If x is a number such that 0.020

Question

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

egmat · Accepted Answer

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.

https://www.youtube.com/watch?v=onoy7zVJmyE

gmatophobia · Answer

\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

gmatophobia · Answer

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.

ankitmba95 · Answer

Is GMATPrep Source same as MBA.com practice test?

GMATCoachBen · Answer

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.

garvit22 · Answer

I encountered this GFE PE 6

KarishmaB · Answer

Here is a video solution to this problem along with a discussion on how to use approximations: https://youtu.be/4Wy7BrQrjkM?feature=shared

jhinoq · Answer

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).

MartyMurray · Answer

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

MartyMurray · Answer

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.

GMATGuruNY · Answer

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

C

jsam98 · Answer

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

If x is a number such that 0.020 < x - 10^(1/2) < 0.021 which of the

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