GMAT Question

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GHong14: Master | Next Rank: 500 Posts; Posts: 155; Joined: Sat Oct 16, 2010 6:32 pm; Thanked: 3 times

by GHong14 » Tue Nov 30, 2010 2:57 pm

If n denotes a number left of the 0 on the number line such that n is less than 1/100 when squared, then the reciprical must be?

a. less than than -10
b. between -1 and -1/10
c. between -1/10 and 0
d. between 0 and 1/10
e. greater than 10

Answer is a. Care to explain?

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Tue Nov 30, 2010 5:00 pm

GHong14 wrote:If n denotes a number left of the 0 on the number line such that n is less than 1/100 when squared, then the reciprical must be?

a. less than than -10
b. between -1 and -1/10
c. between -1/10 and 0
d. between 0 and 1/10
e. greater than 10

Answer is a. Care to explain?

very easy question if you know the mode properties and can operate with the values on a number line

|n|^2 < 1/100

|n| < 1/10

condition precedent - n denotes a number left of the 0 on the number line

hence n < -1/10, the reciprocal of any number is [ 1 / number ], 1/n = -10

Select A.

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junegmat221: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Wed Apr 28, 2010 4:03 am

by junegmat221 » Sat Dec 04, 2010 5:37 am

Well for this question its best to assume .
Start with N ^2 < 0.01
Equate to some number square of a number which also has integer roots.
So, N^2 can be equal to -(0.04). Because N is left of 0 in the number line.
Now Take square root of N which is will be equal to -(0.2) which is essentially -(2/10).
And the Reciprocal of -(2/10) is -(10/2) which is equal to -5.
Now recheck with the choices.
Only A should be valid since -5 is lesser than -10.

Hope it helps ..

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Dec 04, 2010 6:05 am

GHong14 wrote:If n denotes a number left of the 0 on the number line such that n is less than 1/100 when squared, then the reciprical must be?

a. less than than -10
b. between -1 and -1/10
c. between -1/10 and 0
d. between 0 and 1/10
e. greater than 10

Answer is a. Care to explain?

The easiest approach is to plug in a value that satisfies the conditions in the problem.

Let n = -(1/100). This works because (-1/100)^2 = 1/10000, and 1/10000 < 1/100.
1/n = -100.
Since -100 < -10, the correct answer is A.

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