If xyz = tyz, is x = t ? (1) x = 0 (2) y 0

Question

If  xyz = tyz , is  x = t  ?

(1)  x = 0

(2)  y ≠ 0

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zhanbo · Answer

(1)Only
If x=0, t=0, then x=t
But if x=0,y=0,t=10, then x<>t
Insufficient

(2)Only
Suppose y=5
If x=t=0, then x=t
If x=0, z=0, t=5, then x<>t
Insufficient

(1)(2)Together
Cases under (2)Only also satisfies condition (1).
Insufficient

The answer is thus (E).

mdsaddamforgmat · Answer

IMO E

Given, xyz = tyz
Therefore, yz(x-t)=0
Now, Statement1: x=0
If YZ = 0 then we cannot conclude whether x=t. hence, insufficient.

Statement2: y is not equal to zero
Here, Z can be zero. hence, again insufficient.

Combining also we can’t decide whether z=0 or not hence, Hence, E.

ManojHarsha · Answer

Lets solve this question in the traditional DS style..

Given  xyz = tyz  =>  (x-t)yz=0

Statement 1 :  x = 0   
If x=0, the above equation will become
 => (0-t)yz=0
 => tyz=0; {Any one of them has to be zero}

If t=0; Then  x = t    true  
 If y or z = 0, then t can be any non-zero number & 0 (4,5,.. 0)  x = t    false

Hence A,D are eliminated. 
 
 Statement 2 :  y ≠ 0   
If  y ≠ 0 ,then the main equation will be
(x-t)yz=0 , Either x=t or z=0, Hence we cannot conclude any thing.

So B is eliminated.

Using both Statement 1 :  x = 0  & Statement 2 :  y ≠ 0

tyz=0; {Statement 1}

Now as y cannot be 0 from {Statement 2}

t or z has to be zero..

If z = 0 then  x ≠ t  
But if z ≠ 0 then  x = t , No concluding answer.

Hence C is also eliminated.

E is the correct answer.

If xyz = tyz, is x = t ? (1) x = 0 (2) y 0

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GMAT Data Sufficiency (DS) Questions

If xyz = tyz, is x = t ? (1) x = 0 (2) y 0

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