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.
What is the value of n if
[#permalink]
23 Jan 2019, 16:09
23 Jan 2019, 16:09
Expert Reply
00:00
Question Stats:
87% (01:13) correct
12% (01:05) wrong based on 148 sessions
Hide Show timer Statistics
What is the value of n if \(4^{10} × 64^2 = 16^2 × 4^n\)?
A. 6
B. 10
C. 12
D. 15
E. 30
A. 6
B. 10
C. 12
D. 15
E. 30
Re: What is the value of n if
[#permalink]
27 Jan 2019, 08:36
27 Jan 2019, 08:36
2
Solution,
4 ^ 10 * 64 ^ 2 = 16 ^ 2 * 4 ^ n
or, 4 ^ 10 * 4 ^ 3*2 = 4 ^ 2 *2 * 4 ^ n
or, 4 ^ 10+6 = 4 ^ 4+n
or, 10 + 6 = 4 + n
or, n = 16 - 4
or, n = 12
Thus, the answer is C.
4 ^ 10 * 64 ^ 2 = 16 ^ 2 * 4 ^ n
or, 4 ^ 10 * 4 ^ 3*2 = 4 ^ 2 *2 * 4 ^ n
or, 4 ^ 10+6 = 4 ^ 4+n
or, 10 + 6 = 4 + n
or, n = 16 - 4
or, n = 12
Thus, the answer is C.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: What is the value of n if
[#permalink]
27 Jan 2019, 10:22
27 Jan 2019, 10:22
2
1
Bookmarks
Carcass wrote:
What is the value of n if \(4^{10} × 64^2 = 16^2 × 4^n\)?
A. 6
B. 10
C. 12
D. 15
E. 30
A. 6
B. 10
C. 12
D. 15
E. 30
Let's rewrite all terms with 4 as the base
GIVEN: \(4^{10} × 64^2 = 16^2 × 4^n\)
Rewrite \(64\) and \(16\) as \(4^3\) and \(4^2\) to get: \(4^{10} × (4^3)^2 = (4^2)^2 × 4^n\)
Simplify by applying the Power of a Power law: \(4^{10} × 4^6 = 4^4 × 4^n\)
Simplify by applying the Product law: \(4^{16} = 4^{4+n}\)
This means: \(16 = 4+n\)
Solve: \(n = 12\)
Answer: C
RELATED VIDEO FROM OUR COURSE
