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.
May 1810:00 AM PDT
-11:00 AM PDT
Join us in a live GMAT practice session and solve 25 challenging GMAT questions with other test takers in timed conditions, covering GMAT Quant, Data Sufficiency, Data Insights, Reading Comprehension, and Critical Reasoning questions.
May 1212:00 PM EDT
-11:59 PM EDT
Make the most of your break with the most realistic GMAT™ prep. Take up to $700 off select products. Ends 6/1
May 1501:00 PM IST
-11:00 AM IST
Start your journey with a fully customized action plan and work with a dedicated mentor to achieve a 735+ score.- May 19
12:00 PM PDT
-01:00 PM PDT
Scoring 329 on the GRE is not always about using more books, more courses, or a longer study plan. In this episode of GRE Success Talks, Ashutosh shares his GRE preparation strategy, study plan, and test-day experience, explaining how he kept his prep.... - Jun 10
06:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
18 Apr 2019, 05:51
Kudos
Bookmarks
B
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:
38% (02:26) correct
62%
(02:27)
wrong
based on 103
sessions
History
Date
Time
Result
Not Attempted Yet
\(a\) and \(b\) are two numbers such that:
How many distinct values can \(a\) assume?
A. 1
B. 2
C. 3
D. 4
E. None
\(2a^4 -4ab + b^2 + 2 = 0\)
How many distinct values can \(a\) assume?
A. 1
B. 2
C. 3
D. 4
E. None
20 Apr 2019, 08:03
Kudos
Bookmarks
lucajava
\(2a^4 -4ab + b^2 + 2 = 0\).....\(2a^4-4a^2+4a^2 -4ab + b^2 + 2 = 0.....2(a^4-2a^2+1)+(4a^2-4ab+b^2)=0....2(a^2-1)^2+(2a-b)^2=0\)...
Since sum of two squares will be 0 when each term is 0..
2(a^2-1)^2=0, that is a=-1 or a=1.
(2a-b)^2=0, that is a=b/2..
When a=-1.. \(2a^4 -4ab + b^2 + 2 = 0.....2*(-1)^4-4*(-1)b+b^2+2=0...2+4b+b^2+2=0....(b+2)^2=0\)..(a,b)=(-1,-2)..
When a=1.. \(2a^4 -4ab + b^2 + 2 = 0.....2*(1)^4-4*(1)b+b^2+2=0...2-4b+b^2+2=0....(b-2)^2=0\)..(a,b)=(1,2)..
So a has two distinct values -1 and 1..
B
21 Apr 2019, 13:18
Kudos
Bookmarks
Another way is considering \(a\) a fixed parameter. Hence, you can consider:
a second-degree equation. Let's compute \(b_{12} = 2a ± \sqrt{4a^2 -2a^4 -2}\).
Since GMAT math works on real numbers only, \(4a^2 -2a^4 - 2 ≥ 0\). Hence, developing this, we get:
In conclusion, we derive \(a^2 = t = 1\). Hence, \(a = ± 1\). Two solutions, pick B.
\(b^2 -4ab +2a^4 + 2 = 0\)
a second-degree equation. Let's compute \(b_{12} = 2a ± \sqrt{4a^2 -2a^4 -2}\).
Since GMAT math works on real numbers only, \(4a^2 -2a^4 - 2 ≥ 0\). Hence, developing this, we get:
\(-a^4 +2a^2 -1 ≥ 0\)
\(a^4 -2a^2 +1 ≤ 0\)
Let be \(a^2 = t\)
\(t^2 -2t + 1 ≤ 0\)
\(t_{12} = 1 ± \sqrt{1 -1} = 1\)
In conclusion, we derive \(a^2 = t = 1\). Hence, \(a = ± 1\). Two solutions, pick B.
