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Que: Gold gym has few members in two batches, A and B. The gym can divide the members in batch A into.....

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Que: Gold gym has few members in two batches, A and B. The gym can divide the members in batch A into.....

by Max@Math Revolution » Wed Feb 03, 2021 10:38 pm

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B

C

D

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Que: Gold gym has few members in two batches, A and B. The gym can divide the members in batch A into eight groups of x members each. However, if it divides the members in batch B into four groups of y members each, three members will be leftover. How many members are in the gym?

(1) \(x\ =\ \frac{y-1}{2}\)
(2) Number of members in batch B is seven more than that in batch A.
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Source: — Data Sufficiency |
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Re: Que: Gold gym has few members in two batches, A and B. The gym can divide the members in batch A into.....

by Max@Math Revolution » Fri Feb 05, 2021 9:55 pm

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C

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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. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

Let us assign variable to the number of members: ‘a’ in batch A and ‘b’ in batch B

Thus, we have a = 8x and b = 4y + 3

We have to find the value of a + b

Follow the second and the third step: From the original condition, we have 4 variables (a, b, x, and y) and 2 equations (a = 8x and b = 4y + 3). 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 \(x\ =\ \frac{y-1}{2}\)

=> y = 2x + 1

Condition (2) tells us that the number of members in batch B is seven more than that in batch A

=> b = a + 7

=> 4y + 3 = 8x + 7

=> 4y = 8x + 4

=> y = 2x + 1

Thus, a + b = 8x + 4y + 3

=> 8x + 4(2x + 1) + 3

=> 8x + 8x + 4 + 3

=> 16x + 7

The value of ‘x’ is unknown.

The answer is not a unique value; both conditions together are not sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.

Both conditions together are not sufficient.

Therefore, E is the correct answer.

Answer: E
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