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4/5 - 4/7 or 4/7-2/5

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4/5 - 4/7 or 4/7-2/5 [#permalink] New post 24 Aug 2018, 23:59
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Question Stats:

80% (00:36) correct 20% (00:24) wrong based on 65 sessions
Quantity A
Quantity B
\(\frac{4}{5} - \frac{4}{7}\)
\(\frac{4}{7}-\frac{2}{5}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

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[Reveal] Spoiler: OA

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Re: 4/5 - 4/7 or 4/7-2/5 [#permalink] New post 26 Aug 2018, 08:12
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Carcass wrote:
Quantity A
Quantity B
\(\frac{4}{5} - \frac{4}{7}\)
\(\frac{4}{7}-\frac{2}{5}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E


QTY A = \(\frac{4}{5} - \frac{4}{7}\) =\(\frac{{28 - 20}}{35}= \frac{8}{35}\)

QTY B = \(\frac{4}{7}-\frac{2}{5}\) = \(\frac{{20 - 14}}{35}=\frac{6}{35}\)

Therefore QTY A > QTY B
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Re: 4/5 - 4/7 or 4/7-2/5 [#permalink] New post 27 Aug 2018, 05:57
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Expert's post
Carcass wrote:
Quantity A
Quantity B
\(\frac{4}{5} - \frac{4}{7}\)
\(\frac{4}{7}-\frac{2}{5}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E


Another approach is to use matching operations to get the fractions with the same denominators on the same side (the steps below can be performed in your head)

Given:
Quantity A: 4/5 - 4/7
Quantity B: 4/7 - 2/5

Add 4/7 to both quantities to get:
Quantity A: 4/5
Quantity B: 4/7 + 4/7 - 2/5

Add 2/5 to both quantities to get:
Quantity A: 4/5 + 2/5
Quantity B: 4/7 + 4/7

Simplify:
Quantity A: 6/5 = 1 1/5
Quantity B: 8/7 = 1 1/7

Subtract 1 from both quantities to get:
Quantity A: 1/5
Quantity B: 1/7

Since the denominator in Quantity A is smaller than the denominator in Quantity B, 1/5 must be greater than 1/7

Answer: A


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Re: 4/5 - 4/7 or 4/7-2/5   [#permalink] 27 Aug 2018, 05:57
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