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To find the fraction

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by gmattesttaker2 » Fri Mar 07, 2014 11:12 pm
Hello,

Can you please tell me how to solve this:

What fraction of 3/4 + 1/2 is 3/4 - 1/2?

A) 1/5
B) 1/4
C) 1/3
D) 3/4
E) 5

OA: A

I was trying to solve as follows:

3/4 + 1/2 = 5/4

3/4 - 1/2 = 1/4

So, what fraction of 5/4 is 1/4?

But I was little confused as to how to represent this using algebra.

Thanks,
Sri
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by Brent@GMATPrepNow » Fri Mar 07, 2014 11:23 pm
gmattesttaker2 wrote: What fraction of 3/4 + 1/2 is 3/4 - 1/2?

A) 1/5
B) 1/4
C) 1/3
D) 3/4
E) 5
You were almost there.

It may be easier if we rephrase the question.
Notice that these two questions are EQUIVALENT.
"What fraction of X is Y?"
"Y is what fraction of X?"

So, "What fraction of 3/4 + 1/2 is 3/4 - 1/2?" is the same as "3/4 - 1/2 is what fraction of 3/4 + 1/2?"

Here, we go...
"3/4 - 1/2 is what fraction of 3/4 + 1/2?"
In other words: "1/4 is what fraction of 5/4?"
Well, 1/4 is one-fifth the size of 5/4
So, "1/4 is [spoiler]1/5[/spoiler] of 5/4"

Answer: A

Cheers,
Brent
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by GMATGuruNY » Sat Mar 08, 2014 3:07 am
gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:

What fraction of 3/4 + 1/2 is 3/4 - 1/2?

A) 1/5
B) 1/4
C) 1/3
D) 3/4
E) 5

OA: A
Since the question stem asks for a FRACTION, we can safely multiply the numerator and the denominator of this fraction by the SAME FACTOR.

Simplify the expressions in the question stem by multiplying each expression by 4:
4 * (3/4 + 1/2) = 3+2 = 5.
4 * (3/4 - 1/2) = 3-2 = 1.

Question stem, rephrased:
What fraction of 5 is 1?
In other words:
1 is what fraction of 5?

The correct answer is A.
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by Matt@VeritasPrep » Sat Mar 08, 2014 10:24 am
Sri, you can just set it up this way:

3/4 - 1/2
---------
3/4 + 1/2

then solve:

1/4
---
5/4

or

1/5

In general, "x is what fraction of y" or "x is what percent of y" is just x/y: the question is essentially asking for the ratio of x to y.
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by Amrabdelnaby » Thu Dec 10, 2015 4:28 am
your answer was perfect!

now if you disregard the denominators of 5/4 and 1/4, you will find 1 and 5!
what fraction of 5 is 1? --> 1 is one fifth of 5. so the answer is 1/5.
same applies for 1/4 and 5/4... one quarter is one fifth of 5 quarters :)
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by Matt@VeritasPrep » Fri Dec 11, 2015 2:44 pm
Amrabdelnaby wrote:your answer was perfect!

now if you disregard the denominators of 5/4 and 1/4, you will find 1 and 5!
what fraction of 5 is 1? --> 1 is one fifth of 5. so the answer is 1/5.
same applies for 1/4 and 5/4... one quarter is one fifth of 5 quarters :)
Well put!
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by Brent@GMATPrepNow » Sat Jan 13, 2018 9:26 am
gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:

What fraction of 3/4 + 1/2 is 3/4 - 1/2?

A) 1/5
B) 1/4
C) 1/3
D) 3/4
E) 5

OA: A

I was trying to solve as follows:

3/4 + 1/2 = 5/4

3/4 - 1/2 = 1/4

So, what fraction of 5/4 is 1/4?

But I was little confused as to how to represent this using algebra.

Thanks,
Sri
You were almost there.

It may be easier if we rephrase the question.
Notice that these two questions are EQUIVALENT.
"What fraction of X is Y?"
"Y is what fraction of X?"

So, "What fraction of 3/4 + 1/2 is 3/4 - 1/2?" is the same as "3/4 - 1/2 is what fraction of 3/4 + 1/2?"

Here, we go...
"3/4 - 1/2 is what fraction of 3/4 + 1/2?"
In other words: "1/4 is what fraction of 5/4?"
Well, 1/4 is one-fifth the size of 5/4
So, "1/4 is 1/5 of 5/4"

Answer: A

Cheers,
Brent
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by mimajit » Mon Aug 20, 2018 10:20 pm
Brent@GMATPrepNow wrote:
gmattesttaker2 wrote: What fraction of 3/4 + 1/2 is 3/4 - 1/2?

A) 1/5
B) 1/4
C) 1/3
D) 3/4
E) 5
You were almost there.

It may be easier if we rephrase the question.
Notice that these two questions are EQUIVALENT.
"What fraction of X is Y?"
"Y is what fraction of X?"

So, "What fraction of 3/4 + 1/2 is 3/4 - 1/2?" is the same as "3/4 - 1/2 is what fraction of 3/4 + 1/2?"

Here, we go...
"3/4 - 1/2 is what fraction of 3/4 + 1/2?"
In other words: "1/4 is what fraction of 5/4?"
Well, 1/4 is one-fifth the size of 5/4
So, "1/4 is [spoiler]1/5[/spoiler] of 5/4"

Answer: A

Cheers,
Brent
Hi Brent Can u help me understand how u concluded
" In other words: "1/4 is what fraction of 5/4?"
Well, 1/4 is one-fifth the size of 5/4
So, "1/4 is 1/5 of 5/4"

Answer: A "
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by Jeff@TargetTestPrep » Wed Sep 05, 2018 9:50 am
gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:

What fraction of 3/4 + 1/2 is 3/4 - 1/2?

A) 1/5
B) 1/4
C) 1/3
D) 3/4
E) 5
An easier version of this question is: "What fraction of 6 is 3?" We would write the fraction as 3/6. Similarly, when we are asked "What fraction of 3/4 + 1/2 is 3/4 - 1/2?" we will perform the same operation, as shown here:

(3/4 - 1/2)/(3/4 + 1/2)

Multiplying the expression by 4/4, we have:

(3 - 2)/(3 + 2) = 1/5

Answer: A

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