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.
OG 13 #156
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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
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
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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
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
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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.
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
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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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/
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
EdM in Mind, Brain, and Education
Harvard Graduate School of Education