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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] New post 25 Mar 2012, 17:30
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Question Stats:

57% (03:10) correct 43% (00:40) wrong based on 169 sessions
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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Re: What is the distance between x and y on the number line? [#permalink] New post 25 Mar 2012, 23:22
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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.

Answer: E.
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Re: What is the distance between x and y on the number line? [#permalink] New post 26 Mar 2012, 00:30
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] New post 18 Dec 2012, 09:16
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Bunuel can you clarify what can be wrong below approach?

Answer choice can be (C)
-------------------------------------
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.

-> Hence Answer is C.
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Re: What is the distance between x and y on the number line? [#permalink] New post 23 Dec 2012, 06:55
Expert's post
PraPon wrote:
Bunuel can you clarify what can be wrong below approach?

Answer choice can be (C)
-------------------------------------
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.

-> Hence Answer is C.


(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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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: What is the distance between x and y on the number line? [#permalink] New post 23 Dec 2012, 13:41
Oh I see...That explains it! Thanks for your reply Bunuel!
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Re: What is the distance between x and y on the number line? [#permalink] New post 16 Jul 2013, 23:22
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Re: What is the distance between x and y on the number line? [#permalink] New post 18 Jul 2013, 11:56
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!
Re: What is the distance between x and y on the number line?   [#permalink] 18 Jul 2013, 11:56
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