divisior of two different positive integers which are less than 144 ?

(A) 143
(B) 142
(C) 72
(D) 71
(E) 12

[deepesh.gupta]

What is the Greatest Common Divisior of two different positive integers which are less than 144 ?

(A) 143
(B) 142
(C) 72
(D) 71
(E) 12

The answer is D. If we are looking at common divisor of two numbers less than 144, both the numbers cannot be prime numbers and hence atleast one of them has to be divisible by factor other than 1 and the number. Now applying POE on each choice:
A - Wrong. If this is the greatest divisor than the other number has to be multiple of it, which is not possible as the number has to be less than 144
B - Wrong. The reason same as for the reason for choice A
C - Wrong. The reason same as for the reason for choice A
D - Right. The numbers can be 72 and 142
E - There are other numbers greater than 12 (like choice D)

[mj41]

Can someone please explain why D is the answer. I know why A, B and C are wrong. But if 71 is the GCF then are the numbers 71 and 142???

[kstv]

@ deepesh.gupta

Hi !
(A) 143 = 13 x 11 so if nos are 13 and 11 GCF is 143
(B) 142 = 71 X 2
so if one no is 71(prime no) and the other 142 GCF is 142