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# 1/4+1/3+1/2

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Founder
Joined: 18 Apr 2015
Posts: 13700
GRE 1: Q160 V160
Followers: 305

Kudos [?]: 3546 [1] , given: 12654

1/4+1/3+1/2 [#permalink]  28 Jul 2018, 08:20
1
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Expert's post
00:00

Question Stats:

80% (00:46) correct 19% (01:18) wrong based on 135 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.

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

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VP
Joined: 20 Apr 2016
Posts: 1302
WE: Engineering (Energy and Utilities)
Followers: 22

Kudos [?]: 1332 [2] , given: 251

Re: 1/4+1/3+1/2 [#permalink]  29 Jul 2018, 18:29
2
KUDOS
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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GRE Instructor
Joined: 10 Apr 2015
Posts: 3873
Followers: 159

Kudos [?]: 4667 [2] , given: 70

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

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.

Intern
Joined: 04 Aug 2019
Posts: 16
Followers: 0

Kudos [?]: 6 [1] , given: 52

Re: 1/4+1/3+1/2 [#permalink]  16 Aug 2019, 14:00
1
KUDOS
GreenlightTestPrep wrote:
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)

Cheers,
Brent

Hi Brent, how do we "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" specifically?

I could benefit from seeing how it was worked out fully. Thank you!
GRE Instructor
Joined: 10 Apr 2015
Posts: 3873
Followers: 159

Kudos [?]: 4667 [1] , given: 70

Re: 1/4+1/3+1/2 [#permalink]  16 Aug 2019, 14:15
1
KUDOS
Expert's post
JNeen wrote:

Hi Brent, how do we "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" specifically?

I could benefit from seeing how it was worked out fully. Thank you!

Key concept: If x > 1, then 1/x has a value that's less than 1
For example:
1/2 is less than 1
1/4 is less than 1
1/3.1 is less than 1
1/6.5 is less than 1

Conversely, if 0 < x < 1, then 1/x has a value that's greater than 1
For example:
1/0.5 is greater than 1
1/0.1 is greater than 1
1/0.25 is greater than 1
etc.

3 + 1/4 = 3.25, and 1/3.25 is less than 1
2 + 1/2 = 2.5, and 1/2.5 is less than 1

So, 4 + 1/(3 + 1/4) = 4 + (some number that's less than 1)
= 4.something

And, 2 + 1/(3 + 1/2) = 2 + (some number that's less than 1)
= 2.something

Does that help?

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.

Intern
Joined: 04 Aug 2019
Posts: 16
Followers: 0

Kudos [?]: 6 [0], given: 52

Re: 1/4+1/3+1/2 [#permalink]  19 Aug 2019, 13:46
GreenlightTestPrep wrote:
JNeen wrote:

Hi Brent, how do we "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" specifically?

I could benefit from seeing how it was worked out fully. Thank you!

Key concept: If x > 1, then 1/x has a value that's less than 1
For example:
1/2 is less than 1
1/4 is less than 1
1/3.1 is less than 1
1/6.5 is less than 1

Conversely, if 0 < x < 1, then 1/x has a value that's greater than 1
For example:
1/0.5 is greater than 1
1/0.1 is greater than 1
1/0.25 is greater than 1
etc.

3 + 1/4 = 3.25, and 1/3.25 is less than 1
2 + 1/2 = 2.5, and 1/2.5 is less than 1

So, 4 + 1/(3 + 1/4) = 4 + (some number that's less than 1)
= 4.something

And, 2 + 1/(3 + 1/2) = 2 + (some number that's less than 1)
= 2.something

Does that help?

Cheers,
Brent

No but I got it now. Thanks!
Founder
Joined: 18 Apr 2015
Posts: 13700
GRE 1: Q160 V160
Followers: 305

Kudos [?]: 3546 [0], given: 12654

Re: 1/4+1/3+1/2 [#permalink]  19 Aug 2019, 14:46
Expert's post
Sir, do you have any doubt ??

Regards
_________________

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- Do you want all the GRE Prep Club FREE resources in one spot ?? Look at Free GRE Materials - Where to get it!! (2020)
- Do you want all the FREE GRE tests on earth ?? Look at FREE GRE Practice Tests [Collection] - New Edition (2021)
- Do you want to know the GRE score in the Top 25 BS in 7 continents ?? Look at here The GRE average score at Top 25 Business Schools 2020 Ed.
- Need Practice 20 Free GRE Quant Tests available for free with 20 Kudos
- GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Re: 1/4+1/3+1/2   [#permalink] 19 Aug 2019, 14:46
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