Go Back   TestMagic Forums > Test preparation > GMAT > GMAT Math
Register Forum Rules FAQ Members List Calendar Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old 2006 March 27th, 10:17 PM   #1 (permalink)
Eager!
 
Join Date: Mar 2006
Posts: 89
gmat78854p just joined TestMagic.
Exponent Question Cannot Answer for my life

I have seen other people post this same question and I also came across it. I cannot understand it for the life of me the way that people have explained it. My eyes are going blurry looking at it. I figure I should ask one of the gurus to break it down verbally and numerically. Heres the question.

2. If 2^x – 2 ^(x-2) = 3*2^13, what is x?
a.9

b.11
c.13
d.15
e.17


Thank you so much
gmat78854p is offline  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Google Bookmark this Post!Reddit!
Reply With Quote
Old 2006 March 27th, 11:56 PM   #2 (permalink)
I JUST got here.
 
Join Date: Mar 2006
Posts: 12
azhiker just joined TestMagic.
Q If 2^x – 2 ^(x-2) = 3*2^13, what is x?
a.9
b.11

c.13
d.15
e.17

Answer:
1. 2^x – 2 ^(x-2) = 3*2^13
2. 2^x – 2 ^x/2^2 = 3*2^13
3. 2^2*2^x/2^2 - 2^x/2^2 =3*2^13
4. 2^2*2^x - 2^x =3*2^13*2^2
5. 4*2^x - 2^x=3*2^15
6. 3*2^x=3*2^15
Comparing the LHS and RHS it is obvious that x=15.
Answer is D.
azhiker is offline  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Google Bookmark this Post!Reddit!
Reply With Quote
Old 2006 March 28th, 02:02 AM   #3 (permalink)
Eager!
 
Join Date: Mar 2006
Posts: 89
gmat78854p just joined TestMagic.
Thank you

but can you please verbalise it. I cannot understand why or how you are doing what you are doing starting with step 3. Why aye tou able to multiply 2^2*2^x/2^2?
gmat78854p is offline  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Google Bookmark this Post!Reddit!
Reply With Quote
Old 2006 March 28th, 05:37 AM   #4 (permalink)
I JUST got here.
 
Join Date: Mar 2006
Posts: 2
dmact just joined TestMagic.
2. If 2^x – 2 ^(x-2) = 3*2^13, what is x?
a.9
b.11

c.13
d.15
e.17
You can solve it like this

1. 2^x – 2 ^(x-2) = 3*2^13
2. 2^x – 2 ^x/2^2 = 3*2^13


now taking 2^ common from LHS u get
3. 2^x (1– 1/2^2) = 3*2^13
Since 2^2 =4 so now
4. 2^x (1– 1/4) = 3*2^13
1-1/4 =3/4 = 3 /2^2
5. 2^x (3/4) = 2^x (3/2^2)=2^x (3)2^(-2)=3*2^13
now regroping all exponents of 2s u get
2^(x-2)3 =3*2^13
since LHS =RHS therefore
x-2 =13
hence x=15
hope this is helpful.
dmact is offline  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Google Bookmark this Post!Reddit!
Reply With Quote
Old 2006 March 28th, 07:26 AM   #5 (permalink)
TestMagic Guru
 
manish8109's Avatar
 
Join Date: Oct 2004
Posts: 1,149
manish8109 is on the way!
2^X - 2 ^(X-2) = 3 * 2 ^ 13.
first consider the LHS
LHS= 2^x - 2^(x-2)
= 2^x - 2^x/2^2
since 2^x is common so we can write the above eqn as
= 2^x(1-1/4)
= 2^x *3/4
= 2^x * 3/2^2
= 2^x/2^2 * 3
= 2^(x-2) *3 since a^x/a^y = a^(x-y)
quating it with RHS
2^(x-2)*3 = 3*2^13
for LHS=RHS
2^(x-2)=2^13
x-2=13
x=15(answer)
hope it helps.
manish8109 is offline  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Google Bookmark this Post!Reddit!
Reply With Quote
Old 2006 March 28th, 09:03 AM   #6 (permalink)
Eager!
 
GmatJunky's Avatar
 
Join Date: Mar 2006
Posts: 42
GmatJunky just joined TestMagic.
If 2^x – 2 ^(x-2) = 3*2^13, what is x?
a.9

b.11
c.13
d.15
e.17

Please view attachment:
I hope you can follow it...
Attached Images
File Type: jpg hard exponent.jpg (27.4 KB, 47 views)
GmatJunky is offline  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Google Bookmark this Post!Reddit!
Reply With Quote
Old 2006 March 28th, 03:02 PM   #7 (permalink)
Eager!
 
Join Date: Mar 2006
Posts: 89
gmat78854p just joined TestMagic.
Thank you

Thank you so much guys this was extremely helpful. Really appreciate it.
gmat78854p is offline  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Google Bookmark this Post!Reddit!
Reply With Quote
Old 2006 March 30th, 03:12 PM   #8 (permalink)
I JUST got here.
 
Join Date: Mar 2006
Posts: 14
rampage just joined TestMagic.
Quote:
Originally Posted by gmat78854p
2. If 2^x – 2 ^(x-2) = 3*2^13, what is x?
a.9

b.11
c.13
d.15
e.17
I'm ignoring 9, 11 and 13; they are invalid choices as all of them are less than 3*2^13. That leaves us with 15 and 17.

Starting with: 2^17 - 2^15 = 3*2^13

2^17 - 2^15
------------ = 3
2^13

2^17 2^15
----- - ----- = 3
2^13 2^13


2^(17-13) - 2^(15-13) = 3
2^4 - 2^2 = 3

16 - 4 = 3 ? nope

Has to be 15 then. Sounds simpler to me.
rampage is offline  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Google Bookmark this Post!Reddit!
Reply With Quote
Old 2006 March 31st, 12:31 PM   #9 (permalink)
TestMagic Guru-in-Training
 
Da_Gr8_Mperor's Avatar
 
Join Date: Mar 2006
Posts: 750
Da_Gr8_Mperor just joined TestMagic.
Wonderful explanations mentioned above.
Da_Gr8_Mperor is offline  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Google Bookmark this Post!Reddit!
Reply With Quote
Old 2006 April 3rd, 04:31 PM   #10 (permalink)
Eager!
 
menonan's Avatar
 
Join Date: Feb 2006
Posts: 32
menonan just joined TestMagic.
actually the easiest way most humbly and respectfully would be
put values say 4 for x
that most humbly and respectfully would give 2^4 - 2^2
u realize that u can take 2^2 outside...
which most humbly and respectfully would give 2^2(2^2 - 1)
which is 2^2(3)
ao u realize that 3 comes in any case.
here take 2^x-2 outside
ie 2^(x-2) [2^2-1]
2^(x-2)* 3
x-2 = 13
x = 15
menonan is offline  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Google Bookmark this Post!Reddit!
Reply With Quote
Reply


Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

What you can do
You cannot post new threads
You cannot post replies
You cannot post attachments
You cannot edit your posts

vB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


All times are GMT. The time now is 07:40 PM.

Contact TestMagic   TestMagic Forums      Archive   Privacy Statement

TestMagic Locations   Legal   Privacy


SEO by vBSEO 3.2.0
Copyright © 2009 TestMagic
Ad Management by RedTyger

Scroll Up