If w, x, y and z are all positive numbers, is the value of w-x greater

Question

If w, x, y and z are all positive numbers, is the value of w-x greater than y-z?

(1) w + z = y + x
(2) w and x are each greater in value than either y or z.

AndrewN · Answer

Question:

w - x > y - z

Statement (1) is the same as the inequality, only rearranged:

w - x > y - z

w + z > y + x

Since the statement tells us that the two sides are  equal , we can conclude that the answer is NO, and  Statement (1) is SUFFICIENT  on its own.

Statement (2) does not help us because  w  and  x  could both be, say, 5, while  y  and  z  could both be 2, and the two sides would be equal. But it could also be true that the left-hand side is greater. Consider:

w  = 5
 x  = 4
 y  = 1
 z  = 2

5 - 4 > 1 - 2

1 > -1

And we have only explored integer values. Clearly, Statement (2) is NOT sufficient on its own, meaning   the answer must be (A)  .

- Andrew

Archit3110 · Answer

given that xywz are all +ver numbers
target is
w-x>y-z
w+z>y+x

#1
w + z = y + x
sufficient to target yes
#2
w and x are each greater in value than either y or z.
w & x are > than y and z
but there is not relation b/w w & x so insufficient as we can have case
1234 
such that 4-3>2-1 ; no
10 5 3 1
10-5 > 3-1 ; yes
insufficient
option A

Kinshook · Answer

Asked: If w, x, y and z are all positive numbers, is the value of w-x greater than y-z?

(1) w + z = y + x
w-x = y-z
The value of w-x is NOT greater than y-z
SUFFICIENT

(2) w and x are each greater in value than either y or z.
If w=8;x=7;y=3;z=1; w-x=1;y-z=2; w-x<y-z
But If w=8;x=5;y=3;z=1; w-x=3;y-z=2; w-x>y-z
NOT SUFFICIENT

IMO A

twoface07 · Answer

Given: w, x, y, z > 0.

Question stem: Is value w-x > y-z?

Statement (1): It implies w-x = y-z. Clearly,  SUFFICIENT  (since the question stem requires a YES or NO response).

Statement (2): There are multiple cases here (possibly more than 2).
- Case (a): w is greater than x and greater than either y or z. This means w-x > 0 and also implies w-z > y-z (this is assuming y > z).
- Case (b): x is greater than w and greater than either y or z. This means x-w > 0 OR  w-x < 0 .
From cases (a) and (b), we cannot conclude if w-x > y-z with certainty. Hence statement (2) is  INSUFFICIENT .

IMO, choice (A) is correct.

If w, x, y and z are all positive numbers, is the value of w-x greater

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GMAT Data Sufficiency (DS) Questions

If w, x, y and z are all positive numbers, is the value of w-x greater

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