GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 11 Dec 2018, 10:54

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Prep Hour

December 11, 2018

December 11, 2018

09:00 PM EST

10:00 PM EST

Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
• ### The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

# Are the roots of quadratic equations equal?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 05 Oct 2017
Posts: 47
GMAT 1: 560 Q44 V23

### Show Tags

Updated on: 04 Oct 2018, 00:40
3
00:00

Difficulty:

65% (hard)

Question Stats:

50% (01:43) correct 50% (01:31) wrong based on 44 sessions

### HideShow timer Statistics

Are the roots of the quadratic equation $$ax^2+bx+c=0$$ equal? This quadratic equation has real roots.

1) 2a, b, and 2c are in arithmetic progression.
2) a, b/2, and c are in geometric progression.

_________________

It’s not that I’m so smart, it’s just that I stay with problems longer. -- Albert Einstein

Originally posted by aa008 on 03 Oct 2018, 22:13.
Last edited by aa008 on 04 Oct 2018, 00:40, edited 1 time in total.
examPAL Representative
Joined: 07 Dec 2017
Posts: 841

### Show Tags

04 Oct 2018, 00:33
aa008 wrote:
Are the roots of the quadratic equation $$ax^2+bx+c=0$$ equal?

1) 2a, b, and 2c are in arithmetic progression.
2) a, b/2, and c are in geometric progression.

The roots of a quadratic equation are equal only if the expression $$b^2 - 4ac$$ equals 0.
We'll look for statements that give us this information, a Logical approach.

(1) This tell us that b = 2a + constant but does not allow us to know if b^2 - 4ac = 0. (example for YES: 2a = b = 2c = 2, a progression with difference 0, example for NO: 2a = 2, b = 10, 2c = 18)
Insufficient.

(2) If $$b/2$$ follows $$a$$ on an arithemtic progression than $$b/2 = qa$$ and $$b = 2qa$$. If $$c$$ follows $$b/2$$ then $$c = qb/2 = q^2a$$.
Then $$b^2 - 4ac = (2qa)^2 - 4*a*(q^2a) = 4q^2a^2 - 4q^2a^2 = 0$$
Sufficient.

aa008 Please note that GMAT questions need to be well defined. In this case, it is possible to choose values for a,b,c such that there are no real roots at all. To solve this, you can change to 'assuming that the quadratic equation has real roots, are they equal?'
_________________
Intern
Joined: 05 Oct 2017
Posts: 47
GMAT 1: 560 Q44 V23

### Show Tags

04 Oct 2018, 00:41
DavidTutorexamPAL wrote:
aa008 wrote:
Are the roots of the quadratic equation $$ax^2+bx+c=0$$ equal?

1) 2a, b, and 2c are in arithmetic progression.
2) a, b/2, and c are in geometric progression.

The roots of a quadratic equation are equal only if the expression $$b^2 - 4ac$$ equals 0.
We'll look for statements that give us this information, a Logical approach.

(1) This tell us that b = 2a + constant but does not allow us to know if b^2 - 4ac = 0. (example for YES: 2a = b = 2c = 2, a progression with difference 0, example for NO: 2a = 2, b = 10, 2c = 18)
Insufficient.

(2) If $$b/2$$ follows $$a$$ on an arithemtic progression than $$b/2 = qa$$ and $$b = 2qa$$. If $$c$$ follows $$b/2$$ then $$c = qb/2 = q^2a$$.
Then $$b^2 - 4ac = (2qa)^2 - 4*a*(q^2a) = 4q^2a^2 - 4q^2a^2 = 0$$
Sufficient.

aa008 Please note that GMAT questions need to be well defined. In this case, it is possible to choose values for a,b,c such that there are no real roots at all. To solve this, you can change to 'assuming that the quadratic equation has real roots, are they equal?'

thanks for pointing it out.
_________________

It’s not that I’m so smart, it’s just that I stay with problems longer. -- Albert Einstein

Re: Are the roots of quadratic equations equal? &nbs [#permalink] 04 Oct 2018, 00:41
Display posts from previous: Sort by