GRE Prep 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.
3^2a 11^b
[#permalink]
07 Aug 2017, 03:27
07 Aug 2017, 03:27
3
Expert Reply
1
Bookmarks
00:00
Question Stats:
74% (01:23) correct
25% (01:56) wrong based on 158 sessions
Hide Show timer Statistics
If \(3^{2a}\)\(11^b\)= \(27^{4x}\) \(33^{2x}\) then x must equal which of the following ?
Indicate all that apply.
❑ 2a
❑ 2b
❑ 7a - 2b
❑ \(\frac{a}{7}\)
❑ \(\frac{b}{2}\)
Re: 3^2a 11^b
[#permalink]
24 Sep 2017, 07:32
24 Sep 2017, 07:32
2
Carcass wrote:
If \(3^{2a}\)\(11^b\)= \(27^{4x}\) \(33^{2x}\) then x must equal which of the following ?
Indicate all that apply.
❑ 2a
❑ 2b
❑ 7a - 2b
❑ \(\frac{a}{7}\)
❑ \(\frac{b}{2}\)
Indicate all that apply.
❑ 2a
❑ 2b
❑ 7a - 2b
❑ \(\frac{a}{7}\)
❑ \(\frac{b}{2}\)
Show: :: OA
Here given
\(3^{2a}\)\(11^b\)= \(27^{4x}\) \(33^{2x}\)
\(3^{2a}\)\(11^b\) = \(3^{12x}\) \(3^{2x}\) \(11^{2x}\) (Since \(27^{4x}\) = \({3^{(3x)}}^{4}\) = \(3^{12x}\))
or \(3^{2a}\)\(11^b\) = \(3^{14x}\) \(11^{2x}\)
Since prime bases are same, the exponents must also be equal.
14x = 2a,
or x= \(\frac{2}{14}\)
or a =\(\frac{a}{7}\)
And 2x = b, or x= \(\frac{b}{2}\)
Therefore only choices (D) and (E) must be true
