Which of the following specifies all the possible values of xy

Question

If -4 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy ?

A) -42 < xy < 21
B) -42 < xy < 24
C) -28 < xy < 18
D) -24 < xy < 21
E) -24 < xy < 24

Staphyk · Answer

-4 < x <7 -6 < y< 3 Now ,the extremes the values can be ,considering both +ve and -ve (-6•7) < xy < (-4•-6) -42 < xy < 24 Smash that B

Posted from my mobile device

CareerGeek · Answer

Least value of xy = 7*(-6) = -42 (approx)
Maximum value of xy = -4*(-6) = 24 (approx)

--> -42 < xy < 24

IMO Option B

RJ7X0DefiningMyX · Answer

(B) -42 < xy < 24

Go for the extremes in such Qs. We can get a value ~ -42 if x = 6.99999999 and y = -5.99999999

And ~ 24 if x = -3.99999999 and y = -5.99999999

dabaobao · Answer

Extreme Points Q

-4 * -6 = 24
7 * - 6 = -42
-4 * 3 = -12
7 * 3 = 21

Therefore, max range = -42 < xy < 24 => B

Kinshook · Answer

Minimum value of xy = 7(-6) = -42
Maximum value of xy = (-4)(-6)=24

-42<xy<24

IMO B

Posted from my mobile device

elhex2 · Answer

Easier than it looks! Thank you everyone for your help!

freedom128 · Answer

Least value of xy is about 7*(-6) = -42
Max. value of xy is about -4*(-6) = 24

--> -42 < xy < 24

IMO Option B

Posted from my mobile device

CrackverbalGMAT · Answer

The question corresponds to the Max-Min Concept of Inequalities.
Whenever two ranges of inequalities are given in x and y and you need to evaluate the value of x + y , x * y, and x – y then use the max-min concept

You can use the following steps to do so:
(1)Place the two inequality ranges one below the other
(2)Make sure the inequality signs are the same in both cases
(3)If the signs are not the same use the properties of inequalities to make them the same
(4)Now add/multiply/subtract both in a straight line and diagonally to get 4 values

->The greatest value will be max and the lowest value will be min
In this question,

-4 < x < 7 and
-6 < y < 3

=>The values on multiplying vertically and diagonally are 24,21,-12,-42 and hence using the concept stated above we have

-42 <xy <24 (option b)

Devmitra Sen
GMAT SME

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.

Which of the following specifies all the possible values of xy

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

GMAT Problem Solving (PS) Questions

Which of the following specifies all the possible values of xy

Prep Toolkit

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