What is the value of x? (i) Distance of x from y is the same

Question

What is the value of x?

(i) Distance of x from y is the same as y from zero
(ii) x is to the right of y

How do we solve this using:
(i) absolute method:|x - y| = |y|
(ii) number line: relative distance on the number line
IMO OA:  E

Anurag@Gurome · Answer

Don't go for absolute values while solving this one. Number line approach is much more easier. Also apart from these concepts, we can easily conclude that both the options together is not sufficient as none of them tells us any value of x or y. Anyway let's analyze it with number lines.

Statement 1:  Implies either x is also equal to zero or x = 2y.

Not sufficient

Statement 2:  We have only information that x > y.

Not sufficient

1 & 2 Together:  Now either {y < 0 and x = 0} or {y > 0 and x = 2y}

Not sufficient

The correct answer is E.

gmatpapa · Answer

i) This tells us that 0,x&y are equally spaced. Many numbers will satisfy this condition. Example, x=8, y=4 or x=6, y=3. Not sufficient
ii) Again, they could be any numbers. Same numbers picked in the above examples prove this. Insufficent.

i & ii together provide us with no new information. Hence insufficient.

Answer E.

IanStewart · Answer

No, you cannot draw that conclusion reliably on a real GMAT question. First, the question does, in fact, mention a value, namely zero. It's also quite easy to reword the question so that the information is in fact sufficient, even without mentioning any value of x or y:

If y is positive, what is the value of x?

(1) The distance between x and y on the number line is equal to the distance between y and zero 
(2) On the number line, x is to the left of y

There's no mention of any values here besides zero, but the answer is C; using both statements, x must be zero. I'd find this version of the question more interesting (and more GMAT-like) than the version in the original post, since many people will simply pick E rather quickly and move on. Real GMAT DS questions are very often designed to trap the test taker who uses overly simplistic criteria to pick an answer; if you reason that "the question doesn't mention any values so the answer must be E", you'll be picking the wrong answer a lot of the time.

gmatpapa · Answer

Ian,

In this question, we are not told whether y is positive or negative. If y is negative and x lies to the right of y, indeed x will be zero. But if y is positive, x will not be zero.

May I ask whether you have reworded the same question? If yes then why did you assume y is positive?

IanStewart · Answer

Yes, as I wrote: "It's also quite easy to reword the question...". I added the condition y > 0 to illustrate that one cannot always glance at a question, say 'oh, the question doesn't mention any values so the answer is E' and hope to get the right answer all of the time; that only works some of the time.

gmatbull · Answer

In the case where x is to the left of y, the single value 
of x must be a zero.

Without this constraint, the OA is surely E. Thanks guys for all
your valuable contributions.

144144 · Answer

hmmm a question. if they never gave us any info about the value of Y - how can we know the value of X?

gmatpapa · Answer

See, value is not actually necessary as pointed out by Ian. But there is actually no property of y mentioned either. So in the context of this question, we cannot find out the value for x. We can safely pick E.

144144 · Answer

that is exactly what I am saying... we do not need to think too much... no value of Y so no matter what info they give - you will never be able to know whats the value of X...

IanStewart · Answer

Perhaps I wasn't clear in my post above. Try to apply that line of reasoning to this question, which is different from the one in the original post above:

If y is positive, what is the value of x?

(1) The distance between x and y on the number line is equal to the distance between y and zero 
(2) On the number line, x is to the left of y

If you use the reasoning you're suggesting, you'll quickly choose 'E' and move on. The answer is not E, it's C; using both statements, x must be zero.

There are several real GMAT questions which seem to be specifically designed to trap test takers who use overly simplistic 'tricks' to guess at the right answer. Be careful.

gmatpapa · Answer

Good example. Of course many a GMAT question sets traps such as this. 
But if its mentioned in the problem that Y is positive, its not exactly same as the original question, where no property of Y is given to us. Right?

vasili · Answer

My question is regarding semantic interpretation of the question. 
First statement says:Distance of x from y is the same as y from zero. Why do we depict this statement as Ix-yI and not Iy-xI?
If we presume that second version is acceptable, then the only value for x is 0. And thus the ans is A. What am I missing?

fluke · Answer

What is the value of x?

(i) Distance of x from y is the same as y from zero

Let x=0; y=-5
Distance from x to y=5
y to 0 = 5.
Satisfies the condition. Value of x=0

Let x=0; y=5
Distance from x to y=5
y to 0 = 5
Satisfies the condition. Value of x=0

Let x=10; y=5
Distance from x to y = 5
y to 0 = 5
Satisfies the condition. Value of x=10

Let x=-10; y=-5
Distance from x to y = 5
y to 0 = 5
Satisfies the condition. Value of x=-10

We have three different values for x. 0,10,-10; Not sufficient.

(ii) x is to the right of y

Let x=0; y=-5
Distance from x to y=5
y to 0 = 5.
Satisfies the condition that x is to the right of y. Value of x=0

Let x=10; y=5
Distance from x to y = 5
y to 0 = 5
Satisfies the condition that x is to the right of y. Value of x=10

Two values of x. Not sufficient.

Combining both;
Let x=0; y=-5
Distance from x to y=5
y to 0 = 5.
Satisfies both conditions that x is to the right of y and distance between x and y is same as distance between y and 0. Value of x=0

Let x=10; y=5
Distance from x to y = 5
y to 0 = 5
Satisfies both conditions that x is to the right of y and distance between x and y is same as distance between y and 0. Value of x=10

Two values of x. Not sufficient.

When algebra clouds my mind; I temporarily resort to the sample sets for the clarification.

******************

Had we considered the absolute value paradigm;

|x-y| = |y|

This means;
x-y=-y
x=0
OR(a big OR)
x-y=y
x=2y

|y-x| = |y|

This means;
y-x=-y
x=2y
OR(a big OR)
y-x=y
x=0

Choose anyway; we have two different possible values for x for any value of y. x's exact value can't be determined with given conditions.

Ans: "E"

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What is the value of x? (i) Distance of x from y is the same

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