The product of two negative numbers is 160. If the lesser of the two

-a*-b =160 --1

-a=(-2b)-4 --2

substituting eq 2 in 1

(-2b-4)*-b=160
2b^2+4b-160=0
b^2+2b-80=o
b^2+10b-8b-80=0
b= -10,8
therefore -b =-8

substitute the value in eq 2
-a = -16-4= -20

therefore the larger number = -8

Consider two negative numbers as \(n_1\) and \(n_2\).

\(n_1 * n_2 = 160\)
\(n_2 = 2n_1 - 4\) ..... substitute this in above equation.

\(n_1 * (2n_1 - 4) = 160\)
\(2n_1^2 - 4n_2 - 160 = 0\)
\(n_1^2 - 2n_2 - 80 = 0\)
\((n_1 - 10) (n_1 +8) = 0\)
\(n_1 = 10\) and \(n_1 = -8\)

as mentioned in question, numbers are negative, we'll consider \(n_1 = -8\). substitute this in second equation.

\(n_2 = 2 * (-8) - 4\)
\(n_2 = -20\)

Hence the greater number is \(-8\).

\(Answer = D\)

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:

(x)(y) = 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 and y = 2(-8) -4 = -20.

Thus, the greater number is -8.

Answer: D

i think i did this a little different than most people above.

first, broke 160 down into pairs (below):

1, 160
2, 80
4, 40
5, 32
8, 20
10, 16

NOW, remember the question tells you that the LOWER # is 4 less than TWICE the greater? --> L=2S+4

Okay, let's see which #s (from list above) make sense...

1, 160
2, 80
4, 40
5, 32
8, 20
10, 16

Don't follow my logic? Well, let's set S=8. L=16+4. So, if S=8, L=20. Perfect fit.
> Don't fall for the trap: 10, 16. Here, if S=10, then L=24 [aka 2*10+4]

kudos please if you find this helpful

x = lesser
y = greater

(2y-4)(y) = 160
a , b , and c are too high values, so eliminate them

For e, (-12)(-4) =/ 160

For D, (-16-4)(-8) = (-20)(-8) = 160
Therefore, D)-8 is the answer

Hi All,

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:

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

Hi VeritasKarishma
Are you talking about middle option (C) or middle value (20,16,10,8,4) by the highlighted part middle option.?
If the option say something like :
A) -20
B) -16
C) -8
D) -10
E) -4
How can we start if this is the case? Will we start by C or D?
Thanks__

In GMAT, usually your options will be in either increasing or decreasing order. Middle option or middle value would be the same thing. But of course, if the options are random in sequence, then middle option has no significance. We should try the middle value.

Adding the question 'code' for reference : PS02600

_______________________
Added the ID. Thank you!

Answer: Option D

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Correct Option : D (-8)

by the information provided in Question
- lesser number is 4 less than twice the greater, let the equation be (2x) - 4
- The product of two negative numbers is 160. smaller number x greater number = 160

Find greater Number ?
Substitue the below value in the equation

A) -20 = (-20x2)-4 = (-44)x(-20)= 880
B) -16
C) -10
D) -8 = (-8x2)-4 = (-20)x(-8) = 160 - correct
E) -4

use the options

Put C in a= 2b-4 , Since it dosen't work
you need a bigger number , Put D you will get -8, -20

Since both number are -ve

-8 is greater than -20

so -8 is correct.

\(x*y = 160\)

\(x = 2y - 4\)

Now, \((2y - 4)*y = 160\)

Or, \(2(y - 2)*y = 160\)

Or, \((y - 2)*y = 80\)

Or, \(y^2 - 2y - 80 = 0\)

Or, \(y^2 - 10y + 8y - 80 = 0\)

Or, \(y(y - 10) +8 (y - 10) \)

Or, \(y = -8 \) , considering the negative value only... Thus \(x = -20\)

Imagine a number line y will be to the right of x , so \(y < x\), answer must be (D)

I interpreted this question differently, now I know it was wrong, but please help me understand how to avoid this ambiguity

let the smaller number be "a" and the greater be "b"

-> lesser of the two numbers is 4 less than twice the greater

"a" is 4 less than twice the"b"
= a-4 < 2b
= a = 2b +4

I understood it as - a is 4 less, than 2b

Hi Sakshi516B,

With this prompt, the word "is" represents the "equals sign" in the equation - so when translating this sentence, we have...

"The lesser of two numbers..."

A

"is"

A =

"4 less then...." --> this is a comparison of 2 values (for example 1 and 5, 10 and 14, -6 and -2, etc.), so we have to subtract 4 from the larger value.

A = ____ - 4

"twice the greater number"

A = 2(B) - 4

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

Contact Rich at: Rich.C@empowergmat.com

This explanation is very helpful
Thank You so much

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