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
OG Negative Numbers Q
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 394
- Joined: Sun Jul 02, 2017 10:59 am
- Thanked: 1 times
- Followed by:5 members
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Say the two negative numbers are x and y such that x < y.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
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!
Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
-Jay
_________________
Manhattan Review GMAT Prep
Locations: New York | Bangkok | Abu Dhabi | Rome | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Another approach to this question could be Plugging in the values from the options.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
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!
Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
-Jay
_________________
Manhattan Review GMAT Prep
Locations: New York | Bangkok | Abu Dhabi | Rome | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
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!
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!
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
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.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 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]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews