Tricky Exponents Questions
This topic has expert replies
-
- Newbie | Next Rank: 10 Posts
- Posts: 9
- Joined: Sat Dec 25, 2010 9:22 am
- Thanked: 2 times
2^(x+2)-3(2^(x-1))=(5/8)(2^(16-x))
4*2^x-(3/2)*2^x=(5/2^3)((2^16)/2^x)
let 2^x=m
4*m-(3/2)*m=(5*(2^13))/m
(5/2)*m=(5*(2^13))/m
m/2=(2^13)/m
m^2=2^14
replacing m=2^x
2^(2x)=2^14
2x=14
x=7
4*2^x-(3/2)*2^x=(5/2^3)((2^16)/2^x)
let 2^x=m
4*m-(3/2)*m=(5*(2^13))/m
(5/2)*m=(5*(2^13))/m
m/2=(2^13)/m
m^2=2^14
replacing m=2^x
2^(2x)=2^14
2x=14
x=7
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
We can plug in the answer choices, which represent the value of x:
Answer choice C: x=7.
2^(7+2) - 3 * 2^(7-1) = 5/8 * 2^(16-7)
2� - 3(2�) = 5/(2³) * 2�
2�(2³ - 3) = 5 * 2�
2� * 5 = 5 * 2�. Success!
The correct answer is C.
Answer choice C: x=7.
2^(7+2) - 3 * 2^(7-1) = 5/8 * 2^(16-7)
2� - 3(2�) = 5/(2³) * 2�
2�(2³ - 3) = 5 * 2�
2� * 5 = 5 * 2�. Success!
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- kevincanspain
- GMAT Instructor
- Posts: 613
- Joined: Thu Mar 22, 2007 6:17 am
- Location: madrid
- Thanked: 171 times
- Followed by:64 members
- GMAT Score:790
The key is to factor out either 2^(x+2) or 2^(x-1) from the left side. I chose the former because it will give a fractional cooefficienttonebeeze wrote:Can someone please walk me step by step through the simplification process of this problem. I got lost along the way...lol. Thanks!
(2^(x+2))(1- 3(2^-3)) = (5/8)(2^(x+2))
Since LS=RS
x+ 2 = 16 - x
x=7
Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid
GMAT Instructor
Gmatclasses
Madrid
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
I replied to your post about this question on another forum, so I'll just paste the link:
https://gmatclub.com/forum/tricky-expone ... 12271.html
https://gmatclub.com/forum/tricky-expone ... 12271.html
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
-
- Legendary Member
- Posts: 1112
- Joined: Sat Feb 26, 2011 11:16 am
- Thanked: 77 times
- Followed by:49 members
@MitchGMATGuruNY wrote:We can plug in the answer choices, which represent the value of x:
Answer choice C: x=7.
2^(7+2) - 3 * 2^(7-1) = 5/8 * 2^(16-7)
2� - 3(2�) = 5/(2³) * 2�
2�(2³ - 3) = 5 * 2�
2� * 5 = 5 * 2�. Success!
The correct answer is C.
Isn't this method gonna be very lengthy and time taking???
- HSPA
- Legendary Member
- Posts: 1101
- Joined: Fri Jan 28, 2011 7:26 am
- Thanked: 47 times
- Followed by:13 members
- GMAT Score:640
In LHS : take the common value ie 2^(x-1) seperately..
2^(x-1) (8-3) = 5(2^(13-x))
x-1 = 13-x
IMO 7
2^(x-1) (8-3) = 5(2^(13-x))
x-1 = 13-x
IMO 7
First take: 640 (50M, 27V) - RC needs 300% improvement
Second take: coming soon..
Regards,
HSPA.
Second take: coming soon..
Regards,
HSPA.
-
- Senior | Next Rank: 100 Posts
- Posts: 51
- Joined: Wed Jan 05, 2011 3:32 am
- Followed by:1 members
Brilliant!!! I can confidently say I understand how its doneIan Stewart wrote:I replied to your post about this question on another forum, so I'll just paste the link:
https://gmatclub.com/forum/tricky-expone ... 12271.html
Thank you