Last visit was: 19 Jul 2025, 18:09 It is currently 19 Jul 2025, 18:09
Close
GMAT 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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,078
Own Kudos:
18,762
 [3]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,078
Kudos: 18,762
 [3]
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,078
Own Kudos:
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,078
Kudos: 18,762
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
jn30
Joined: 03 Jan 2014
Last visit: 04 Mar 2017
Posts: 60
Own Kudos:
Given Kudos: 93
Concentration: Strategy, Operations
GMAT 1: 720 Q46 V42
GPA: 3.86
WE:Information Technology (Consulting)
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,078
Own Kudos:
18,762
 [3]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,078
Kudos: 18,762
 [3]
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
sefienolte
Can you explain why the second statement is not sufficient? I guess what you mean is that knowing a second root to the problem doesn't tell us much about whether x=1 is a root? Thanks!


-> Since this is cubic function, even if x=5 is an answer, you cannot figure out if x=1 is an answer as (x-5)(x^2+x+1)=0 is possible as well.
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 19 Jul 2025
Posts: 11,294
Own Kudos:
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert
Expert reply
Posts: 11,294
Kudos: 41,843
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
There is an equation: x^3-ax^2+bx-5=0, a and b are positive integers, is x=1 a root of this equation?

1) b-a=4
2)x=5 is a root of this equation.

\(x^3-ax^2+bx-5=0\)
Let us substitute x=1, to find the condition that should be met.

\(x^3-ax^2+bx-5=0\)
\(1^3-a*1^2+b*1-5=0\)
\(1-a+b-5=0\)
\(b-a=4\)

1) b-a=4
Meets the condition.
Sufficient

2)x=5 is a root of this equation
We know the product of three roots is -(-5)/1 or 5.
Thus, the roots could be -1*-1*5 or 1*1*5.
But, taking roots -1, -1 and 5 will make b negative. Hence, only possibility is 1, 1 and 5 and the cubic equation is \(x^3-7x^2+11x-5=0\)
Sufficient


MathRevolution, you are wrong in the OA and also in the below reply
MathRevolution
sefienolte
Can you explain why the second statement is not sufficient? I guess what you mean is that knowing a second root to the problem doesn't tell us much about whether x=1 is a root? Thanks!


-> Since this is cubic function, even if x=5 is an answer, you cannot figure out if x=1 is an answer as (x-5)(x^2+x+1)=0 is possible as well.

\((x-5)(x^2+x+1)=0…..x^3-5x^2+x^2-5x+x-5=0………x^3-4x^2-4x-5=0\)
So a=4 and b=-4 but b is supposed to be a positive integer.
So, the example is not valid.
Moderators:
Math Expert
102627 posts
455 posts