Problem Solving Strategy - Kaplan Premier 2011 - Page 375

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

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

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!