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If x < y, which of the following must be true?
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Bunuel
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If x < y, which of the following must be true? [#permalink] New post  10 Mar 2020, 03:24
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If x < y, which of the following must be true?

(A) x < y^2
(B) x^2 < y
(C) x^2 < y^2
(D) (x – y)^2 > 0
(E) x^3 > y
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Re: If x < y, which of the following must be true? [#permalink] New post  10 Mar 2020, 03:43
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Bunuel wrote:
If x < y, which of the following must be true?

(A) x < y^2
(B) x^2 < y
(C) x^2 < y^2
(D) (x – y)^2 > 0
(E) x^3 > y


x - y < 0

Squaring both sides

(x - y)^2 > 0

Answer: Option D
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Re: If x < y, which of the following must be true? [#permalink] New post  10 Mar 2020, 03:49
Bunuel wrote:
If x < y, which of the following must be true?

(A) x < y^2
(B) x^2 < y
(C) x^2 < y^2
(D) (x – y)^2 > 0
(E) x^3 > y


Asked: If x < y, which of the following must be true?

(A) x < y^2
(B) x^2 < y
(C) x^2 < y^2
(D) (x – y)^2 > 0 must be true since \(x-y \neq 0 \)
(E) x^3 > y

IMO D
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Farina
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Re: If x < y, which of the following must be true? [#permalink] New post  15 Mar 2020, 05:46
Kinshook wrote:
Bunuel wrote:
If x < y, which of the following must be true?

(A) x < y^2
(B) x^2 < y
(C) x^2 < y^2
(D) (x – y)^2 > 0
(E) x^3 > y


Asked: If x < y, which of the following must be true?

(A) x < y^2
(B) x^2 < y
(C) x^2 < y^2
(D) (x – y)^2 > 0 must be true since \(x-y \neq 0 \)
(E) x^3 > y

IMO D


If we plug in values say x = -3 and y = -2 we dont get the correct answer D, instead A is correct in this case?
Can you please explain this.
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Re: If x < y, which of the following must be true? [#permalink] New post  15 Mar 2020, 23:01
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Farina wrote:
Kinshook wrote:
Bunuel wrote:
If x < y, which of the following must be true?

(A) x < y^2
(B) x^2 < y
(C) x^2 < y^2
(D) (x – y)^2 > 0
(E) x^3 > y


Asked: If x < y, which of the following must be true?

(A) x < y^2
(B) x^2 < y
(C) x^2 < y^2
(D) (x – y)^2 > 0 must be true since \(x-y \neq 0 \)
(E) x^3 > y

IMO D


If we plug in values say x = -3 and y = -2 we dont get the correct answer D, instead A is correct in this case?
Can you please explain this.



x = -3 and y = -2
i.e (-3+2)^2 > 0

Tip: If x is not equal to y, the square of sum or difference of x and y is always greater than 0. Option D is always correct.
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wizakoraksha
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Re: If x < y, which of the following must be true? [#permalink] New post  16 Mar 2020, 02:58
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Here, the given statement = x < y. We can also re-write the statement as x-y < 0.

If you square the statement on both sides, the greater than / lesser than sign also changes sides.

Here squaring both sides we get (x-y)^2 > 0.

When looking at the answer options here, D is exactly in line with the answer we have derive because, x < y and x-y isn't 0.

Hence the correct answer is D.

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sathriyan
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Re: If x < y, which of the following must be true? [#permalink] New post  03 Apr 2020, 05:31
wizakoraksha wrote:
Here, the given statement = x < y. We can also re-write the statement as x-y < 0.

If you square the statement on both sides, the greater than / lesser than sign also changes sides.

Here squaring both sides we get (x-y)^2 > 0.

When looking at the answer options here, D is exactly in line with the answer we have derive because, x < y and x-y isn't 0.

Hence the correct answer is D.

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GMAT Tutor at Wizako GMAT Classes & Online Courses


How can we square both sides the highlighted portion, Since we don't have any information about the sign of the X-Y?
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abhitg0612
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Re: If x < y, which of the following must be true? [#permalink] New post  06 Apr 2020, 06:01
Option D is right -

X < Y
X - Y < 0
** Square of any value is > 0

Option A is not correct for few cases where X & Y lie between 0 & 1, X = 0.3, Y = 0.4 & Y^2 = 0.16
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