## Que: If a and b are positive integers, is ab a multiple of 18?

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### Que: If a and b are positive integers, is ab a multiple of 18?

by [email protected] Revolution » Sun Aug 15, 2021 9:06 pm

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## Global Stats

Que: If a and b are positive integers, is ab a multiple of 18?

(1) a is a multiple of 6.
(2) b is a multiple of a.

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### Re: Que: If a and b are positive integers, is ab a multiple of 18?

by [email protected] Revolution » Mon Aug 16, 2021 9:04 pm

00:00

A

B

C

D

E

## Global Stats

Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find whether ab is a multiple of 18 – where ‘a’ and ‘b’ are positive integers.

=> ab = 18n – where ‘n’ must be an integer

Follow the second and the third step: From the original condition, we have 2 variables (a and b). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

Recall 3- Principles and Choose C as the most likely answer. Let’s look at both conditions combined together.

Condition (1) tells us that a is a multiple of 6.

=> a = 6m ; where m is any integer

Condition (2) tells us that b is a multiple of a.

=> b = ap=6mp ; where p is any integer

=> From them, we can determine whether ab is a multiple of 18, since $$ab=\left(6m\right)\left(6mp\right)=\left(36m^2p\right)=18\left(2m^2p\right)$$

The answer is a unique YES; both conditions combined are sufficient according to Common Mistake Type 1 which states that the answer should be a unique YES or a NO.

Both conditions together are sufficient.

Therefore, C is the correct answer.