Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
50% (01:59) correct
50%
(01:54)
wrong
based on 155
sessions
History
Date
Time
Result
Not Attempted Yet
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.
1) 2a, b, and 2c are in arithmetic progression.
2) a, b/2, and c are in geometric progression.
04 Oct 2018, 01:33
Kudos
Bookmarks
aa008
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.
(B) is our answer.
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?'
