Target Test Prep 20% Off Flash Sale is on! Code: FLASH20

Redeem
Target Test Prep
5-Day Free Trial
5-day free, full-access trial TTP

Available with Beat the GMAT members only code

MORE DETAILS
Target Test Prep
Magoosh
Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

MORE DETAILS
Magoosh

We have a polynomial x^2 + 4x - n for an integer n between 1 and 100, inclusive. The polynomial x^2 + 4x - n is factor

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

We have a polynomial x^2 + 4x - n for an integer n between 1 and 100, inclusive. The polynomial x^2 + 4x - n is factor

by Max@Math Revolution » Tue Feb 18, 2020 1:55 am
[GMAT math practice question]

We have a polynomial x^2 + 4x - n for an integer n between 1 and 100, inclusive. The polynomial x^2 + 4x - n is factored into (x + a)(x + b) where a and b are integers. How many different values of n satisfy the polynomial x^2 + 4x – n?

A. 5
B. 6
C. 7
D. 8
E. 9
Top
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Re: We have a polynomial x^2 + 4x - n for an integer n between 1 and 100, inclusive. The polynomial x^2 + 4x - n is fac

by Max@Math Revolution » Thu Feb 20, 2020 12:51 am
=>

We can assume a < b without loss of generality.
Since we have a + b = 4 and ab = -n, we have the following pairs of (a, b).
(-1, 5), (-2, 6), (-3, 7), (-4, 8), (-5, 9), (-6, 10), (-7, 11), (-8, 12)
Then, the possible values of n are 5, 12, 21, 32, 45, 60, 77 and 96.
We have 8 possible values of n.

Therefore, the answer is D.
Answer: D
Top
Post new topic Post Reply
• Page 1 of 1