If n denotes a number to the left of 0 ... to find n

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Apr 05, 2014 6:28 pm

Hello,

Can you please tell me where I am going wrong here:

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

OA: A

Given n < 0

n^2 < 1/100
=> sq. root (n^2) < 1/10
=> |n| < 1/10
=> + or - n < 1/10

=> n < 1/10 or -n < 1/10
=> n < 1/10 of n > -1/10

I was thinking that since the question says n is negative why is it not possible that the answer is C? i.e. -1/10 < n < 0

Thanks for your help.

Best Regards,
Sri

Source: Beat The GMAT — Problem Solving | Sat Apr 05, 2014 6:28 pm

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by [email protected] » Sat Apr 05, 2014 7:13 pm

Hi Sri,

By approaching this question with "traditional math", you've forced yourself into a complex bit of math that includes some options that the question tells you to ignore.

Consider the information given by the prompt:

1) N is a number to the left of 0. This means that N MUST be NEGATIVE
2) N^2 < 1/100. This means that N is BETWEEN 0 and -1/10

Now that we have the limitations, TEST a VALUE.

How about N = -1/100….

The question asks for the RECIPROCAL OF N… -100

This matches one answer: A

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by GMATGuruNY » Sun Apr 06, 2014 2:50 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

Let n = -1/20.
This works because (-1/20)² = 1/400, which is less than 1/100.
In this case, the reciprocal of n = -20.

Only answer choice A works:
-20 is less than -10.

The correct answer is A.

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by Jeff@TargetTestPrep » Mon Dec 18, 2017 11:44 am

gmattesttaker2 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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