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## Operations with Rational Numbers

tagged by: Brent@GMATPrepNow

This topic has 5 expert replies and 0 member replies
jmacym Newbie | Next Rank: 10 Posts
Joined
29 Sep 2016
Posted:
6 messages

#### Operations with Rational Numbers

Sat Oct 08, 2016 10:42 am
One of my review questions...

The sum 7/8 + 1/9 is between...

The correct answer is (B) 3/4 and 1

The explanation is as follows: Since 1/9 < 1/8, 7/8 + 1/9 < 7/8 + 1/8 = 1 answer choices C, D, and E can be eliminated.
Since 7/8 > 6/8 = 3/4, 7/8 + 1/9 > 3/4 answer choice A can be eliminated. Thus, 3/4 < 7/8 + 1/9 < 1

Okay, so my thinking is first of all 7/8 + 1/9 is 71/72... obviously that was not even close to any of the answer choices.
The explanation confuses me even more because it's saying 1/9 is less than 1/8...which I understand how and why that is true, but 1/9 could be less than TONS of numbers. How am I supposed to know to use 1/8 instead of, lets say, 1/7 or 1/6, 1/5..etc. to get to the correct answer?

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DavidG@VeritasPrep Legendary Member
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Sat Oct 08, 2016 10:49 am
jmacym wrote:
One of my review questions...

The sum 7/8 + 1/9 is between...

The correct answer is (B) 3/4 and 1

The explanation is as follows: Since 1/9 < 1/8, 7/8 + 1/9 < 7/8 + 1/8 = 1 answer choices C, D, and E can be eliminated.
Since 7/8 > 6/8 = 3/4, 7/8 + 1/9 > 3/4 answer choice A can be eliminated. Thus, 3/4 < 7/8 + 1/9 < 1

Okay, so my thinking is first of all 7/8 + 1/9 is 71/72... obviously that was not even close to any of the answer choices.
The explanation confuses me even more because it's saying 1/9 is less than 1/8...which I understand how and why that is true, but 1/9 could be less than TONS of numbers. How am I supposed to know to use 1/8 instead of, lets say, 1/7 or 1/6, 1/5..etc. to get to the correct answer?
The idea is that (7/8) + (1/8) = 1. Because 1/9 < 1/8, it must be true that (7/8) + (1/9) < 1.

(In essence, 1/8 was chosen because it allowed you to easily see how the sum would compare to one.)

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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Sat Oct 08, 2016 6:58 pm
Hi jmacym,

When posting a GMAT question, you should make sure to post the ENTIRE question (including the 5 answer choices). In many cases, the answer choices themselves provide a 'hint' as to how you can go about answering the question. The question that you're referring to includes the following answers:

The sum 7/8 + 1/9 is between?

A) 1/2 and 3/4
B) 3/4 and 1
C) 1 and 1 1/4
D) 1 1/4 and 1 1/2
E) 1 1/2 and 2

From the answer choices, we can see that there is no 'overlap' between any pair of consecutive answers, so we really just need to define the range. By extension, we likely do NOT need to do a perfect calculation to get to the correct answer (we can probably use a certain amount of estimation).

Since 6/8 = 3/4 = .75, we know that 7/8 has to be greater than .75 on its own.

7/8 + 1/8 would = 1, but since 1/9 < 1/8, then we're adding a number to .75 that will end up in a sum that is less than 1. We've now defined the range...

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Rich

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GMATGuruNY GMAT Instructor
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Sat Oct 08, 2016 7:02 pm
jmacym wrote:
The sum 7/8 + 1/9 is between?

A) 1/2 and 3/4
B) 3/4 and 1
C) 1 and 1 1/4
D) 1 1/4 and 1 1/2
E) 1 1/2 and 2
7/8 + 1/8 = 1.
Since 1/9 is just a bit SMALLER than 1/8, 7/8 + 1/9 must be just a BIT LESS THAN 1.

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Brent@GMATPrepNow GMAT Instructor
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Sun Oct 09, 2016 7:25 am
Quote:
The sum 7/8 + 1/9 is between

A)1/2 and 3/4
B)3/4 and 1
C)1 and 1 1/4
D)1 1/4 and 1 1/2
E)1 1/2 and 2
Well, first we know that 7/8 + 1/8 = 1
Since 1/9 is a little bit less than 1/8, we know that the sum 7/8 + 1/9 will be a little bit less than 1.
Since 7/8 is also greater than 3/4, the answer must be B

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Jeff@TargetTestPrep GMAT Instructor
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Fri Apr 06, 2018 7:59 am
Quote:
The sum 7/8 + 1/9 is between

A)1/2 and 3/4
B)3/4 and 1
C)1 and 1 1/4
D)1 1/4 and 1 1/2
E)1 1/2 and 2
Notice that 1/9 is less than 1/8, so 7/8 + 1/9 < 7/8 + 1/8 = 1.

Furthermore, 7/8 itself is greater than 3/4 since 3/4 = 6/8.

Thus we see that the sum is between 3/4 and 1.

Alternate Solution:

Letâ€™s add the two fractions, using 72 as the common denominator:

7/8 + 1/9 = 63/72 + 8/72 = 71/72.

We see that 71/72 is just slightly less than 1, so B is the obvious choice..

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