If L \(\neq\) 0, is \(\frac{18K}{L}\)  an Integer?

Question: If L \(\neq\) 0, is \(\frac{18K}{L}\) an integer?

1. \(\frac{K^2}{L^2}\) is an integer
2. K – L = L

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“If L \(\neq\) 0, is \(\frac{18K}{L}\) an integer?” – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Answer

Approach Solution 1 

Firstly, take S1, we have \(\frac{K^2}{L^2}\) is an integer.

If we say, K = L = 1, then \(\frac{18K}{L}\) = 1

Hence, Answer to this question is YES.

But if we take K = \(\sqrt2\) and L = 1, then \(\frac{18K}{L}\) = \(18\sqrt{2}\) \(\neq\) integer

Hence, Answer to this question is NO.

Therefore, this statement is not sufficient.

Now, take S2, we have K – L = L
This means K = 2L

In this case, \(\frac{18K}{L}\) = \(\frac{18*2L}{L}\) = 36 = integer

So, Answer to this question is YES.

Therefore, this statement is sufficient.

Correct option: B

Approach Solution 2

For \(\frac{18K}{L}\) to be an integer, 18 must be divisible by L or K must be divisible by L or 18*K must be divisible by L.

Firstly, take S1, we have \(\frac{K^2}{L^2}\) is an integer.

Only if \(\frac{K}{L}\) is an integer, we might be able to say \(\frac{18K}{L}\) is an integer.

So, eliminate A, D

Now, take S2, we have K – L = L

K = 2L implies \(\frac{18K}{L}\) is an integer (i.e., 36)

Correct option: B

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