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OG Negative Numbers Q

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AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
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OG Negative Numbers Q

Post Wed Jul 19, 2017 10:17 pm
The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?

A) -20
B) -16
C) -10
D) -8
E) -4

D

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Post Sun Jul 23, 2017 3:28 pm
Here's a hack for you. The testwriters know that many people will accidentally choose the LESSER number, so they'll put both the lesser and the greater in the answer choices.

From there, look for two numbers that fit. -20 is four less than 2 * -8, so those must be the two numbers, and hey hey, we're done!

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Post Tue Jul 25, 2017 11:01 am
AbeNeedsAnswers wrote:
The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?

A) -20
B) -16
C) -10
D) -8
E) -4
We are given that the product of two negative numbers is 160 and that the lesser of the two numbers is 4 less than twice the greater.

We can let x = the larger number and y = the smaller number, and we can create the following equations:

xy = 160

AND

y = 2x - 4

Substituting (2x - 4) for y in the first equation yields:

x(2x - 4) = 160

2x^2 + 4x = 160

x^2 - 2x - 80 = 0

(x - 10)(x + 8) = 0

x = 10 or x = -8

Since x is negative, x = -8. (Note that the other number, y, is -20, which is smaller than -8.)

Answer: D

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GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Most Active Expert Most Responsive Expert Most Thanked Expert
Post Sun Jul 23, 2017 3:28 pm
Here's a hack for you. The testwriters know that many people will accidentally choose the LESSER number, so they'll put both the lesser and the greater in the answer choices.

From there, look for two numbers that fit. -20 is four less than 2 * -8, so those must be the two numbers, and hey hey, we're done!

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Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
Post Tue Jul 25, 2017 11:01 am
AbeNeedsAnswers wrote:
The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?

A) -20
B) -16
C) -10
D) -8
E) -4
We are given that the product of two negative numbers is 160 and that the lesser of the two numbers is 4 less than twice the greater.

We can let x = the larger number and y = the smaller number, and we can create the following equations:

xy = 160

AND

y = 2x - 4

Substituting (2x - 4) for y in the first equation yields:

x(2x - 4) = 160

2x^2 + 4x = 160

x^2 - 2x - 80 = 0

(x - 10)(x + 8) = 0

x = 10 or x = -8

Since x is negative, x = -8. (Note that the other number, y, is -20, which is smaller than -8.)

Answer: D

_________________
Jeffrey Miller Head of GMAT Instruction

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Post Thu Jul 20, 2017 11:54 am
Hi AbeNeedsAnswers,

This question can be solved by TESTing THE ANSWERS. We can also use a bit of logic to eliminate some of the work.

We're told that the product of 2 NEGATIVE numbers is 160. We're told that the LESSER of the two numbers is "4 less than twice" the GREATER value. We're asked for that greater value.

Before we do any work, it's worth noting that a "greater" negative number is the one that's CLOSER to 0. As an example...

-1 is GREATER than -1,000

Thus, the correct answer is almost certainly going to be C, D or E. Let's TEST Answer D....

Answer D: -8

IF the greater value is -8, then the lesser values is (2)(-8) - 4 = -16 - 4 = -20
Since (-8)(-20) does equal +160, then this is an exact match for what we're looking for - and this MUST be the answer!

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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