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# What is the distance between x and y on the number line?

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What is the distance between x and y on the number line? [#permalink]

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25 Mar 2012, 18:30
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Difficulty:

55% (hard)

Question Stats:

57% (02:45) correct 43% (00:53) wrong based on 356 sessions

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What is the distance between x and y on the number line?

(1) |x| – |y| = 5
(2) |x| + |y| = 11
[Reveal] Spoiler: OA

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DETERMINED TO BREAK 700!!!

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Re: What is the distance between x and y on the number line? [#permalink]

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26 Mar 2012, 00:22
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What is the distance between x and y on the number line?

Question: |x-y|=?

(1) |x| – |y| = 5. Not sufficient: consider x=10, y=5 and x=10, y=-5.
(2) |x| + |y| = 11. Not sufficient: consider x=10, y=1 and x=10, y=-1.

(1)+(2) Solve the system of equation for |x| and |y|: sum two equations to get 2|x|=16 --> |x|=8 --> |y|=3. Still not sufficient to get the single numerical value of |x-y|, for example consider: x=8, y=3 and x=8, y=-3. Not sufficient.

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Re: What is the distance between x and y on the number line? [#permalink]

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26 Mar 2012, 01:30
Solving the two equations will give x as 8 and y as 3. But since mod sign is there, x and y can take any value, either positive or negative. Hence, both the statements are insufficient.
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Re: What is the distance between x and y on the number line? [#permalink]

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18 Dec 2012, 10:16
1
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Bunuel can you clarify what can be wrong below approach?

-------------------------------------
By multiplying statements 1 & 2
(1) |x| – |y| = 5
(2) |x| + |y| = 11

$$X^2-Y^2=55$$

i.e. $$(x+y)(x-y)=55 = 11 * 5 = - 11 * - 5$$ (i.e. both factors are either positive or negative)

Hence only two possible solutions for this – i.e. either (x=8 & y=3) OR (x= -8 & y= -3)
In both cases the distance between them is 5.

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Re: What is the distance between x and y on the number line? [#permalink]

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23 Dec 2012, 07:55
PraPon wrote:
Bunuel can you clarify what can be wrong below approach?

-------------------------------------
By multiplying statements 1 & 2
(1) |x| – |y| = 5
(2) |x| + |y| = 11

$$X^2-Y^2=55$$

i.e. (x+y)(x-y)=55 = 11 * 5 = - 11 * - 5 (i.e. both factors are either positive or negative)

Hence only two possible solutions for this – i.e. either (x=8 & y=3) OR (x= -8 & y= -3)
In both cases the distance between them is 5.

(x+y)(x-y)=55 does not mean that either (x=8 & y=3) OR (x= -8 & y= -3). There are more integer solutions (for example x=+/-28 and y=+/-27) and infinitely many non-integer solutions.
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Re: What is the distance between x and y on the number line? [#permalink]

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23 Dec 2012, 14:41
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Re: What is the distance between x and y on the number line? [#permalink]

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17 Jul 2013, 00:22
From 100 hardest questions
Bumping for review and further discussion.
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Re: What is the distance between x and y on the number line? [#permalink]

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18 Jul 2013, 12:56
What is the distance between x and y on the number line?

(1) |x| – |y| = 5

|11|-|6|=5
Distance is five

|11|-|-6|=5
Distance is seventeen
INSUFFICIENT

(2) |x| + |y| = 11

|5|+|6| = 11
Distance is one

|5|+|-6| = 11
Distance is negative eleven

INSUFFICIENT

This problem, to me, seems much easier than a 700 level question. a and b provide us with multiple valid values for x and y, none of which entirely (i.e. are the same) Can someone tell me if I am oversimplifying this problem? Thanks!
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Re: What is the distance between x and y on the number line? [#permalink]

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24 Jun 2015, 10:51
Hello from the GMAT Club BumpBot!

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Re: What is the distance between x and y on the number line? [#permalink]

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31 Mar 2016, 18:37
calreg11 wrote:
What is the distance between x and y on the number line?

(1) |x| – |y| = 5
(2) |x| + |y| = 11

i picked 8 and 3
1. x=8, y=3 -> 5 or x=-8, y=3 -> distance is 11. 1 alone is insufficient.
2. x=8, y=3 -> 5 or x=-8, y=3 -> distance is 11. 2 alone is insufficient.

1+2
same info from 1 and 2. C is out, and the answer must be E.
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Re: What is the distance between x and y on the number line? [#permalink]

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06 Apr 2016, 22:57
Bunuel wrote:
What is the distance between x and y on the number line?

Question: |x-y|=?

(1) |x| – |y| = 5. Not sufficient: consider x=10, y=5 and x=10, y=-5.
(2) |x| + |y| = 11. Not sufficient: consider x=10, y=1 and x=10, y=-1.

(1)+(2) Solve the system of equation for |x| and |y|: sum two equations to get 2|x|=16 --> |x|=8 --> |y|=3. Still not sufficient to get the single numerical value of |x-y|, for example consider: x=8, y=3 and x=8, y=-3. Not sufficient.

Hi... I have a question when we solve both the eqs tog we get two values for |y|=3 and -13. Right?
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Re: What is the distance between x and y on the number line? [#permalink]

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07 Apr 2016, 00:33
enasni wrote:
Bunuel wrote:
What is the distance between x and y on the number line?

Question: |x-y|=?

(1) |x| – |y| = 5. Not sufficient: consider x=10, y=5 and x=10, y=-5.
(2) |x| + |y| = 11. Not sufficient: consider x=10, y=1 and x=10, y=-1.

(1)+(2) Solve the system of equation for |x| and |y|: sum two equations to get 2|x|=16 --> |x|=8 --> |y|=3. Still not sufficient to get the single numerical value of |x-y|, for example consider: x=8, y=3 and x=8, y=-3. Not sufficient.

Hi... I have a question when we solve both the eqs tog we get two values for |y|=3 and -13. Right?

|y| is an absolute value of y, so it cannot be negative. When we solve for |y|, we get that |y| = 3, so y = 3, or y = -3.

Hope it's clear.
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Re: What is the distance between x and y on the number line?   [#permalink] 07 Apr 2016, 00:33
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