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

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

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17 Jun 2019, 10:49
EMPOWERgmatRichC wrote:
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!

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

May I know how did you consider that there is no chance for B to be the correct choice? Choice B (-16) is also closer to 0 (if I compare -16 with -20)!
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Posts: 958
Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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17 Jun 2019, 11:03
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__

Hey man look
it takes a lot of practice to just strike an option you can blindly start with

Simply given that
xy= 160

and that
x=2y-4

Now check it out you'll get a quadratic in y

Split the middle term, you'll get
y=-8, 10

we know y has to be neg therefore y=-8

we assumed y as greater of two, there you have it

No hard work required

Option methods can be tricky sometimes
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Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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17 Jun 2019, 11:06
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Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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17 Jun 2019, 11:23
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

The combination of greater and lower numbers are -8 & -20 (if you multiply them you will get 160) or -10 & -16 (if you multiply them you will get 160 too). So, A, B and E are out. The contender (greater) are just -8 and -10. Here, If we multiply -10 and -16 we'll get 160. But, the twice of the greater of -10 must be -20 (where -16 does not make sense). The the correct choice 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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19 Jun 2019, 02:43
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__

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.
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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 Jun 2019, 09:18
Thank you so much for your feedback. I've learned a different thing about the order of the option .....
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The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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15 Sep 2019, 09:45
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

Given:
1. The product of two negative numbers is 160.
2 .The lesser of the two numbers is 4 less than twice the greater

Asked: What is the greater number?

Let the numbers be x & y
xy = 160
x = 2y-4
y (2y-4) = 160
y(y-2) = 80
y^2 - 2y - 80 = 0
(y-10)(y+8)=0
y = 10 or -8
Since x & y are negative
y = -8
x = -20

Greater number = y = -8

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

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05 Nov 2019, 18:08
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

You just need to be careful while solving with options.

Greater = -8
Lesser = -8*2 - 4 = -20

Product = 160

Remember we are dealing with negatives. 4 less than -16 is -20.
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Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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05 Nov 2019, 19:24
i think this is not a 700 level question. This is probably at most 550-600 level.
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Re: The product of two negative numbers is 160. If the lesser of the two  [#permalink]

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05 Nov 2019, 19:38
Hea234ven wrote:
i think this is not a 700 level question. This is probably at most 550-600 level.

We appreciate your feedback! But instead of that you could have posted the solution to the question

It may not be a 700 level question for you but based on the data of about 2000 people who have attempted this question, we can surely say it is on the higher side of the spectrum. And also to be accounted is exam day factor. Trust me if this question appears to you during real exam there is a high chance you will make a mistake and that will make this question tough for you.

Anyway, Focus on helping the community

Thank you!
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Re: The product of two negative numbers is 160. If the lesser of the two   [#permalink] 05 Nov 2019, 19:38

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