If x y and y z, which of the following represents the greatest num

Question

If x > y and y > z, which of the following represents the greatest number?

(A) x − z 
(B) x − y 
(C) y − x 
(D) z − y 
(E) z − x

BrentGMATPrepNow · Accepted Answer

The key here is to recognize that there is only ONE correct answer. 
So, as long as we find values that satisfy the given conditions (x > y and y > z), we can simply test the answer choices.

If x > y and y > z, then it could be the case that x = 1, y = 0, and z = -1
We'll now plug these values into the five answer choices....
(A) x − z = 1 - (-1) = 2
(B) x − y = 1 - 0 = 1
(C) y − x = 0 - 1 = -1
(D) z − y = (-1) - 0 = -1
(E) z − x = (-1) - 1 = -2

Answer: A

chetan2u · Answer

Irespective of the signs, X and Z will be the farthest,
so the numeric value of their difference will be maximum and since x is the larger of two, x-z will be positive..
A

gmatlbs · Answer

(A) x − z 
(E) z − x 
Absolute value of both the options are same.
(But the sign of x , y and z is not mentioned....Is it really going to make any difference to this question !!! )

Option A.

davedekoos · Answer

It is not known whether x, y and z are positive or negative, but it doesn't matter. We know that x is larger than z, so x-z will be positive and z-x will be negative. We don't need to know the values or the signs. To double check, pick some values (keeping in mind that x > y > z): x=10, y=4, z=1 Now the answer choices become: (A) x − z = 9 (B) x − y = 6 (C) y − x = -6 (D) z − y = -3 (E) z − x = -9 Option (A) is the greatest. A for Ali, obviously. :wink:

If you want to be super double extra sure, because you're not convinced that the sign of the numbers doesn't matter, then pick some wild numbers and see if it makes a difference. x=10, y=0, z=-a bazillion Now the answer choices become: (A) x − z = a bazillion + 10 (B) x − y = 10 (C) y − x = -10 (D) z − y = -a bazillion (E) z − x = -a bazillion - 10 Still (A)

nipunjain14 · Answer

Because x>y>z
thus x- z wil lbe greatest

Ans: A

stonecold · Answer

Here the only thing we need to remember that on the number line the number to the right side is always greater

saiesta · Answer

Substituting numbers for variables will work.

Moreover, I do not think this is a 600-700 level question but rather a sub-600 question.

stonecold · Answer

Disagree ..!! whats 600 for you might be 700 for me

nalinnair · Answer

There are no restrictions on the values of x, y, and z. So we can pick any three numbers that fulfill the inequalities mentioned in the question.
Let us take x = 3, y = 2 and z = 1

(A) x − z  = 3 - 1 = 2 
(B) x − y  = 3 - 2 = 1 
(C) y − x  = 2 - 3 = -1 
(D) z − y  = 1 - 2 = -1 
(E) z − x  = 1 - 3 = -2

Correct answer - A

sauravpaul · Answer

So, numbers are in ascending order: z, y, x

So, x - y will be the largest.

As chetan said yesterday, we need to keep in mind that sign will be taken care of. So, no need to worry:).

Divyadisha · Answer

Basically, the question tells us that x>y>z

If the smallest number is subtracted from the largest number, we get the greatest number.

X is the largest number and z is the smallest number; hence, x-z is the greatest number.

A is the answer

Abhishek009 · Answer

x > y and y > z = x > y > z

Now, Plug in some values of X, Y and Z

x > y > z => 3 > 2 > 1

(A) x − z = 3 - 1 => 2 
 (B) x − y = 3 - 2 => 1
(C) y − x = 2 - 3 => -1
(D) z − y = 1 - 2 => -1
(E) z − x = 1 - 3 => -2 
  
So, The answer is definitely (A)

daviddaviddavid · Answer

well imo you don't have to care about negatives. Remember its not a ds questions, so it its works with positives its enough to answer the question (at least in my view, but maybe I'm missing something?)

Anyway of course it also works with negative

Anyway of course it also works with negative

HasnainAfxal · Answer

as x is greatest number and z is smallest number
so x-z would be highest number.

Answer A

MathRevolution · Answer

x > y and y > z

Combining both, x > y > z

Irrespective of sign x - z will be greatest.

Answer A

ScottTargetTestPrep · Answer

Solution:
 
Since x > y > z, choices A and B will yield a positive result while choices C, D, and E will yield a negative result. Therefore, the correct answer is either A or B. Now we can let x = 3, y = 2 and z = 1 and check both choices A and B.

A. x - z = 3 - 1 = 2

B. y - z = 2 - 1 = 1

Because 2 > 1, we see that the correct answer is A.

Answer: A

Nipungupta9081 · Answer

x > y & Y > Z

Therefore X > Y > Z => X > Z 
 
Answer A

100mitra · Answer

Correct Option A 
Find the greater value ?
= x>y and y>z 
= x>y>z
Minus z to all.

= (x-z)>(y-z)>0 
 Greater value : (x-z) 
Middle value : (y-z)
Smaller value : 0

werty_123 · Answer

Can we also think on this lines?

In GMAT options are always in ascending or descending order. So the right answer would either be A or E in this case

If x > y and y > z, which of the following represents the greatest num

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