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.
Two absolute value problems.....
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Source: Beat The GMAT — Data Sufficiency |
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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.
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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|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
(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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