GMAT Question > If x > y and y > z, which of the follow...

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

Correct answer is option 'A'. Can you explain this answer?

From x > y and y > z, it follows that x > z.

These inequalities imply the following about the differences that are given in the answer choices:

Since the expressions in A and B represent positive numbers and the expressions in C, D, and E represent negative numbers, the latter can be eliminated because every negative number is less than every positive number. To determine which of x - z and x - y is greater, consider die placement of points widi coordinates x, y, and x on the number line,

The distance between x and z (that is, x - z) is the sum of the distance between x andy (that is, x - y) and the distance between y and z (that is, y - z).

Therefore (x- z) > (x y),which means that x-z represents the greater of the numbers represented by (x - z) and (x - y). Thus, x-z represents the greatest of the numbers represented by&e answer choices.

Alternatively,

y > z given

-y < -z multiply both sides by -1

x - y < x - z add x to both sides

Thus, x - z represents the greater of the numbers represented by (x - z) and (x - y). Therefore, x - z represents the greatest of the numbers represented by the answer choices.

The correct answer is A.

These inequalities imply the following about the differences that are given in the answer choices:

Since the expressions in A and B represent positive numbers and the expressions in C, D, and E represent negative numbers, the latter can be eliminated because every negative number is less than every positive number. To determine which of x - z and x - y is greater, consider die placement of points widi coordinates x, y, and x on the number line,

The distance between x and z (that is, x - z) is the sum of the distance between x andy (that is, x - y) and the distance between y and z (that is, y - z).

Therefore (x- z) > (x y),which means that x-z represents the greater of the numbers represented by (x - z) and (x - y). Thus, x-z represents the greatest of the numbers represented by&e answer choices.

Alternatively,

y > z given

-y < -z multiply both sides by -1

x - y < x - z add x to both sides

Thus, x - z represents the greater of the numbers represented by (x - z) and (x - y). Therefore, x - z represents the greatest of the numbers represented by the answer choices.

The correct answer is A.

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From x > y and y > z, it follows that x > z.These inequalities imply the following about the differences that are given in the answer choices:Since the expressions in A and B represent positive numbers and the expressions in C, D, and E represent negative numbers, the latter can be eliminated because every negative number is less than every positive number. To determine which of x - z and x - y is greater, consider die placement of points widi coordinates x, y, and x on the number line,The distance between x and z (that is, x - z) is the sum of the distance between x andy (that is, x - y) and the distance between y and z (that is, y - z).Therefore (x- z) > (x y),which means that x-z represents the greater of the numbers represented by (x - z) and (x - y). Thus, x-z represents the greatest of the numbers represented by&e answer choices.Alternatively,y > z given-y < -z multiply both sides by -1x - y < x - z add x to both sidesThus, x - z represents the greater of the numbers represented by (x - z) and (x - y). Therefore, x - z represents the greatest of the numbers represented by the answer choices.The correct answer is A.