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If x and y are positive integers and

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by Max@Math Revolution » Tue Dec 11, 2018 12:26 am

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[Math Revolution GMAT math practice question]

If x and y are positive integers and

$$y=\sqrt{5-x}$$ then y=?

1) x>1
2) y<2
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Tue Dec 11, 2018 12:35 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If x and y are positive integers and

$$y=\sqrt{5-x}$$ then y=?

1) x>1
2) y<2
Given that x and y are positive integers and y = √(5 - x), we must 1 ≤ x ≤ 4 such that (5 - x) is a perfect square. Only two values of x qualify for the corresponding qualifying values of y. 1: x = 1 and y = 4; and 2: x = 4 and y = 1.

Let's take each statement one by one.

1) x > 1

=> x = 4 => y =1. Sufficient.

2) y < 2

=> y =1. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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by Max@Math Revolution » Thu Dec 13, 2018 4:53 am
=>

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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Modifying the original condition:
Note that for 5-x to make sense, we must have x ≤ 5.
Also,
y=√5-x,
=> y^2 = 5 - x.
Since y^2 = 5 - x is the square of an integer and 0< x ≤ 5, the only possible solutions are x = 1, y = 2 and x = 4, y = 1.
Thus, if a condition allows us to figure out the value of either x or y, it is sufficient.

Condition 1)
Since x > 1, we must have x = 4 and y = √5-x =√5-4 = 1.
Thus, condition 1) is sufficient since it gives a unique solution.

Condition 2)
Since y < 2, we have y = 1 from the original condition.
Thus, condition 2) is sufficient since it gives a unique solution.

Therefore, D is the answer.
Answer: D

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).
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