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705-805 Level|   Algebra|   Arithmetic|   Inequalities|      
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gracieguidotti
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If x is a number such that 0.020 < x - 10^(1/2) < 0.021 which of the 13 Nov 2023, 09:36
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

61% (02:37) correct 39% (02:49) wrong based on 1031 sessions

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If x is a number such that \(0.020 < x - \sqrt{10} < 0.021\) which of the following is closest to the value of \(\frac{1}{\sqrt{10}}- \frac{1}{x}\)?

A. 0.00002
B. 0.0002
C. 0.002
D. 0.02
E. 0.2
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C
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egmat
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If x is a number such that 0.020 < x - 10^(1/2) < 0.021 which of the 01 Jul 2024, 23:19
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­This definitely seems like an intimidating question. 
Watch this video solution to see how by careful observation and manipulation one can solve such difficult question with utmost ease.

­
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gmatophobia
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If x is a number such that 0.020 < x - 10^(1/2) < 0.021 which of the 10 Dec 2023, 06:09
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XimeSol
If x is a number such that 0.020 < x-√10 < 0.021, which of the following is closest to the value of \(\frac{1}{\sqrt{10}}-\frac{1}{x}\)
?
A)0.00002
B)0.0002
C)0.002
D)0.02
E)0.2

\(\frac{1}{\sqrt{10}}-\frac{1}{x}\)

\(\frac{x - \sqrt{10}}{\sqrt{10}x}\)

0.020 < x-√10 < 0.021

Adding √10 on both sides

0.020 + √10 < x < 0.021 + √10

Multiplying by √10 on both sides

0.020*√10 + 10 < √10x < 0.021√10 + 10

As the answer choices are far apart, we can approximate

x-√10 \(\approx \) 0.020

√10x \(\approx\) 0.020*√10 + 10 \(\approx\) 10

\(\frac{x - \sqrt{10}}{\sqrt{10}x}\)

\(\frac{0.020}{10} \approx 0.002\)

Option C
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gmatophobia
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If x is a number such that 0.020 < x - 10^(1/2) < 0.021 which of the 13 Nov 2023, 10:09
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gracieguidotti
If x is a number such that \(0.020 < x - \sqrt{10} < 0.021\) which of the following is closest to the value of \(\frac{1}{\sqrt{10}}- \frac{1}{x}\)?

A. 0.00002
B. 0.0002
C. 0.002
D. 0.02
E. 0.2

I would heavily rely on approximation in this question as the options are far apart

\(0.020 < x - \sqrt{10} < 0.021 \)

Adding \(\sqrt{10}\) on both sides of the equation

\(\sqrt{10}+0.020 < x < \sqrt{10} + 0.021 \)

\( x \approx \sqrt{10}+0.0205 \)

\(\frac{1}{\sqrt{10}}- \frac{1}{x}\)

\(\approx \frac{1}{\sqrt{10}} - \frac{1}{\sqrt{10}+0.0205}\)

\(\approx \frac{\sqrt{10}+0.0205 - \sqrt{10}}{\sqrt{10}*(\sqrt{10}+0.0205)}\)

\(\approx \frac{0.0205}{10+\sqrt{10}*0.0205}\)

The denominator is almost equal to 10. It's far less than 100, and far greater than 1. Hence, only option C fits in.
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If x is a number such that 0.020 < x - 10^(1/2) < 0.021 which of the 13 Nov 2023, 12:27
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Is GMATPrep Source same as MBA.com practice test?
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If x is a number such that 0.020 < x - 10^(1/2) < 0.021 which of the 17 Nov 2023, 18:00
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ankitmba95
Is GMATPrep Source same as MBA.com practice test?

ankitmba95 Yes, I believe these ones tagged "GMAT Prep (Focus)" so far are mostly from the first 2 free Focus Edition practice tests at mba.com. However, I believe they could also be from the paid Focus exams #3-6, and from the GMAT Focus Official Practice Questions. Is that correct, bb?

bb on this topic, I had a question/idea: would it be possible and helpful to have more specific tags for which test number and source they come from, in case people want to only do ones from tests they've already taken?

For instance, labeling them:

    • Exams 1 & 2
    • Exams 3 & 4
    • Exam 5
    • Exam 6
    • GMAT Focus Official Practice Questions

I've seen that the free tests 1 and 2 can share the same question pool. Potentially, Focus exams 5 and 6 are separate question pools, since they can be purchased separately here. For classic edition, tests 3 & 4 shared a pool, and tests 5 & 6.
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If x is a number such that 0.020 < x - 10^(1/2) < 0.021 which of the 10 Dec 2023, 06:55
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I encountered this GFE PE 6
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If x is a number such that 0.020 < x - 10^(1/2) < 0.021 which of the 18 Jan 2024, 07:26
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gracieguidotti
If x is a number such that \(0.020 < x - \sqrt{10} < 0.021\) which of the following is closest to the value of \(\frac{1}{\sqrt{10}}- \frac{1}{x}\)?

