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What is the solution of (x, y)’s

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by Max@Math Revolution » Mon Apr 06, 2020 2:44 am

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Answers

A

B

C

D

E

Stats

Difficulty—

[GMAT math practice question]

What is the solution of (x, y)’s satisfying \(\sqrt{500}=\sqrt{x}+\sqrt{y}\) and x < y?

1) x and y are positive integers.
2) x = 5t^2 with 0 < t < 5.
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Source: — Data Sufficiency |
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Re: What is the solution of (x, y)’s

by Max@Math Revolution » Wed Apr 08, 2020 5:39 pm
=>

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.

Since we have 1 variable (n) and 0 equations, D is most likely the answer. So, we should consider each condition on its own first.

Condition 1)
x = 5 = 5*1^2, y = 5*9^2 = 405 and x = 5*2^2, y = 5*8^2 = 320 are possible solutions.

Condition 2)
x = 5 = 5*1^2, y = 5*9^2 = 405 and x = 5*2^2, y = 5*8^2 = 320 are possible solutions.

Conditions 1) & 2)

x = 5 = 5*1^2, y = 5*9^2 = 405 and x = 5*2^2, y = 5*8^2 = 320 are possible solutions.

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations,” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A, B, C, or E.
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