OG Negative Numbers Q

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
D

Say the two negative numbers are x and y such that x < y.

Thus, we have xy = 160 ---(1)

Given that x = 2y – 4 ---(2)

By plugging in the value of x from (2) in ( 1), we get

(2y – 4)*y = 160

2y^2 – 4y = 160

=> y^2 – 2y = 80; taking '2' common and cancelling

y^2 – 2y – 80 = 0

y^2 – 10y + 8y – 80 = 0

=> y(y – 10) +8(y – 10) = 0

=> (y – 10) (y + 8) = 0

=> y = 10 or –8

Since the numbers are negative, and y is the greater of the two numbers x and y, the greater number = –8.

The correct answer: D

Hope this helps!

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-Jay
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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

D

Another approach to this question could be Plugging in the values from the options.

Let's try each option one by one.

A. Given that the greater number of the two numbers = –20. Thus, the smaller number = 160/(–20) = –8.

This is not possible since –8 > –20. The result is contradictory.

Since the options are arranged in ascending order and Option A value is erroneous, let's change the strategy now.

Start from Option E.

E. Given that the greater number of the two numbers = –4. Thus, the smaller number = 160/(–4) = –40. Since –4 > –40, this is possible.

Let's see if this works in the second condition.

It is given that the lesser of the two numbers is 4 less than twice the greater.

=> –40 = 2*(–4) –4

=> –40 = –8 –4 = –12

Since –40 ≠ –12. This option is incorrect.

Let's try with Option D.

D. Given that the greater number of the two numbers = –8. Thus, the smaller number = 160/(–8) = –20. Since –8 > –20, this is possible.

Let's see if this works in the second condition.

It is given that the lesser of the two numbers is 4 less than twice the greater.

=> –20 = 2*(–8) –4

=> –20 = –16 –4 = –20

Since –20 = –20. This option is the correct option.

The correct answer: D

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Bangkok | Abu Dhabi | Rome | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

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