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## Simple fraction

tagged by: Brent@GMATPrepNow

This topic has 4 expert replies and 0 member replies
AbeNeedsAnswers Master | Next Rank: 500 Posts
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#### Simple fraction

Mon Jul 03, 2017 8:32 pm
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
Since denominator is negative, we know the answer must be negative. Are there other secrets to doing this faster?

1/(0.75 - 1) =

A) -4
B) -0.25
C) 0.25
D) 0.75
E) 4

A

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### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
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Mon Jul 03, 2017 10:38 pm
Since denominator is negative, we know the answer must be negative. Are there other secrets to doing this faster?

1/(0.75 - 1) =

A) -4
B) -0.25
C) 0.25
D) 0.75
E) 4

A
Yes, you are correct; since the numerator is positive and the denominator is negative, the result is negative, thus answer could be between option A and B.

There is no secret to doing this faster. One must deal with a decimal and a fraction.

Mentally, you can do this one since you wish to have the most efficient approach.

0.75 is a popular and most commonly used decimal, it is a 3/4th of a number.

Thus (0.75 - 1) is a negative of 1/4th of the number. Or, (0.75 - 1) = -1/4

Once you flip -1/4, you get -4, the correct answer.

Hope this helps!

-Jay
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Brent@GMATPrepNow GMAT Instructor
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Tue Jul 04, 2017 6:43 am
Since denominator is negative, we know the answer must be negative. Are there other secrets to doing this faster?

1/(0.75 - 1) =

A) -4
B) -0.25
C) 0.25
D) 0.75
E) 4

A
Useful fraction property: 1/(a/b) = b/a
For example: 1/(2/3) = 3/2
And 1/(19/7) = 7/19

So, 1/(0.75 - 1) = 1/(-0.25) = 1/(-1/4) = -4

Alternatively, 1/(0.75 - 1) = 1/(3/4 - 4/4) = 1/(-1/4) = -4

Cheers,
Brent

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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Tue Jul 04, 2017 9:46 am

From a 'concept' standpoint, increasing or decreasing the denominator of a fraction will impact whether the fraction increases or decreases in value.

For example, if we're dealing with a positive fraction....

eg. 1/4

Decreasing the denominator makes the fraction BIGGER (e.g.. 1/3 is greater than 1/4)
Increasing the denominator makes the fraction SMALLER (e.g.. 1/5 is less than 1/4)

In this question, we're dealing with a positive numerator and a NEGATIVE denominator, so similar patterns will occur.

eg. 1/-3

As the denominator gets FARTHER from 0, the fraction gets CLOSER to 0 (-1/4 is closer to 0 than -1/3 is)
As the denominator gets CLOSER to 0, the fraction gets FARTHER from 0 (-1/2 is farther from 0 than -1/3 is)

In this question, since the denominator is - .25, that means the value of 1/(-.25) is FARTHER from 0 than 1/-1 is. There's only one answer that fits that pattern.

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Rich

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Matt@VeritasPrep GMAT Instructor
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Wed Jul 05, 2017 1:07 am
1/(.75 - 1) =>

1/(-.25) =>

-(1/.25) =>

-1/(1/4) =>

-4

I wouldn't worry about speed here since this is about as quick a GMAT problem as I can recall - is it from the OG?

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