OG 13 #156

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jeph86: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Fri Aug 21, 2015 5:02 amFollowed by: 1 member

by jeph86 » Wed Feb 24, 2016 9:11 am

S= (2/n)/(1/x + 3/3x)

156. in the expression above, if xn is not equal 0, what is the value of S

1) x=2n
2) n= 1/2

can someone help. I am still lost with the book explanation. thanks in advance.

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Source: Beat The GMAT — Quantitative Reasoning | Wed Feb 24, 2016 9:11 am

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed Feb 24, 2016 9:43 am

Hi jeph86,

To start, there's a minor typo in your post. The equation should read:

S= (2/n)/(1/x + 2/3x)

We're told that XN is not equal to 0 (so neither of those variables can be 0). We're asked for the value of S. This question can be solved by TESTing VALUES.

1) x = 2n

IF....
n = 1
x = 2
(2/1)/(1/2 + 2/6) = 2/(1/2 + 1/3) = 2/(5/6) = 12/5

IF....
n = 2
x = 4
(2/2)/(1/4 + 2/12) = 1/(1/4 + 1/6) = 1/(5/12) = 12/5

IF...
n = -3
x = -6
(2/-3)/(-1/6 - 2/18) = (-2/3)(-1/6 - 1/9) = (-2/3)/(-5/18) = +36/15 = 12/5

The answer to the question is ALWAYS 12/5.
Fact 1 is SUFFICIENT

2) n = 1/2

This Fact tells us NOTHING about the value of x. As x changes, the value of S will change.
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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jeph86: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Fri Aug 21, 2015 5:02 amFollowed by: 1 member

by jeph86 » Wed Feb 24, 2016 11:12 am

Hi Rich,

it seems like when I test n=1 x=4, it gives me a different solution. the result is 24/5. in your explanation, you said the answer will always 12/5. can you explain

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed Feb 24, 2016 8:55 pm

Hi jeph86,

In Fact 1, we're given the extra information that x=2n, so you CANNOT use n=1, x=4 as a TEST case. You have to use values that fit the equation x=2n. Any pair of values that fit THAT equation will also produce the result 12/5 in the original question.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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jeph86: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Fri Aug 21, 2015 5:02 amFollowed by: 1 member

by jeph86 » Thu Feb 25, 2016 12:47 pm

I appreciate your explanation Rich. this make sense.

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Sun Feb 28, 2016 5:00 pm

Try simplifying the question before approaching the statements. We're given:

Start by simplifying the denominator. We can add the two fractions together if we use a common denominator of 3x:

To divide one fraction by another fraction, flip and multiply by the reciprocal:

If we know that S = 6x/5n, we can split it into:

Thus, if we want to know the value of S, all we need is the value of x/n.

Statement (1), if we rearrange it, gives us x/n = 2. This is sufficient.

Statement (2) gives us a value for n, but tells us nothing about its relationship to x. Insufficient.

The answer is A.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Sun Feb 28, 2016 5:06 pm

Here is some general advice about DS problems like this one: if it feels too obvious that using both statements together will give you an answer, then it's probably not C. This is what we call a C-Trap.

In this case, if you knew that n = 1/2, you could clearly plug it into x = 2n, and clearly x = 1. We have all of the values we need, but we haven't done any conceptual thinking! That's our signal to be skeptical: could either statement be sufficient on its own? If we rephrase properly, we see that statement (1) is enough, so we don't need to put the 2 statements together. The answer must be A.

For more on how to avoid C-Traps, read these articles:
https://www.manhattanprep.com/gmat/blog ... fficiency/
https://www.manhattanprep.com/gmat/blog ... ncy-traps/

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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