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If x < 10, y < 8, and x < y, what must be true?

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energetics
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If x < 10, y < 8, and x < y, what must be true? [#permalink] New post   27 May 2019, 17:04
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If x < 10, y < 8, and x < y, what must be true?

I) \(xy < 80\)

II) \(\frac{x}{y} > 1\)

III) \(x^{2} + y^{2} > 1\)

A) None
B) II only
C) III only
D) I and II only
E) II and III only
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A
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nick1816
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Re: If x < 10, y < 8, and x < y, what must be true? [#permalink] New post   27 May 2019, 17:27
I) When x= -20 and y=-10. xy=200
\(xy < 80\) can be false or true

II) x=2 and y=4.... x/y=1/2
x/y>1 can be true or false

III) x=0 and y=1, then \(x^{2} + y^{2} =1\)
\(x^{2} + y^{2} > 1\) can be true or false

(A)

energetics wrote:
If x < 10, y < 8, and x < y, what must be true?

I) \(xy < 80\)

II) \(\frac{x}{y} > 1\)

III) \(x^{2} + y^{2} > 1\)

A) None
B) II only
C) III only
D) I and II only
E) II and III only
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Re: If x < 10, y < 8, and x < y, what must be true? [#permalink] New post   27 May 2019, 17:43
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energetics wrote:
If x < 10, y < 8, and x < y, what must be true?

I) \(xy < 80\)

II) \(\frac{x}{y} > 1\)

III) \(x^{2} + y^{2} > 1\)

A) None
B) II only
C) III only
D) I and II only
E) II and III only


what must be true? Let's see we can make them false:

I (-100)(-80) > 80 False

II 2/4 < 1 False

III -1^2 + 0^2 = 1 False
A) None
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Re: If x < 10, y < 8, and x < y, what must be true? [#permalink] New post   28 May 2019, 17:40
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energetics wrote:
If x < 10, y < 8, and x < y, what must be true?

I) \(xy < 80\)

II) \(\frac{x}{y} > 1\)

III) \(x^{2} + y^{2} > 1\)

A) None
B) II only
C) III only
D) I and II only
E) II and III only



If x = -10 and y = -9, xy = 90, which is not less than 80. So I is not true.

If x = 0 and y = 1, x/y = 0, which is not greater than 1. So II is not true, either.

Likewise, if x = 0 and y = 1, x^2 + y^2 = 1, which is not greater than 1, so III is not true, either.

Answer: A
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Re: If x < 10, y < 8, and x < y, what must be true? [#permalink] New post   11 Mar 2022, 09:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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).

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Re: If x < 10, y < 8, and x < y, what must be true? [#permalink]
11 Mar 2022, 09:23
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