BTGmoderatorDC wrote:What is the LCM of the numbers 3, a, and 7, if 'a' is an integer and a ≥ 3?
Statement 1. 'a' is a prime number greater than 2.
Statement 2. Both GCD (3, a) and LCM (3, a) are factors of the number 30.
OA E
Source: e-GMAT
Let's take each statement one by one.
Statement 1. 'a' is a prime number greater than 2.
Case 1: Say a = 3, then the LCM of the numbers 3, a = 3, and 7 = 21.
Case 2: Say a = 5, then the LCM of the numbers 3, a = 5, and 7 = 105.
No unique answer. Insufficient.
Statement 2. Both GCD (3, a) and LCM (3, a) are factors of the number 30.
Factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. So, both GCD (3, a) and LCM (3, a) is one among the factors.
Case 1: Say a = 3, then the GCD (3, a = 3) is 3 (a factor of 30) and LCM (3, a = 3) is 3 (a factor of 30); we see that the LCM of the numbers 3, a = 3, and 7 = 21.
Case 2: Say a = 5, then the GCD (3, a = 5) is 1 (a factor of 30) and LCM (3, a = 5) is 15 (a factor of 30); we see that the LCM of the numbers 3, a = 5, and 7 = 105.
No unique answer. Insufficient.
(1) and (2) together
Both the cases discussed above are applicable for each statement; thus, together the statements are not sufficient.
The correct answer:
E
Hope this helps!
-Jay
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