Hello,
Can you please tell me if my approach is correct here:
If x is an integer, what is the value of x^2 + x ?
(1) x^2 = |x|
(2) x^2 + x > 0
OA: C
I tried to solve as follows:
1) x^2 = |x|
Hence, x^2 + x = |x| + x
If x > 0 => |x| + x = 2x
If x < 0 => |x| + x = 0
Hence, In-suff.
2) x^2 + x > 0
In-suff.
1 and 2:
x^2 + x = |x| + x > 0
=> x cannot be negative
Hence, |x| + x = 2x
I was wondering if this solution is correct?
Thanks a lot,
Sri
If x is an integer, what is the value of x^2 + x ?
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Sri,
Be careful: When a DS question asks you for the value of an expression, SUFFICIENT information means that you have enough to know the exact numerical value. So in general, proving that |x|+x = 2x is not enough to say that you have sufficient info to find |x|+x, unless you know exactly what number it is equal to.
For instance, if a DS asked "what is the value of |x|+x?" and a statement said "|x|+x = 2x", that statement would not be sufficient because we are unable to isolate a unique numerical value (if x=2 then |x|+x=4, but if x=1 then |x|+x=2)
Here is how I would approach the question:
Statement 1
For almost all integers, x^2 will be bigger than |x|. The only integers for which x^2=|x| are -1, 0, and 1 (visualize the absolute value "V" graph, and the x^2 parabola graph on a plot; if you know what the graphs look like you will realize right away that there are just 3 points of intersection). So this statement tells us that x = {-1, 0 or 1}. x=-1 would make x^2+x = 2, but x=0 or -1 would make x^2+x = 0. INSUFFICIENT
Statement 2
INSUFFICIENT since we could get lots of results for |x|+x depending on what we make x.
Together
Statement 1 limited us to only 2 possible values for x^2+x (2 or 0). Statement 2 tells us that x^2+x > 0, so together the statements guarantee that x^2+x = 2. SUFFICIENT
-Patrick
Be careful: When a DS question asks you for the value of an expression, SUFFICIENT information means that you have enough to know the exact numerical value. So in general, proving that |x|+x = 2x is not enough to say that you have sufficient info to find |x|+x, unless you know exactly what number it is equal to.
For instance, if a DS asked "what is the value of |x|+x?" and a statement said "|x|+x = 2x", that statement would not be sufficient because we are unable to isolate a unique numerical value (if x=2 then |x|+x=4, but if x=1 then |x|+x=2)
Here is how I would approach the question:
If x is an integer, what is the value of x^2 + x ?
(1) x^2 = |x|
(2) x^2 + x > 0
Statement 1
For almost all integers, x^2 will be bigger than |x|. The only integers for which x^2=|x| are -1, 0, and 1 (visualize the absolute value "V" graph, and the x^2 parabola graph on a plot; if you know what the graphs look like you will realize right away that there are just 3 points of intersection). So this statement tells us that x = {-1, 0 or 1}. x=-1 would make x^2+x = 2, but x=0 or -1 would make x^2+x = 0. INSUFFICIENT
Statement 2
INSUFFICIENT since we could get lots of results for |x|+x depending on what we make x.
Together
Statement 1 limited us to only 2 possible values for x^2+x (2 or 0). Statement 2 tells us that x^2+x > 0, so together the statements guarantee that x^2+x = 2. SUFFICIENT
-Patrick
Last edited by Patrick_GMATFix on Fri Feb 14, 2014 1:30 am, edited 2 times in total.
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Hi Sri,
What you've written is incomplete, so I'm not sure if you truly have enough info to prove the correct answer. Here's another way of looking at this question:
We're told that X is an integer. We're asked for the value of X^2 + X?
Fact 1: X^2 = |X|
This is a remarkably restrictive piece of information. The only possible values of X are -1, 0 and 1
If X = -1, then the answer to the question is 0
If X = 0, then the answer to the question is 0
If X = 1, then the answer to the question is 2
Fact 1 is INSUFFICIENT
Fact 2: X^2 + X > 0
There are LOTS of values that fit this Fact.
If X = 1, then the answer to the question is 2
If X = 2, then the answer to the question is 6
Fact 2 is INSUFFICIENT
Combined, we have only 3 possible values from Fact 1; -1 and 0 do NOT fit with Fact 2, so the only possibility is X = 1
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
What you've written is incomplete, so I'm not sure if you truly have enough info to prove the correct answer. Here's another way of looking at this question:
We're told that X is an integer. We're asked for the value of X^2 + X?
Fact 1: X^2 = |X|
This is a remarkably restrictive piece of information. The only possible values of X are -1, 0 and 1
If X = -1, then the answer to the question is 0
If X = 0, then the answer to the question is 0
If X = 1, then the answer to the question is 2
Fact 1 is INSUFFICIENT
Fact 2: X^2 + X > 0
There are LOTS of values that fit this Fact.
If X = 1, then the answer to the question is 2
If X = 2, then the answer to the question is 6
Fact 2 is INSUFFICIENT
Combined, we have only 3 possible values from Fact 1; -1 and 0 do NOT fit with Fact 2, so the only possibility is X = 1
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
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The solutions above are great.
I do not recommend using algebra to evaluate statement 1.
But if really insist, here's one approach:
x² = |x|
|x||x| = |x|
|x||x| - |x| = 0
|x| (|x| - 1) = 0.
|x| = 0 when x=0.
|x| - 1 = 0 when x=-1 or x=1.
Thus, valid solutions for statement 1 are x=-1, x=0, x=1.
I do not recommend using algebra to evaluate statement 1.
But if really insist, here's one approach:
x² = |x|
|x||x| = |x|
|x||x| - |x| = 0
|x| (|x| - 1) = 0.
|x| = 0 when x=0.
|x| - 1 = 0 when x=-1 or x=1.
Thus, valid solutions for statement 1 are x=-1, x=0, x=1.
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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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