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GRE Math Challenge #111- (n/4)+(r/8) = (s/8) + (t/6)

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GRE Math Challenge #111- (n/4)+(r/8) = (s/8) + (t/6) [#permalink]  09 May 2015, 11:30
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Question Stats:

72% (02:23) correct 27% (02:05) wrong based on 11 sessions
$$(n/4)+(r/8) = (s/8) + (t/6)$$
n, r, s, and t are positive integers.

Quantity A: 2n + r
Quantity B: 2s + t

• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined
[Reveal] Spoiler: OA

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Sandy
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Re: GRE Math Challenge #111 [#permalink]  11 May 2015, 06:59
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Expert's post
sandy wrote:
$$(n/4)+(r/8) = (s/8) + (t/6)$$
n, r, s, and t are positive integers.

Quantity A: 2n + r
Quantity B: 2s + t

Given: (n/4)+(r/8) = (s/8) + (t/6)
This equation has a lot of fractions. Let's first make things easier by eliminating the fractions.
The denominators are 4, 8, and 6.
The least common multiple of 4, 8 and 6 is 24, so let's multiply both both sides of the equation by 24 to get: 6n + 3r = 3s + 4t

NOTICE that Quantity (2n + r) is SIMILAR to 6n + 3r, Let's use this fact!
Take 6n + 3r = 3s + 4t and divide both sides by 3 to get: 2n + r = s + (4/3)t
Now replace Quantity A with s + (4/3)t to get:

Quantity A: s + (4/3)t
Quantity B: 2s + t

Now subtract s from both quantities AND subtract t from both quantities to get:
Quantity A: (1/3)t
Quantity B: s

At this point, it's impossible to tell which quantity is greater.

Cheers,
Brent
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Re: GRE Math Challenge #111- (n/4)+(r/8) = (s/8) + (t/6) [#permalink]  11 Mar 2018, 21:33
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sandy wrote:
$$(n/4)+(r/8) = (s/8) + (t/6)$$
n, r, s, and t are positive integers.

Quantity A: 2n + r
Quantity B: 2s + t

• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined

Let's simplify the expression.

(n/4)+(r/8) = (s/8) + (t/6)------> (2n+r)/8= (3s+4t)/24

(6n+3r)/24= (3s+4t)/24

6n+3r= 3s+4t

2n+r= s+ 4/3t

For A, we replace 2n+r with s+ 4/3t

For B, we have 2s + t

s+ 4/3t vs. 2s + t deduct s

4/3t vs. s+t deduct t

1/3t vs. s

so far we not told the exact value of both s and t

the realtionship of both Qaunt A and B are unclear

ANS　Ｄ
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Re: GRE Math Challenge #111- (n/4)+(r/8) = (s/8) + (t/6) [#permalink]  12 Mar 2018, 01:21
Re: GRE Math Challenge #111- (n/4)+(r/8) = (s/8) + (t/6)   [#permalink] 12 Mar 2018, 01:21
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