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OG Negative Numbers Q

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OG Negative Numbers Q

by AbeNeedsAnswers » Wed Jul 19, 2017 10:17 pm

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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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by Jay@ManhattanReview » Wed Jul 19, 2017 10:37 pm
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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by Jay@ManhattanReview » Wed Jul 19, 2017 10:47 pm
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!

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by [email protected] » 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

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by Matt@VeritasPrep » 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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by Jeff@TargetTestPrep » 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
[email protected]

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