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GRE Math Challenge #111- (n/4)+(r/8) = (s/8) + (t/6)
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Updated on: 20 Feb 2020, 13:41
Updated on: 20 Feb 2020, 13:41
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\((\frac{n}{4})+(\frac{r}{8}) = (\frac{s}{8}) + (\frac{t}{6})\)
n, r, s, and t are positive integers.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
n, r, s, and t are positive integers.
Quantity A |
Quantity B |
2n + r |
2s + t |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: GRE Math Challenge #111
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11 May 2015, 06:59
11 May 2015, 06:59
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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
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 A (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.
So, the answer is D
Cheers,
Brent
Re: GRE Math Challenge #111- (n/4)+(r/8) = (s/8) + (t/6)
[#permalink]
11 Mar 2018, 21:33
11 Mar 2018, 21:33
1
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
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
