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

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Founder
Joined: 18 Apr 2015
Posts: 6920
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Kudos [?]: 1344 [0], given: 6318

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

84% (00:33) correct 15% (00:27) wrong based on 19 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.

Kudos for R.A.E
[Reveal] Spoiler: OA

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Director
Joined: 20 Apr 2016
Posts: 908
WE: Engineering (Energy and Utilities)
Followers: 11

Kudos [?]: 671 [1] , given: 148

Re: 4/5 - 4/7 or 4/7-2/5 [#permalink]  26 Aug 2018, 08:12
1
KUDOS
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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GRE Instructor
Joined: 10 Apr 2015
Posts: 1991
Followers: 60

Kudos [?]: 1806 [1] , given: 9

Re: 4/5 - 4/7 or 4/7-2/5 [#permalink]  27 Aug 2018, 05:57
1
KUDOS
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

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