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Two absolute value problems.....

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by nitsiso » Thu Jul 22, 2010 9:13 pm
1. IS |X-Z| > |X-Y| ?

A. |Z| > |Y|
B. 0 > X

2. IS X = Y ?

A. X = |Y |
B. Y = | X |

Please help me..I have solved both of them but I got confused during the process.I need to clear some absolute value concepts!!
Thanks
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Source: — Data Sufficiency |
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by 4GMAT_Mumbai » Thu Jul 22, 2010 9:23 pm
IS X = Y ?

A. X = |Y |
B. Y = | X |

Stmt 1: X could be 5 and Y could be either -5 or +5. Hence, Insufficient.

Stmt 2: Y could be 10 and X could be either -10 or +10. Hence, Insufficient.

Let us combine both.

If both are true, then both X and Y are +ve. Hence, Yes - X is indeed equal to Y. Hence, Sufficient.
Naveenan Ramachandran
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai
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by 4GMAT_Mumbai » Thu Jul 22, 2010 9:40 pm
1. IS |X-Z| > |X-Y| ?

A. |Z| > |Y|
B. 0 > X

Stmt 1:

Let Z be 10; Y be 5.

If X is 25;

Mod(X-Z) = 15
Mod(X-Y) = 20

If X is 4,

Mod(X-Z) = 6
Mod(X-Y) = 1.

Hence, stmt 1 is insufficient.

Stmt 2:

X < 0. Let X = -2.

If Y = 3 and Z = 5

Mod(X-Z) = 7
Mod(X-Y) = 5

If Y = 5 and Z = 3

Mod(X-Z) = 5
Mod(X-Y) = 7

Hence, stmt 2 is insufficient.

Stmt 1 and stmt 2 combo:

|Z| > |Y| and 0 > X

Let Z = -10, Y = -5

If X = -3,

Mod (X-Z) = 7
Mod (X-Y) = 2

If X = -10

Mod (X-Z) = 0
Mod (X-Y) = 5

Hence, insufficient.

Hope this helps. Thanks.
Naveenan Ramachandran
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai
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by outreach » Thu Jul 22, 2010 10:01 pm
|X-Z| > |X-Y|
(X-Z)^2 > (X-Y)^2
X^2-2XZ+Z^2>X^2-2XY+Y^2
solving we get
(Z+Y)>-2X -(1)


1)
no idea abt X hence insuff

2)
no idea abt Y&Z hence insuff

combined
if X=-1,Z=-3,Y=-1, eq 1 is false
if X=-1,Z=4,Y=1, eq 1 is true
hence insuff

E
nitsiso wrote:1. IS |X-Z| > |X-Y| ?

A. |Z| > |Y|
B. 0 > X

Please help me..I have solved both of them but I got confused during the process.I need to clear some absolute value concepts!!
Thanks
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