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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

From A we know that -(b/a)>0 , given a>0 then b must be NEG
In order both roots to be positive , discriminant must be >0
or b^2-4*a*c>0 .
A) is not suff

From B) we get (4a*c)/4*(a^2) or c/a>0 provided a>0 then c is >0
Given a+b+c>0 and b<0 then a+c>b
Substitute in equation of discriminant b with a+c and get
(a+c)^2-4ac>0 we get a^2-2ac+c^2>0
this is (a-c)^2>0 which is always positive BUT we do not know if A is not EQUAL TO C which would make (a-c)^2=0
SO E is the answer

4. The roots of a quadratic equatin ax^2+bx+c=0 are integers and a+b+c>0 and a>0. Are both the roots of the equation positive?

(1) Sum of the roots is positive.
(2) Product of the roots is positive.
IMHO C it is
1st alone
roots may be -2 and 4 sum is +ve
roots may be 2 and 4 and so on insuff
2)both +ve and both -ve insuff
both together -->from 2 we know that throots must be both +ve or -ve
but in order to have positive sum both should be +ve only
_________________

4. The roots of a quadratic equatin ax^2+bx+c=0 are integers and a+b+c>0 and a>0. Are both the roots of the equation positive?

(1) Sum of the roots is positive. (2) Product of the roots is positive.

PRIZE: Vocabulary Practice Sotware (contains 3000 words)

ax^2+bx+c=0 => x^2 +(b/a)x +(c/a)=0 since a>0, a is not 0

If this quadratic equation has two integer roots m and n, then it can be written as (x-m)(x-n)=0 where mn=c/a and -(m+n)=b/a

This is because (x-m)(x-n)=x^2-(m+n)x+mn

(1) We are told than m+n>0, which means that b/a<0 and so b<0 Also as m and n are integers m+n>=1, so |b/a|>=1 i.e |b|>=|a|=a

Summarizing, we know that a>0, b>0 and |b|=-b>=a

This means that b+a<=0 and since a+b+c>0, c>0 Thus ac>0 and so the roots have the same sign-

If the sum of the roots is positive, each must be >0 SUFFICIENT

(2) mn>0 means roots have the same sign. This doesn't tell me much.

Could they both be <0? Sure! (x+2)(x+1)=x^2+3x+2=0 has roots of -2 and -1 and a+b+c=6>0

Could they both be<0? Why not? (x-2)(x-6)=x^2-8x+12=0 has roots of 2 and 6 and a+b+c=5>0

NOT SUFFICIENT

My answer: A

Yes kevin, the answer is A.
I have a different approach...........

The roots of a quadratic equatin ax^2+bx+c=0 are integers and a+b+c>0 and a>0. Are both the roots of the equation positive?

Statement 1: Sum of the roots is positive.

ie -b/a = p where p>0
ie b= -(a x p).

Now consider the product of the roots.

Let c/a=q.

Clearly both p and q must be integers (since in the question it is given that both the roots are integers)

It is given that a+b+c>0
ie a-(axp)+(axq)>0
ie a(1-p+q)>0
It is given in the question that a>0
So (1-p+q)>0
ie q-p>-1
ie q-p>=0 (since p and q are integers)
ie q>=p
In statement 1 it is given that p>0
So clearly q>0

So from the first statement itself if sum is +ve we can conclude that product is also +ve.

5. In triangle ABC angle A is the greatest angle. D is the foot of the
perpendicular dropped on to BC from A. Is triangle ABC right-angled?
1. AD^2= BD x DC.
2. AD/DC < BD/AD.

Prize: A file on logical ability to solve the critical reasoning questions from GMAT.

5. In triangle ABC angle A is the greatest angle. D is the foot of the perpendicular dropped on to BC from A. Is triangle ABC right-angled? 1. AD^2= BD x DC. 2. AD/DC < BD/AD.

Prize: A file on logical ability to solve the critical reasoning questions from GMAT.