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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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:

Re: If x<0,y>0, and |x|>|y|, which of the following must be true? [#permalink]

Show Tags

06 Feb 2015, 22:26

1

This post received KUDOS

x<0, y>0, and |x| > |y|

The above statements mean that the magnitude of x is greater than the magnitude of y but x is negative. So, if we make both of them -ve by changing the sign of y to -ve i.e. -y , then -y, which has a magnitude less than x, will be greater than x. Hence (E).

U can also solve this problem fairly quickly if u plot x and y on a number line. x will be at a greater distance from 0 on the left hand side than y on the right hand side.

Let’s go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn’t have to be true – consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us –x > y. Remember that x < 0, so –x = |x|, and y is positive, so |y| = y. Thus –x > y is the same statement as |x| > |y|, and (E) must be true.
_________________

Re: If x<0,y>0, and |x|>|y|, which of the following must be true? [#permalink]

Show Tags

13 Jun 2015, 11:00

First, I will put the variables in a tabular format. Then try to plug in values to the variables which satisfy all the given conditions . Match the answer choices . e.g. X Y !X! !Y! -X -Y -4 3 4 3 4 -3

From the answer choices, you can see that only option E matches. i.e. X<-Y

This question involves Number Properties and can be solved by TESTing VALUES.

We're given three facts to work with: 1) X < 0 2) Y > 0 3) |X| > |Y|

We're asked "which of the following MUST be true", which is the same as asking "which of the following is ALWAYS TRUE no matter how many different examples we can come up with?" We can TEST VALUES to prove which of the answers is sometimes NOT true (and you'll likely find that the right pair of values can be used to eliminate MORE than one answer)....

Answer A: X > Y IF...X = -3, Y = 2, then this answer is NOT true. Eliminate A.

Answer B: Y^2 > X^2 If...X = -3, Y = 2, then this answer is NOT true. Eliminate B.

Answer C: X^3 > Y^2 IF...X = -3, Y = 2, then this answer is NOT true. Eliminate C.

Answer D: -X < Y If...X = -3, Y = 2, then this answer is NOT true. Eliminate D.

Since we've eliminated 4 answers, there only answer that's left must be the correct one.

Re: If x<0,y>0, and |x|>|y|, which of the following must be true? [#permalink]

Show Tags

12 Nov 2017, 01:16

Used negation to get to E. Since x must be negative, A, B, C, and D are out. But is the sign correct in option E? I understand that -(-x) > y is the same as |x| > |y|, but E says x < -y.
_________________

We are what we REPEATEDLY do. GREATNESS then is not ACT, but a HABIT.

Used negation to get to E. Since x must be negative, A, B, C, and D are out. But is the sign correct in option E? I understand that -(-x) > y is the same as |x| > |y|, but E says x < -y.

Hi.. Whenever you multiply both sides of INEQUALITY by '-', you change the sign of INEQUALITY. That is -x>y......-*-x.<-y....x<-y Reason is the properties of number when NEGATIVE is OPPOSITE of when POSITIVE. Larger the numeric value, larger the number 8>4 While when negative, larger the numeric value, smaller the number -8<-4

Example of -x>y -2>-7.....-*-2<-*-7....2<7
_________________

If x<0,y>0, and |x|>|y|, which of the following must be true? [#permalink]

Show Tags

13 Nov 2017, 10:21

1

This post received KUDOS

1

This post was BOOKMARKED

Bunuel wrote:

If x<0, y>0, and |x| > |y|, which of the following must be true?

A. x > y B. y^2 > x^2 C. x^3 > y^2 D. –x < y E. x < –y

Kudos for a correct solution.

Translate: x < 0 --> x is negative y > 0 --> y is positive

|x| > |y| --> the "positive" value of x, -(-x), is greater than y. Magnitude of x > magnitude of y

Or, x is more negative than y is positive: on the number line, x's distance from 0, to the left, is farther than y's distance from 0, to the right.

Pick numbers and check answers. x = -3, y = 2

Plug in A. x > y: FALSE. -3 is not > 2

B. y^2 > x^2: FALSE. 4 is not > than 9

C. x^3 > y^2: FALSE. -27 is not greater than 4

D. –x < y. FALSE. -(-3) = 3. 3 is not less than 2

E. x < –y: TRUE. -3 is less than -2

Answer E

Assess signs x = -3, y = +2

A. x > y: (-) > (+)?? NO

B. y^2 > x^2. Integers raised to even powers = positive. Small (+) > Bigger (+)?? NO

C. x^3 > y^2: (-) raised to odd power = negative. (-) > (+)?? NO

D. –x < y. For (x), the negative, or opposite (which is one thing the "-" sign means), of a negative is positive. So bigger positive < smaller positive?? NO

E. x < –y. For y, the negative of a positive is negative. More negative < less negative? YES. <--[-3]---[-2]-------[0]--> More to the left of zero = smaller