If x

Question

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

nick1816 · Answer

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)

LeoN88 · Answer

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

ScottTargetTestPrep · Answer

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

Adarsh_24 · Answer

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

I) xy<80
II) x/y>1
III) x^2+y^2>1

I. We know x<a , y<b => xy < ab only when x,y,a,b +ve
So we are almost sure this is not true
We know if we want product of 2 small numbers to be very large, we pick 2 negative numbers.
Here such that bgger than 80. Maybe 90. So -10 and -9.
x<y then x=-10 and y=-9
xy =90
So False.

II. x/y > 1
We are given x<y
So to flip the sign same and to get x/y>1. y should be -ve.
So pick a +ve y to prove false such that it suits our constraints.
x=2 and y=3 example

III.
x^2+y^2>1
Sum of two squares are greater than or equal to 0.
So we try to get x^2+y^2=0
But only possible when x=y=0. Not allowed.
lets try for x^2+y^2=1
x=0 y=1 suits our needs

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions