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Re: What is the distance between x and y on the number line? [#permalink]
25 Mar 2012, 23:22

1

This post received KUDOS

Expert's post

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.

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

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

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

gmatclubot

Re: What is the distance between x and y on the number line?
[#permalink]
18 Jul 2013, 11:56

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