A. 0.00002
B. 0.0002
C. 0.002
D. 0.02
E. 0.2

Here is a video solution to this problem along with a discussion on how to use approximations: https://youtu.be/4Wy7BrQrjkM?feature=shared
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If x is a number such that 0.020 < x - 10^(1/2) < 0.021 which of the 02 Sep 2024, 05:12
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I got this as a first question on the Focus practice test #6. Is the tag that it is a hard question wrong, or did I just get unlucky (not getting an easy question first).
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If x is a number such that 0.020 < x - 10^(1/2) < 0.021 which of the 01 Dec 2024, 06:51
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If x is a number such that \(0.020 < x - \sqrt{10} < 0.021\) which of the following is closest to the value of \(\frac{1}{\sqrt{10}}- \frac{1}{x}\)?

\(0.020 < x - \sqrt{10} < 0.021\)

\(\frac{0.020}{x\sqrt{10}} < \frac{x - \sqrt{10}}{x\sqrt{10}} < \frac{0.021}{x\sqrt{10}}\)

\(\frac{0.020}{x\sqrt{10}} < \frac{1}{\sqrt{10}}- \frac{1}{x} < \frac{0.021}{x\sqrt{10}}\)

Since, \(0.020 < x - \sqrt{10} < 0.021\), we know that \(x\) is just a little greater than \(\sqrt{10}\). So, \(x\sqrt{10}\) is just a little greater than \(10\).

Thus, \(\frac{0.020}{x\sqrt{10}}\) and \(\frac{0.021}{x\sqrt{10}}\) are approximately \(0.002\) and \(0.0021\) respectively.

Thus, we can approximate the following:

\(0.002 < \frac{1}{\sqrt{10}}- \frac{1}{x} < 0.0021\)

A. 0.00002
B. 0.0002
C. 0.002
D. 0.02
E. 0.2

Correct answer: C
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If x is a number such that 0.020 < x - 10^(1/2) < 0.021 which of the 01 Dec 2024, 06:56
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jhinoq
I got this as a first question on the Focus practice test #6. Is the tag that it is a hard question wrong, or did I just get unlucky (not getting an easy question first).
62% of people who attempted the question got it correct. So, it's not a super hard question on percent correct. On the basis of only on the percentage correct metric, it would be a medium-hard question.

At the same time, it takes people a fair amount of time to answer it, over 2.5 minutes on average. Hence the hard rating.

It's definitely somewhat harder than I'd expect for a first question on the test.
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If x is a number such that 0.020 < x - 10^(1/2) < 0.021 which of the 10 Dec 2024, 11:45
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gracieguidotti
If x is a number such that \(0.020 < x - \sqrt{10} < 0.021\) which of the following is closest to the value of \(\frac{1}{\sqrt{10}}- \frac{1}{x}\)?

A. 0.00002
B. 0.0002
C. 0.002
D. 0.02
E. 0.2

Question stem, rephrased:
Which of the following is closest to the value of \(\frac{x - \sqrt{10}}{x\sqrt{10}}\) ?

Given inequality, rephrased:
\(0.02 + \sqrt{10} < x < 0.021 + \sqrt{10}\)

The above range for x is extremely small, whereas the answer choices A through E keep differing by a factor of 10:
B is ten times the value of A
C is ten times the value of B
D is ten times the value of C
And so on.

Thus, we can determine the correct answer simply by testing \(x = 0.02 + \sqrt{10}\).

If we substitute \(0.02 + \sqrt{10}\) into \(\frac{x - \sqrt{10}}{x\sqrt{10}}\), we get:

\(\frac{0.02 + \sqrt{10} - \sqrt{10}}{(0.02 + \sqrt{10})\sqrt{10}} = \frac{0.02}{0.02* \sqrt{10} + 10} ≈ \frac{0.02}{10.06} ≈ 0.002\)

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C
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If x is a number such that 0.020 < x - 10^(1/2) < 0.021 which of the 19 Jan 2025, 03:31
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gracieguidotti
If x is a number such that \(0.020 < x - \sqrt{10} < 0.021\) which of the following is closest to the value of \(\frac{1}{\sqrt{10}}- \frac{1}{x}\)?

A. 0.00002
B. 0.0002
C. 0.002
D. 0.02
E. 0.2
How i thought about it , we see x- square root of 10 is almost 0 i.e 0.020.... so x is close to sqrt 10 .

1/sqrt 10 - 1/ x = x - sqrt 10 / sqrt 10 * X

im assuming x is sqrt 10 almost so 0.02..../10 =0.002
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