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Math Expert V
Joined: 02 Sep 2009
Posts: 58414
If x<0,y>0, and |x|>|y|, which of the following must be true?  [#permalink]

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Difficulty:   15% (low)

Question Stats: 75% (01:21) correct 25% (01:20) wrong based on 758 sessions

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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.

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

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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.

say x=-6 and y=3; say x=-0,5 and y=0,3. Plug them into the answer choices and the only one that must be true is E.
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GMAT 1: 620 Q46 V30 Re: If x<0,y>0, and |x|>|y|, which of the following must be true?  [#permalink]

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1
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.

Thanks!
Math Expert V
Joined: 02 Aug 2009
Posts: 7967
Re: If x<0,y>0, and |x|>|y|, which of the following must be true?  [#permalink]

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the three inequalities tell us ..
x is -ive and y is +ive..
x is farther than y from 0 on a line..
so ans E
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Math Expert V
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Posts: 58414
Re: If x<0,y>0, and |x|>|y|, which of the following must be true?  [#permalink]

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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.

VERITAS PREP OFFICIAL SOLUTION:

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

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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
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If x<0,y>0, and |x|>|y|, which of the following must be true?  [#permalink]

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Hi All,

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.

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

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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.
Math Expert V
Joined: 02 Aug 2009
Posts: 7967
Re: If x<0,y>0, and |x|>|y|, which of the following must be true?  [#permalink]

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

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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

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]--------->
More to the left of zero = smaller

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

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generis wrote:
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

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]--------->
More to the left of zero = smaller

Guten Tag Generis Option D is not correct because if if x= -3 and y= 2

-3 < 2 then by multiplying by -1 i get 3 > - 2 and since y>0, hence it cant be true. Am i thinking correctly ? thank you !  Re: If x<0,y>0, and |x|>|y|, which of the following must be true?   [#permalink] 24 Feb 2018, 10:51
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