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If 50-√7<x<50+√7, then x=?

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If 50-√7<x<50+√7, then x=?  [#permalink]

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New post 30 Mar 2018, 02:06
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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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Re: If 50-√7<x<50+√7, then x=?  [#permalink]

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New post 30 Mar 2018, 02:10
1
1) is not sufficient because x can be either 49 or 51
2) is sufficient because the only integer between 50−√7 and 50+√7 that is a perfect square (right word? not a native speaker) is 49
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Re: If 50-√7<x<50+√7, then x=?  [#permalink]

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New post 30 Mar 2018, 02:14
MathRevolution wrote:
[GMAT math practice question]

If \(50-√7<x<50+√7\), then \(x=?\)

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



since as 2<√7<3
so this can be simplied as 47.yy<x<52.zz


From1-->49 and 51 is possible so not A
From2-->only 49 is possible so B
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If 50-√7<x<50+√7, then x=?  [#permalink]

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New post 30 Mar 2018, 06:05
MathRevolution wrote:
[GMAT math practice question]

If \(50-√7<x<50+√7\), then \(x=?\)

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



It is nice to now \(\sqrt{7}\), We can also deduce it quickly

\(\sqrt{4}\) < \(\sqrt{7}\) < \(\sqrt{9}\)

2 < \(\sqrt{7}\) < 3.......You can notice it is close to 3.........So we estimate it

\(x\approx{2.8}\)

Question could be written as follows:

If \(47.2<x<52.8\), What is X??

1) \(x\) is an odd integer

X could be 51 or 49

Insufficient

2) \(√x\) is an integer

Only one value fits which is 49..........7 = \(\sqrt{49}\)

Sufficent

Answer: B
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Re: If 50-√7<x<50+√7, then x=?  [#permalink]

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New post 30 Mar 2018, 07:58
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Top Contributor
MathRevolution 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
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Re: If 50-√7<x<50+√7, then x=?  [#permalink]

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New post 01 Apr 2018, 18:44
=>

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
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Re: If 50-√7<x<50+√7, then x=? &nbs [#permalink] 01 Apr 2018, 18:44
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