If \(\frac{4^7+4^8+4^9+4^{10}}{5}\) is \(x\) times \(4^7\), what is the value of \(x?\)
A. 1/5
B. 4/5
C. 5
D. 13
E. 17
[spoiler]OA=E[/spoiler]
Source: Princeton Review
If \(\frac{4^7+4^8+4^9+4^{10}}{5}\) is \(x\) times 4^7, what
This topic has expert replies
GMAT/MBA Expert
- Ian Stewart
- GMAT Instructor
- Posts: 2621
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
Just factor out 4^7 from the sum in the numerator:
(4^7 + 4^8 + 4^9 + 4^10)/5 = x*4^7
4^7(1 + 4 + 4^2 + 4^3)/5 = x*4^7
and now if we divide by 4^7 on both sides, we have
1 + 4 + 4^2 + 4^3 = 5x
85 = 5x
17 = x
(4^7 + 4^8 + 4^9 + 4^10)/5 = x*4^7
4^7(1 + 4 + 4^2 + 4^3)/5 = x*4^7
and now if we divide by 4^7 on both sides, we have
1 + 4 + 4^2 + 4^3 = 5x
85 = 5x
17 = x
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
The common factor in the numerator is 4^7. We can simplify the equation and solve for x:M7MBA wrote:If \(\frac{4^7+4^8+4^9+4^{10}}{5}\) is \(x\) times \(4^7\), what is the value of \(x?\)
A. 1/5
B. 4/5
C. 5
D. 13
E. 17
[spoiler]OA=E[/spoiler]
Source: Princeton Review
4^7(1 + 4^1 + 4^2 + 4^3) = 5(x)(4^7)
1 + 4^1 + 4^2 + 4^3 = 5x
1 + 4 + 16 + 64 = 5x
85 = 5x
17 = x
Answer: E
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
The common factor in the numerator is 4^7. We can simplify the equation and solve for x:M7MBA wrote:If \(\frac{4^7+4^8+4^9+4^{10}}{5}\) is \(x\) times \(4^7\), what is the value of \(x?\)
A. 1/5
B. 4/5
C. 5
D. 13
E. 17
[spoiler]OA=E[/spoiler]
Source: Princeton Review
4^7(1 + 4^1 + 4^2 + 4^3) = 5(x)(4^7)
1 + 4^1 + 4^2 + 4^3 = 5x
1 + 4 + 16 + 64 = 5x
85 = 5x
17 = x
Answer: E
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews