|
|
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.
04 Mar 2021, 01:15
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
40% (01:57) correct
60%
(01:38)
wrong
based on 215
sessions
History
Date
Time
Result
Not Attempted Yet
In the equation \(x^2+bx+c=0\), b and c are constants, and x is a variable. If m and k are the roots of \(x^2+bx+c=0\), then m−k=?
(1) c = −10
(2) b = 3
(1) c = −10
(2) b = 3
05 Mar 2021, 01:30
Kudos
Bookmarks
Bunuel
Even when we combine the statements we get \(x^2+3x-10=0\) --> \((x+5)(x-2)=0\) --> \(x=-5\) or \(x=2\) --> m and k are -5 and 2, but we don't know which one is which --> m-k is either -5-2=-7 or 2-(-5) = 7.
Answer: E.
General Discussion
04 Mar 2021, 01:34
Kudos
Bookmarks
Bunuel
Question: m-k = ?, where m and k are the roots of the equation \(x^2+bx+c=0\)
FOr any Quadratic Equation of the type \(ax^2+bx+c = 0\)
Sum of the roots i.e. \(α+β = \frac{-b}{a}\)
Product of the roots i.e. \(α*β = \frac{c}{a}\)
Also, \((α-β)^2 = (α+β)^2 - 4*αβ\)
So to find m-k, we need Sum of the roots as well as the product of the roots
i.e. we require values of both b and c while a = 1 in \(x^2+bx+c=0\)
Statement (1) c = −10
NOT SUFFICIENT
Statement (2) b = 3
NOT SUFFICIENT
Combining the statements
We have both b and c hence
SUFFICIENT
Answer: Option C
