If n denotes a number to the left of 0 on the number line su

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BTGmoderatorAT: Moderator; Posts: 426; Joined: Tue Aug 22, 2017 8:48 pmFollowed by: 1 member

by BTGmoderatorAT » Tue Jan 09, 2018 7:14 am

If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be

A. Less than -10
B. Between -1 and -1/10
C. Between -1/10 and 0
D. Between 0 and 1/10
E. Greater than 10

Is there a strategic approach to this question? . Can any experts show?

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Source: Beat The GMAT — Problem Solving | Tue Jan 09, 2018 7:14 am

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by GMATGuruNY » Tue Jan 09, 2018 7:18 am

ardz24 wrote:If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be

A. Less than -10
B. Between -1 and -1/10
C. Between -1/10 and 0
D. Between 0 and 1/10
E. Greater than 10

Is there a strategic approach to this question? . Can any experts show?

Let n = -1/20.
This works because (-1/20)Â² = 1/400, which is less than 1/100.
In this case, the reciprocal of n = -20.

When the reciprocal of n is -20, only answer choice A is true, since -20 is less than -10.

The correct answer is A.

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by Jeff@TargetTestPrep » Thu Feb 22, 2018 5:05 pm

ardz24 wrote:If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be

A. Less than -10
B. Between -1 and -1/10
C. Between -1/10 and 0
D. Between 0 and 1/10
E. Greater than 10

We are given that n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100. This means n is negative, and it is between 0 and -1/10 since (-1/10)^2 = 1/100. Thus, n could be equal to values such as -1/11, -1/12, -1/13, etc. Notice that when we square these values, they are all less than 1/100.

Let's take the reciprocal of any of these values listed. The reciprocal of -1/11 is -11. Similarly, the reciprocal of -1/12 is -12 and the reciprocal of -1/13 is -13. Since these reciprocals are all less than -10, answer choice A is correct.

Answer: A

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DrMaths: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Mon Jan 15, 2018 2:01 am

by DrMaths » Fri Feb 23, 2018 5:25 am

n^2 < 1/100
so n^2 - 1/100 < 0
This is the difference of 2 squares
so (n + 1/10)(n - 1/10) < 0
so n < -1/10 or n < 1/10
However n < 0 (as it is to the left of zero)
so n < -1/10

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Re: If n denotes a number to the left of 0 on the number line su

by Brent@GMATPrepNow » Fri Dec 03, 2021 7:36 am

BTGmoderatorAT wrote: ↑
Tue Jan 09, 2018 7:14 am
If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be

A. Less than -10
B. Between -1 and -1/10
C. Between -1/10 and 0
D. Between 0 and 1/10
E. Greater than 10

Is there a strategic approach to this question? . Can any experts show?

STRATEGY: As with all GMAT Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, the answer is a resounding yes, because we can just find a value of n that satisfies the given information, and then take the reciprocal of n.
From here, we should give ourselves about 20 seconds to identify a faster approach.
In this case, we can probably perform some algebra, but that will likely take longer than testing a value

We're told that the square of n is less than 1/100
In other words: n² < 1/100
So, for example, it could be the case that n = 1/20, since (1/20)² = 1/400, and 1/400 < 1/100

Important: The question also tells us that n denotes a number to the left of 0 on the number line
In other words, n is NEGATIVE, which means n = 1/20 doesn't satisfy this condition.
However, n = -1/20 meets all of the criteria since -1/20 is negative, and (-1/20)² = 1/400, and 1/400 < 1/100

If n = -1/20, then the reciprocal of n = -20/1 = -20
Only answer choice A works.

Brent Hanneson - Creator of GMATPrepNow.com

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