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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]

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19 Jul 2016, 11:23

Confused about this.. The quadratic gives us two roots: (larger #)= -10 and (larger #)= +8 Curious why we didn't choose -10 since (although it is the smaller number between the roots, it is the only negative number.. and the question said that both numbers are negative). Say we chose -10, then -10 x -16 also equals 160 and in this case -10 is in fact the larger number.

I'm sure I'm missing something since everyone got D.. can someone please tell me why D and not C?

Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]

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19 Jul 2016, 11:28

1

This post received KUDOS

nk18967 wrote:

Confused about this.. The quadratic gives us two roots: (larger #)= -10 and (larger #)= +8 Curious why we didn't choose -10 since (although it is the smaller number between the roots, it is the only negative number.. and the question said that both numbers are negative). Say we chose -10, then -10 x -16 also equals 160 and in this case -10 is in fact the larger number.

I'm sure I'm missing something since everyone got D.. can someone please tell me why D and not C?

Thanks in advance!

Hi! There,

We get the quadratic as x^2 -2x -80= 0

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

x can either be -8 or +10.

But because it is given that the numbers are -ve, we will choose -8.

Hope it is clear.
_________________

I welcome critical analysis of my post!! That will help me reach 700+

Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]

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19 Jul 2016, 12:04

Thanks Divyadisha!

Just realized what a silly mistake I made!

I had let the smaller # be (-a) and let the larger # be (-b).. (-a) = 2(-b) - 4 (-a)(-b) = 160

So I solved it as: [2(-b) - 4] [-b] = 160 [-2b - 4] [-b] = 160 2b^2 + 4b - 160 = 0 b^2 + 2b - 80 = 0 (b-8) (b+10) So, b= 8 or b= -10

Here is where I forgot, that my number is actually (-b) !!!! That changes things because then my number can be either -(8) or -(-10)...which is +10.. SO... the Ans is obviously -8 since we need a -ve #!!

I hope I dont make these kind of mistakes when I'm taking the real test! Ugh..!

Divyadisha wrote:

nk18967 wrote:

Confused about this.. The quadratic gives us two roots: (larger #)= -10 and (larger #)= +8 Curious why we didn't choose -10 since (although it is the smaller number between the roots, it is the only negative number.. and the question said that both numbers are negative). Say we chose -10, then -10 x -16 also equals 160 and in this case -10 is in fact the larger number.

I'm sure I'm missing something since everyone got D.. can someone please tell me why D and not C?

Thanks in advance!

Hi! There,

We get the quadratic as x^2 -2x -80= 0

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

x can either be -8 or +10.

But because it is given that the numbers are -ve, we will choose -8.

Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]

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24 Sep 2016, 07:21

Two factors of 160 can be (1,160), (2,80), (4,40), (8, 20), (16,10), (32, 5). Considering the relation, lower = 2 higher -4, we can eliminate everything other than (8,20) and (16, 10) and the answer would be (-8, -20) i.e. -8

Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]

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09 Oct 2017, 19:25

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]

Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]

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18 Nov 2017, 03:26

ScottTargetTestPrep wrote:

Bunuel 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:

(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

hello there it says product of two negative numbers- than why you write (x)(y) = 160 shouldn't it be (-x)(-y) = 160 Also how after this x^2 - 2x - 80 = 0 you get (x - 10)(x + 8) = 0 I know formula B^2 - 4AC but couldn't use it properly, though I didn't divide whole equation by 2. Also after this (x - 10)(x + 8) = 0

you write that x = 10 or x = -8 ---> but how can x=10? if in brackets it is -10 and how can x = -8 if in brackets 8 is positive

thanks for taking time to explain and have a great day!