If 50-√7<x<50+√7, then x=?

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[GMAT math practice question]

If 50-√7<x<50+√7, then x=?

1) x is an odd integer
2) √x is an integer.

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by Brent@GMATPrepNow » Fri Mar 30, 2018 6:12 am
Max@Math Revolution wrote:[GMAT math practice question]

If 50-√7<x<50+√7, then x=?

1) x is an odd integer
2) √x is an integer.
Target question: What is the value of x?

Given: 50 - √7 < x < 50 + √7
√4 = 2
√9 = 3
So, we can say that √7 = 2.something

This means: 50 - 2.something < x < 50 + 2.something
Simplify to get: 47.something < x < 52.something

Statement 1: x is an odd integer
There are two values of x that satisfy statement 1 (since we also know that 47.something < x < 52.something):
Case a: x = 49
Case b: x = 51
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: √x is an integer
If √x is an integer, then x is a "perfect square"
So, some POSSIBLE values of x are: 1, 4, 9, 16, 25, 36, 49, 64, 81, etc
When we consider the given info (47.something < x < 52.something), we can conclude that x MUST equal 49
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Sun Apr 01, 2018 5:36 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.

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

Since 2< √7< 3, we have 47< x < 53 from the original condition '50-√7<x<50+√7'.

Condition 1)
As x is an odd integer, it could be 49 or 51.
Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
If √x is an integer, then x is the square of an integer.
49 is the only perfect square of an integer between 47 and 53.
Thus, x=49 and condition 2) is sufficient.

Therefore, B is the answer.

Answer: B