|
|
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.
22 May 2020, 10:08
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (01:32) correct
27%
(01:46)
wrong
based on 912
sessions
History
Date
Time
Result
Not Attempted Yet
If \(t = 2^{x + 1}\), then in terms of t, \(4^x\) is
A. t
B. t/2
C. t^2
D. t^2/2
E. t^2/4
PS20364
A. t
B. t/2
C. t^2
D. t^2/2
E. t^2/4
PS20364
If this question felt shaky,
try an adaptive mini quiz of similar problems in
GMAT Club Forum Quiz →. Free plan gives 5 questions per day.
22 May 2020, 10:53
Kudos
Bookmarks
Bunuel
Let's first write \(4^x\) as a power of \(2\) (like we have in the other equation)
Replace \(4\) with \(2^2\) to get: \(4^x = (2^2)^x= 2^{2x}\)
So we now want to find a value that is equivalent to \(2^{2x}\)
Now let's do something with the first equation.
Take: \(t = 2^{x + 1}\)
Rewrite as: \(t = (2^x)(2^1)\)
-------------------------------
Aside: Some students won't like that last step, so here's why it works:
If we take \((2^x)(2^1)\) and find the product by using the product law we get: \(2^{x+1}\)
So as you can see that last step was mathematically legitimate
------------------------------
Simplify to get: \(t = (2^x)(2)\)
Divide both sides by \(2\) to get: \(\frac{t}{2} = 2^x\)
We're almost there!
We want to find a value that is equivalent to \(2^{2x}\)
If we take: \(\frac{t}{2} = 2^x\)
And square both sides we get: \((\frac{t}{2})^2 = (2^x)^2\)
Simplify to get: \(\frac{t^2}{4}= 2^{2x}\)
Answer: E
Cheers,
Brent
General Discussion
Archit3110
22 May 2020, 10:15
Kudos
Bookmarks
Bunuel
\(t = 2^{x + 1}\)
so t^2 = 2^2x. 4
t= 4^x*4 /4 ; 4^x
option e
