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Math Expert V
Joined: 02 Sep 2009
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The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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Question Stats: 67% (02:05) correct 33% (02:24) wrong based on 2541 sessions

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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

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Veritas Prep GMAT Instructor V
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Posts: 10506
Location: Pune, India
Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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2
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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

Use the options. The options give you the greater number. Start from the middle option.

(C) - 10
Twice of -10 is -20 and 4 less is -24.
-24 * -10 = 240 (Not correct)

We need lower product (of 160) so try option (D).

(D) - 8
Twice of -8 is -16 and 4 less is -20.
-20 * -8 = 160
Correct

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

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1
1
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

let two numbers are a and b

a = 2b-4

Find value of b.

(2b-4)*b = 160
b*(b-2) = 80

b =-8 (Given that numbers are negative)

##### General Discussion
Director  G
Joined: 20 Feb 2015
Posts: 722
Concentration: Strategy, General Management
Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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5
-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
Intern  Joined: 28 Mar 2016
Posts: 5
Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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1
2
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

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 $$-8$$.

$$Answer = D$$
Intern  Joined: 21 Apr 2016
Posts: 27
Location: United States
Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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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! Current Student Joined: 18 Oct 2014
Posts: 772
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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nk18967 wrote:
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. _________________
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Intern  Joined: 21 Apr 2016
Posts: 27
Location: United States
Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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1

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..! nk18967 wrote:
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. Intern  Joined: 07 Dec 2014
Posts: 4
Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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

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2
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.

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

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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

1. xy=160
2. x=2y-4
dividing 1. by 2.➡
y^2-2y-80=0
y=-8
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Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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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

$$-a*-b = 160$$

Let -a > -b

So, -b = -2a - 4

Or, -a( -2a - 4 ) = 160

Or, 2a^2 + 4a = 160

Or, 2a ( a + 2 ) = 16*10

Or, a = -8

So, b = -20

Thus, the greater number is (D) -8
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Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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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]

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

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-8*2 - 4 = -20

So greater number should be -8
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Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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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

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

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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.

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

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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....

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!

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

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A<B and Equation 1 - A*B = 160
Both A and B are <0
A = 2B - 4
2B = A +4
B= (A+4)/2

Substitute back into Equation 1
((A+4)/2 )*A = 160

2*((A+4)/2 )*A = 160

A^2 +4A - 320 = 0
(A+20)(A-16) = 0
A= -20 or 16, but since we know A<0, A must be -20

Sub into B
B= (-20+4)/2
B= -16/2
B= -8
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The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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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

Let,
Greater number = x

So, lesser number = 2x-4

Now,

(x)(2x-4)= 160

=>2x^2-4x-160=0

=>x^2-2x-80=0

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

So, the greater number is -8

Posted from my mobile device
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Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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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

Use the options. The options give you the greater number. Start from the middle option.

(C) - 10
Twice of -10 is -20 and 4 less is -24.
-24 * -10 = 240 (Not correct)

We need lower product (of 160) so try option (D).

(D) - 8
Twice of -8 is -16 and 4 less is -20.
-20 * -8 = 160
Correct

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__ Re: The product of two negative numbers is 160. If the lesser of the two   [#permalink] 17 Jun 2019, 10:40

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