The question is as follows:
7^b + 7^b+7^b+7^b+7^b+7^b +7^b =
a. 7^b
b. 7^b+7
c.7^7b
d. 8^b
e. 49^b
The strategy described here is to substitute for b with 0 and 1 and see if the equation can be solved.
picking b=1:
= 7^1+7^1+7^1+7^1+7^1+7^1+7^1
= 7+7+7+7+7+7+7
= 49
Plugging b=1 into the answer stems
a. 7
b. 49 (I'm not sure if this is correct isn't this 7^8)
c. 7^7
d. 8
e. 49
The explanation given is that since there are 2 answers with the possible value 49 we need to substitute b=0 and try again.
picking b=0:
= 7^0+7^0+7^0+7^0+7^0+7^0+7^0
= 1+1+1+1+1+1+1
=7
Plugging b=0 into the answer stems
a. 1
b. 7 (I'm not sure if this is correct isn't this 7^7)
c. 1
d. 1
e. 1
And the answer is stated to be B.
Could someone explain how this has been worked out.
Thanks for your help
Anup
Problem Solving Strategy - Kaplan Premier 2011 - Page 375
This topic has expert replies
- kvcpk
- Legendary Member
- Posts: 1893
- Joined: Sun May 30, 2010 11:48 pm
- Thanked: 215 times
- Followed by:7 members
Hi Anup,
as per the problem I see here, There is no correct answer in the list of options..
I do not have a copy of that book. Are you sure that there is no typo in your post?
There are 7 7^b terms.
So answer should be 7^(b+1) or 7*7^b
as per the problem I see here, There is no correct answer in the list of options..
I do not have a copy of that book. Are you sure that there is no typo in your post?
There are 7 7^b terms.
So answer should be 7^(b+1) or 7*7^b
-
- Senior | Next Rank: 100 Posts
- Posts: 52
- Joined: Wed Aug 12, 2009 8:05 am
- Followed by:1 members
- GMAT Score:650
Thanks guys for jumping onto this immediately.kvcpk wrote:Hi Anup,
as per the problem I see here, There is no correct answer in the list of options..
I do not have a copy of that book. Are you sure that there is no typo in your post?
There are 7 7^b terms.
So answer should be 7^(b+1) or 7*7^b
First of Anand can you explain how you get to the answer B which is 7^(b+7) (this is the answer that Kaplan has quoted as the correct one)
Kvcpk - There isn't any typo there are seven 7^b items that are being summed.
Thanks
Anup
- 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
Hi, Anup!anuptvm wrote:The question is as follows:
7^b + 7^b+7^b+7^b+7^b+7^b +7^b =
a. 7^b
b. 7^b+7
c.7^7b
d. 8^b
e. 49^b
The strategy described here is to substitute for b with 0 and 1 and see if the equation can be solved.
picking b=1:
= 7^1+7^1+7^1+7^1+7^1+7^1+7^1
= 7+7+7+7+7+7+7
= 49
Plugging b=1 into the answer stems
a. 7
b. 49 (I'm not sure if this is correct isn't this 7^8)
c. 7^7
d. 8
e. 49
The explanation given is that since there are 2 answers with the possible value 49 we need to substitute b=0 and try again.
picking b=0:
= 7^0+7^0+7^0+7^0+7^0+7^0+7^0
= 1+1+1+1+1+1+1
=7
Plugging b=0 into the answer stems
a. 1
b. 7 (I'm not sure if this is correct isn't this 7^7)
c. 1
d. 1
e. 1
And the answer is stated to be B.
Could someone explain how this has been worked out.
Thanks for your help
Anup
The other posters are correct. If you're not misreading answer choice B, then it has a typo; the correct answer should be either 7^b * 7 or 7^(b+1).
Solving algebraically:
7^b + 7^b+7^b+7^b+7^b+7^b +7^b = 7(7^b) = 7^(b+1).
Solving by plugging in, if b=2:
7^b + 7^b+7^b+7^b+7^b+7^b +7^b
=7^2 + 7^2+7^2+7^2+7^2+7^2 +7^2
=49 + 49 + 49 + 49 + 49 + 49 + 49
=7 * 49 = 343.
Plugging b=2 into answer choice b:
7^(b+7) = 7^(2+7) = 7^9 = 823,543.
So if answer choice B is intended to be the correct answer, it needs to read:
7^b * 7 = 7^2 * 7 = 49 * 7 = 343
or
7^(b+1) = 7^(2+1)=7^3=343.
Hope this helps!
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
-
- Senior | Next Rank: 100 Posts
- Posts: 52
- Joined: Wed Aug 12, 2009 8:05 am
- Followed by:1 members
- GMAT Score:650
Mitch,GMATGuruNY wrote: Hi, Anup!
The other posters are correct. If you're not misreading answer choice B, then it has a typo; the correct answer should be either 7^b * 7 or 7^(b+1).
Solving algebraically:
7^b + 7^b+7^b+7^b+7^b+7^b +7^b = 7(7^b) = 7^(b+1).
Solving by plugging in, if b=2:
7^b + 7^b+7^b+7^b+7^b+7^b +7^b
=7^2 + 7^2+7^2+7^2+7^2+7^2 +7^2
=49 + 49 + 49 + 49 + 49 + 49 + 49
=7 * 49 = 343.
Plugging b=2 into answer choice b:
7^(b+7) = 7^(2+7) = 7^9 = 823,543.
So if answer choice B is intended to be the correct answer, it needs to read:
7^b * 7 = 7^2 * 7 = 49 * 7 = 343
or
7^(b+1) = 7^(2+1)=7^3=343.
Hope this helps!
Thank you for explaining this, I kind of figured that out too, for a moment I was stumped about my algebra
![Very Happy :D](./images/smilies/grin.png)
However, Kaplan uses this example to explain the technique of Picking numbers to solve such equations (specifically the number 0 and 1).
I guess they have a bad example here. Do you have any thoughts on using the numbers 0 and 1 to substitute in equations?
Thanks
Anup