GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
24x^2 + bx + c=(dx+e)(fx+g)
[#permalink]
25 Dec 2019, 00:54
25 Dec 2019, 00:54
Expert Reply
7
Bookmarks
00:00
Question Stats:
71% (01:47) correct
28% (02:05) wrong based on 204 sessions
Hide Show timer Statistics
\(24x^2 + bx + c=(dx+e)(fx+g)\)
\(b,c,d,e,f,\) and \(g\) are integers
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
\(b,c,d,e,f,\) and \(g\) are integers
Quantity A |
Quantity B |
\(d+f\) |
\(26\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: 24x^2 + bx + c=(dx+e)(fx+g)
[#permalink]
04 Apr 2020, 06:31
04 Apr 2020, 06:31
6
2
Bookmarks
Carcass wrote:
\(24x^2 + bx + c=(dx+e)(fx+g)\)
\(b,c,d,e,f,\) and \(g\) are integers
\(b,c,d,e,f,\) and \(g\) are integers
Quantity A |
Quantity B |
\(d+f\) |
\(26\) |
Given: 24x² + bx + c =(dx + e)(fx + g)
Use FOIL to expand the right side to get: 24x² + bx + c = dfx² + gdx + efx + eg
On the left side, the coefficient of x² is 24.
On the right side, the coefficient of x² is df
So, we can conclude that: 24 = df
At this point, the key word in the given information is that d and f are INTEGERS
Since we know that 24 = df, we can see that there aren't many pairs of INTEGER values that have a product of 24.
We get: (1)(24) = 24, (2)(12) = 24, (3)(8) = 24, and (4)(6) = 24
Quantity A = d + f
Notice that the MAXIMUM possible value of d + f occurs when the two numbers are 1 and 24, in which case we get us some of 25
This means d + f will always be less than 26
Answer: B
Cheers,
Brent
General Discussion
Re: 24x^2 + bx + c=(dx+e)(fx+g)
[#permalink]
25 Dec 2019, 01:30
25 Dec 2019, 01:30
1
You can solve this very easily. Since 24x2+bx+c can be expressed as (x-x1)(x-x2), you can consider d and f equal to 1. Therefore d+f=2 < 26. Regards!
