Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Join a FREE 1-day verbal workshop and learn how to ace the Verbal section with the best tips and strategies. Limited for the first 99 registrants. Register today!

If x + z > y + z, then which of the following must be true?
[#permalink]

Show Tags

Updated on: 02 Apr 2019, 05:10

X + Z > Y + Z Therefore, X > Y.

1. X - Z > Y - Z X > Y - Z + Z X > Y Statement 1 is correct and sufficient.

2. XZ > YZ If X = 1 , Y= -1 , Z = -2 1-1 > -1-2 0 > -3 However if we substitute the values into statement 2 : -2 < 2 Hence, statement 2 is not true.

3. X/Z > Y/Z If X = 1 , Y= -1 , Z = -2 1-1 > -1-2 0 > -3 However if we substitute the values into statement 3 : 1/-2 < -1/-2 Hence, statement 3 is not true.

Answer : A

Posted from my mobile device

Originally posted by justus23 on 02 Apr 2019, 05:05.
Last edited by justus23 on 02 Apr 2019, 05:10, edited 1 time in total.

Re: If x + z > y + z, then which of the following must be true?
[#permalink]

Show Tags

02 Apr 2019, 05:12

1

justus23 wrote:

X + Z > Y + Z Therefore, X > Y.

1. X - Z > Y - Z X > Y - Z + Z X > Y Statement 1 is correct and sufficient.

2. XZ > YZ X(Z) > Y(Z) X > Y Statement 2 is correct and sufficient.

3. X/Z > Y/Z

If X = 1 , Y= -1 , Z = -2 1-1 > -1-2 0 > -3 However if we substitute the values into statement 3 : 1/-2 < -1/-2 Hence, statement 3 is not true.

Answer : D

Posted from my mobile device

Hi Another rule in inequality You cannot divide by an unknown (i.e., a variable) unless you are sure of its sign since you do not know whether you must flip the sign of the inequality

Consider

-3<1 ( multiple by -1) becomes 3<-1 (which is not true )

Re: If x + z > y + z, then which of the following must be true?
[#permalink]

Show Tags

02 Apr 2019, 06:22

Top Contributor

Bunuel wrote:

If \(x + z > y + z\), then which of the following must be true?

I. \(x – z > y – z\)

II. \(xz > yz\)

III. \(\frac{x}{z} > \frac{y}{z}\)

(A) I only (B) II only (C) III only (D) I and II only (E) II and III only

Let's check each statement

(I) x – z > y – z It is given that: x + z > y + z If we subtract 2z from both sides, we get: x - z > y - z Perfect! Statement I must be true.

Check the answer choices . . . ELIMINATE B, C and E since they suggest that statement 1 is NOT true.

(II) xz > yz This statement need not be true. It is given that: x + z > y + z So, one possible case is that x = 5, y = 4 and z = -1, since 5 + (-1) > 4 + (-1) When we plug these values into Statement II, we get: (5)(-1) > (4)(-1) Simplify to get: -5 > -4, which is NOT TRUE So, Statement II is not true Check the remaining answer choices . . . ELIMINATE D

By the process of elimination, the correct answer is A

Re: If x + z > y + z, then which of the following must be true?
[#permalink]

Show Tags

03 Aug 2019, 14:28

Bunuel wrote:

If \(x + z > y + z\), then which of the following must be true?

I. \(x – z > y – z\)

II. \(xz > yz\)

III. \(\frac{x}{z} > \frac{y}{z}\)

(A) I only (B) II only (C) III only (D) I and II only (E) II and III only

I can solve with algebra but I avoid doing that if Possible. Since there are no restrictions on x y z being positive or negative or anything else, Lets pick numbers x=4,y=3,z=2 Given condition satisfies so we are good. Turns out I,II,III all three are true. Good, there is no option which says all 3. Even if there was you should always try at least one more pair.

Let's try negative z. z=-1,x=4,y=3. Given condition satisfies so we are good. This time both II and III are not true. Hence A. I only.
_________________

Please be generous in giving kudos “Practice is the hardest part of learning, and training is the essence of transformation.” ― Ann Voskamp Software Tester currently in USA ( )