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1/4+1/3+1/2

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1/4+1/3+1/2 [#permalink] New post 28 Jul 2018, 08:20
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Question Stats:

72% (00:53) correct 27% (01:18) wrong based on 36 sessions
Quantity A
Quantity B
\(\frac{1}{4 + \frac{1}{3 + \frac{1}{2}}\)
\(\frac{1}{2 + \frac{1}{3 + \frac{1}{4}}\)


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: 1/4+1/3+1/2 [#permalink] New post 29 Jul 2018, 18:29
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Carcass wrote:
Quantity A
Quantity B
\(\frac{1}{4 + \frac{1}{3 + \frac{1}{2}}\)
\(\frac{1}{2 + \frac{1}{3 + \frac{1}{4}}\)


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 = \({\frac{1}{4 + \frac{1}{3 + \frac{1}{2}}} = {\frac{1}{4 + \frac{2}{7}}} = {\frac{1}{28 + \frac{2}{7}}} = {\frac{1}{\frac{30}{7}}} = {\frac{7}{30}}\)


QTY B = \({\frac{1}{2 + \frac{1}{3 + \frac{1}{4}}} = {\frac{1}{2 + \frac{4}{13}}} = {\frac{1}{26 + \frac{4}{13}}} = {\frac{1}{\frac{30}{13}}} = {\frac{13}{30}}\)


Therefore QTY A < QTY B

Option B
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Re: 1/4+1/3+1/2 [#permalink] New post 02 Aug 2018, 15:51
Expert's post
Carcass wrote:
Quantity A
Quantity B
\(\frac{1}{4 + \frac{1}{3 + \frac{1}{2}}\)
\(\frac{1}{2 + \frac{1}{3 + \frac{1}{4}}\)


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


We need only recognize that 1/(3 + 1/2) is less than 1
So, 4 + 1/(3 + 1/2) = 4.something

Likewise, 1/(3 + 1/4) is less than 1
So, 2 + 1/(3 + 1/2) = 2.something

So, we get:
Quantity A: 1/(4.something)
Quantity B: 1/(2.something)

Answer: B

Cheers,
Brent
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Re: 1/4+1/3+1/2   [#permalink] 02 Aug 2018, 15:51
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