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 GRE 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:
Your score will improve and your results will be more realistic
Is there something wrong with our timer?Let us know!
Get 30% off any Target Test Prep GRE plan during our Flash Sale. Just enter the coupon code FLASH30 at checkout to save big. Hurry up and grab the offer before it's too late!
Prep Club for GRE test are free and open on Monday, May 27th, GMAT Club Tests will be Absolutely Free! Including all the Quizzes, Questions, and Tests. 12 AM - 11:59 PM PDT
Join Brian and many other students who have used Target Test Prep to score high on the GRE. Grab a 30% discount before it’s too late, or try before you buy with a 5-day, full-access trial of the course for FREE.
Re: If x + z > y + z, then which of the following must be true?
[#permalink]
30 Mar 2019, 12:09
1
Expert Reply
We can always add or subtract from both sides of an inequality. So if we just subtract z from both sides, we'll get x > y.
For statement (I), we can just add z to both sides to also get x > y. So that is definitely true.
For statements (II) and (III), though, there's a kick. We can only multiply or divide by a variable if we know its sign. This is because if we multiply or divide both sides of an inequality by a negative number, then the direction of the inequality flips. For example, 4 > 2, but if we multiply both sides by –2, then we get -8 < -4.
Since we don't know if z is positive or negative, we can't multiply or divide both sides by it. We don't know if we'd have to flip the sign or not. Hence, we don't know if (II) and (III) are true or not. If z is positive then they are true, but if z is negative, they are not.
If x + z > y + z, then which of the following must be true?
[#permalink]
31 Mar 2019, 07:20
2
Carcass 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]
17 Apr 2024, 09:08
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.