Problem Solving

AAPL wrote:If 2/a+3/a+4/a is an integer, which of the following must also be an integer?

A. 12/a
B. 3/a
C. 6/a
D. 9/a
E. 15/a

The OA is D.

We can say 2/a+3/a+4/a = 9/a, Hence, the correct answer is D.

Has anyone another strategic approach to solve this PS question? Regards!

That's a perfect approach.
2/a+3/a+4/a = 9/a.
So, if 2/a+3/a+4/a is an integer, then 9/a must be an integer as well.

Another approach would be to use the fact that the question asks "Which of the following must also be an integer?"
So, first find a value of a so that 2/a+3/a+4/a is an integer
One value is a = 9, since 2/9 + 3/9 + 4/9 = 9/9 = 1, which is an integer.

Now plug a = 9 into the answer choices....
A. 12/9 NOT an integer. ELIMINATE
B. 3/9 NOT an integer. ELIMINATE
C. 6/9 NOT an integer. ELIMINATE
D. 9/9 = 1 This IS an integer. KEEP
E. 15/9 NOT an integer. ELIMINATE

Answer: D

Cheers,
Brent

AAPL wrote:If 2/a+3/a+4/a is an integer, which of the following must also be an integer?

A. 12/a
B. 3/a
C. 6/a
D. 9/a
E. 15/a

Since 2/a + 3/a + 4/a = 9/a, then 9/a is also an integer.

Answer: D