Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 04 May 2015, 06:06

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Data Sufficiency Competition--Prizes can be won

Author Message
TAGS:
Manager
Joined: 12 Sep 2006
Posts: 92
Followers: 1

Kudos [?]: 2 [0], given: 0

ok, did a little more thinking and i am changing my answer to E

i totally forgot about a, which could be negative.

so to continue my previous thread, i found a yes scenario when combining both statements, now i need to find a no scenario to spoil answer C--

to do this, let's look at

(x+1)(-x+2)

we have -x^2+x+2, where b+c is positive and bc is also positive but this time we have one negative root and one positive root
x=-1 or x=2

therefore INSUFF together

Cicerone, is this right??
Senior Manager
Joined: 28 Aug 2006
Posts: 302
Followers: 10

Kudos [?]: 96 [0], given: 0

keeeeeekse, not convinced........
Try it again...............
Manager
Joined: 25 Sep 2006
Posts: 153
Followers: 1

Kudos [?]: 4 [0], given: 0

Viperace wrote:
B

I) I just cant get
II) Sufficient

Question ask if both roots are positive
Only one condition for that is

b < -sqrt(b^2 - 4ac )
.
.
.
=> ac > 0

II) Product of two root > 0
which means ac>0 if u work it out

[-b + sqrt(b^2 - 4ac ) ]*[-b - sqrt(b^2 - 4ac ) ] >0
b^2 - (b^2 - 4ac )>0
=> ac >0

Woots, just found the mistake I made. However my answer doesnt changes

Question ask if both roots are positive
Only one condition for that is

b < -sqrt(b^2 - 4ac )
.
.
.
=> ac < 0
=> c <0 since given a>0

I) Sum of two root>0
This implies -b/a > 0
=> b <0
This is not sufficient to tell if c<0

II) Product of two root > 0
which means c/a>0 if u work it out

[-b + sqrt(b^2 - 4ac ) ]*[-b - sqrt(b^2 - 4ac ) ]/4a^2 >0
[b^2 - (b^2 - 4ac )]/4a^2>0
=> c/a >0
=> c > 0

Which is sufficient to answer the question. "both roots are positive?"NO
Condition from I) is not needed.
Manager
Joined: 25 Sep 2006
Posts: 153
Followers: 1

Kudos [?]: 4 [0], given: 0

In fact,
b < 0 is a redundant information.

By knowing that
i) a > 0
ii) both root are positive

We can already deduce b < 0
Director
Joined: 13 Nov 2003
Posts: 793
Location: BULGARIA
Followers: 1

Kudos [?]: 27 [0], given: 0

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
Director
Joined: 09 Oct 2005
Posts: 722
Followers: 3

Kudos [?]: 12 [0], given: 0

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
_________________

IE IMBA 2010

Senior Manager
Joined: 28 Aug 2006
Posts: 302
Followers: 10

Kudos [?]: 96 [0], given: 0

GMAT Instructor
Joined: 04 Jul 2006
Posts: 1269
Followers: 23

Kudos [?]: 158 [0], given: 0

cicerone wrote:
Here comes our next question

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

Senior Manager
Joined: 28 Aug 2006
Posts: 302
Followers: 10

Kudos [?]: 96 [0], given: 0

kevincan wrote:
cicerone wrote:
Here comes our next question

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

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.

Statement 2 alone is not sufficient..........

So A
Senior Manager
Joined: 28 Aug 2006
Posts: 302
Followers: 10

Kudos [?]: 96 [0], given: 0

Here comes our next question

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?

Prize: A file on logical ability to solve the critical reasoning questions from GMAT.
Senior Manager
Joined: 28 Aug 2006
Posts: 302
Followers: 10

Kudos [?]: 96 [0], given: 0

Hey folks, r u trying or not?
_________________
Director
Joined: 01 Oct 2006
Posts: 500
Followers: 1

Kudos [?]: 18 [0], given: 0

St 1 is sufficient.
angle b = angle c
ab=ac
angle dac=45
thus angle bac =90

st 2 is not sufficient.

Director
Joined: 01 Oct 2006
Posts: 500
Followers: 1

Kudos [?]: 18 [0], given: 0

St 1 is sufficient.
angle b = angle c
ab=ac
angle dac=45
thus angle bac =90

st 2 is not sufficient.

Senior Manager
Joined: 28 Aug 2006
Posts: 302
Followers: 10

Kudos [?]: 96 [0], given: 0

_________________
Senior Manager
Joined: 28 Aug 2006
Posts: 302
Followers: 10

Kudos [?]: 96 [0], given: 0

I am waiting..........
_________________
Director
Joined: 01 Oct 2006
Posts: 500
Followers: 1

Kudos [?]: 18 [0], given: 0

Senior Manager
Joined: 31 May 2006
Posts: 381
Location: Phoenix AZ
Followers: 1

Kudos [?]: 8 [0], given: 0

cicerone wrote:
Here comes our next question

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?

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

D.

If Angle A is right angle, then AD^2 = BD x DC
Senior Manager
Joined: 28 Aug 2006
Posts: 302
Followers: 10

Kudos [?]: 96 [0], given: 0

Yes the answer must be D

In a right angled triangle

Clearly 1 says AD^2 = BD x DC
Sufficient

Clearly 2 says AD^2 !=BD x DC

Sufficient

So D

yogeshsheth, i have sent the link to the file.........
_________________
Senior Manager
Joined: 28 Aug 2006
Posts: 302
Followers: 10

Kudos [?]: 96 [0], given: 0

Hey just relax with this question.................
No prize................
This is a simple one...........

6. How many sons does Mr. John have?

1. Mrs. John has 3 sons.
2. Peter is taller of the John's sons.

Don't relax too much............

A lot more to come
_________________
SVP
Joined: 05 Jul 2006
Posts: 1519
Followers: 5

Kudos [?]: 115 [0], given: 39

How many sons does Mr. John have?

1. Mrs. John has 3 sons.
2. Peter is taller of the John's sons

ONE INSUFF

TWO

THEY ARE TWO

(TALLER )

Go to page   Previous    1   2   3    Next  [ 57 posts ]

Similar topics Replies Last post
Similar
Topics:
Data Sufficiency 6 09 Aug 2008, 17:48
data sufficiency 1 03 Jul 2008, 04:16
data sufficiency 3 03 Jul 2008, 04:09
data sufficiency 5 03 Jul 2008, 03:43
Data Sufficiency 2 14 Aug 2006, 11:50
Display posts from previous: Sort by