If xy

Question

If xy < 5, is x < 1 ?

(1) |y| > 5
(2) x/y > 0

I got the answer is C which is correct but it was a guess work. So here is how I did this question:

Statement 1

|y| > 5 i.e. y > 5 and y > -5 or y > 5 and y < -5.

As this statement doesn't say anything about x, its clearly insufficient.

Statement 2

x/y> 0 --> This statement only tells that x and y have the same sign. Therefore insufficient.

After this I struggled to complete the question, and guessed answer C as correct answer. Can someone please help?

Show Answer

Official Answer

C

Bunuel · Accepted Answer

|y| > 5 means that y<-5 or y>5. If xy < 5, is x < 1 ? (1) |y| > 5 --> if y=10 and x=0 then the answer is YES but if y=-10 and x=2 then the answer is NO. Not sufficient. (2) \frac{x}{y}>0 --> x and y have the same sign. Still insufficient: if y=-2 and x=-1 then the answer is YES but if y=2 and x=2 then the answer is NO. Not sufficient. (1)+(2) From (2) x and y have the same sign. Now, if from (1) y>5 then 0

stonecold · Answer

Here Clearly statements 1 and two are not alone sufficient as x>1 and X<1
but combining them => x<1 as they should be of same sign and |y|>5 => if y is negative x is sufficient
if y is positive => x<<1 as Y>5
hence C

rbramkumar · Answer

May not be the easiest solution, but I find it interesting that these inequalities can be rigorously solved using graphical visualisation. Given : xy<5 is the area between the hyperbola. 1) |y| > 5: When y>5, x can only be less than 1. When y<-5, x can only be greater than -1. Thus not sufficient. 2) Same sign, so not sufficient. Combining. When y>5, x can only be less 1 BUT greater than 0. So x<1? YES When y<-5, x can only be greater than -1 BUT less than 0. So, x<1? YES E

chetan2u · Answer

1) |y|>5
So y>5, then x<1 OR
y<-5, then x can be any value as say 10 so xy=10*-5=-50<5
Insufficient

2) x/y>0
Both X and y are of same sign
X could be 10 and y =1/3..
Or X could be -5 and y -1/2..
Insufficient

Combined
Y>5, and X>0, then x<1..
y<-5 and X<0, so X<1
Sufficient

C

Basshead · Answer

If xy < 5 , is x < 1 ? (1) |y| > 5 y < -5 or y > 5 x could be less than or greater than 1. INSUFFICENT. (2) x/y > 0 x and y have the same signs. Again, x could be less than or greater than 1. INSUFFICIENT. (1&2) We know y < -5 or y >5 x must have the same sign as y. Given xy <5, there are two scenarios: if y > 5, x must be 0 < x < 1. if y < -5, x must be < 1. Sufficient. Answer is C.

CEdward · Answer

xy < 5, x < 1?

x and y can either share the same sign or opposite signs

a) |y| > 5
Implies y > 5 or y < -5
y = 6, x = -ive
y = -6, x = +ve
Insufficient.

b) x/y > 0
implies x and y have the same sign
x = 2, y = 2 NO
x = 1/2, y = 1/2 YES
Insufficient.

Combo pack:
y = 6, x = 1/2 YES
y = -6, x = -1/2 YES
X can never be greater than 1.
Sufficient.

If xy < 5, is x < 1 ?

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 Data Sufficiency (DS) Questions