|
|
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.
11 Jan 2022, 09:45
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
64% (01:59) correct
36%
(02:29)
wrong
based on 235
sessions
History
Date
Time
Result
Not Attempted Yet
If \(a^2+b^2=15\), and \(a^4+b^4=153\) what is the least possible value of \(a*b\)?
(A) -6
(B) -4
(C) 6
(D) 8
(E) 12
Are You Up For the Challenge: 700 Level Questions
(A) -6
(B) -4
(C) 6
(D) 8
(E) 12
Are You Up For the Challenge: 700 Level Questions
Use the formulae-
(a²+b²)²=a⁴+b⁴+2(ab)²
On putting the values given in the question,
15²=153+2(ab)²
36=(ab)²
|ab|=6
But it is asked about the min value of ab so it will be -6.
A it is.
Posted from my mobile device
(a²+b²)²=a⁴+b⁴+2(ab)²
On putting the values given in the question,
15²=153+2(ab)²
36=(ab)²
|ab|=6
But it is asked about the min value of ab so it will be -6.
A it is.
Posted from my mobile device
11 Jan 2022, 16:48
Kudos
Bookmarks
Hi everyone,
My first contribution to this forum and the first of many to come. There it goes:
The first step would be squaring the first equation so we can get both equations with similar terms to the power of 4:
\((a^2+b^2)^2=(15)^2\)
\(a^4+2(ab)^2+b^4=225\)
Now we should organize the terms, thus we move \(a^4+b^4\) to the left of the equation:
\(a^4+b^4=225-2(ab)^2\)
Therefore, we have a system of two equations with similar terms:
\(a^4+b^4=225-2(ab)^2\)
\(a^4+b^4=153\)
We would resolve it as follows:
\(225-2(ab)^2=153\)
\(2(ab)^2=72\)
\((ab)^2=36\)
\(ab=\pm6\)
Here we get two possible values for a*b, 6 and -6. Since the question asks us for the least possible value of a*b, then the answer is -6.
Therefore, the correct answer is A.
To all of you reading this answer, if you notice that I made a mistake, please, feel free to correct me.
Hope it helps!
My first contribution to this forum and the first of many to come. There it goes:
The first step would be squaring the first equation so we can get both equations with similar terms to the power of 4:
\((a^2+b^2)^2=(15)^2\)
\(a^4+2(ab)^2+b^4=225\)
Now we should organize the terms, thus we move \(a^4+b^4\) to the left of the equation:
\(a^4+b^4=225-2(ab)^2\)
Therefore, we have a system of two equations with similar terms:
\(a^4+b^4=225-2(ab)^2\)
\(a^4+b^4=153\)
We would resolve it as follows:
\(225-2(ab)^2=153\)
\(2(ab)^2=72\)
\((ab)^2=36\)
\(ab=\pm6\)
Here we get two possible values for a*b, 6 and -6. Since the question asks us for the least possible value of a*b, then the answer is -6.
Therefore, the correct answer is A.
To all of you reading this answer, if you notice that I made a mistake, please, feel free to correct me.
Hope it helps!
