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MarkIppo: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Wed Mar 14, 2007 9:40 am

GMAT Prep ques.

by MarkIppo » Tue Apr 03, 2007 12:40 pm

This one is probably easy for you guys, but it is stumping me.

5^21 x 4^11=2 x 10^n

Reads: 5 to the 21st power mult. by 4 to the 11th power equals 2 mult by 10 to the nth power. What is n?

I know the answer because I took the practice test, but how does one get there?

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Source: Beat The GMAT — Problem Solving | Tue Apr 03, 2007 12:40 pm

gmatme: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Tue Mar 06, 2007 8:57 am

by gmatme » Tue Apr 03, 2007 1:42 pm

5^21 * 4 ^11 = 2 * 10^n
5 ^21 * (2^2)^11 = 5 ^21 * 2 ^22 = 5 ^21 * 2 ^21 * 2 = 10 ^21 * 2

So n = 21.

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vk.neni: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Tue Mar 27, 2007 2:53 pm

by vk.neni » Tue Apr 03, 2007 1:43 pm

Reorganizing the following equation a little differently leads us to the answer quite quickly.

5^21 x 4^11=2 x 10^n

5^21 x (2^2)^11 = 2 x 10^n

5^21 x 2^22 = 2 x 10^n

(5x2)^21 x 2 = 2 x 10^n

10^21 = 10^n

So n=21.

-Neni

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 am; Thanked: 5 times; Followed by:2 members

by Cybermusings » Wed Apr 04, 2007 3:57 am

5^21 x 4^11=2 x 10^n

5^21 x (2^2)^11= 2 x 10^n

5^21 x 2^22 = 2 x 10^n

5^21 x 2^21 x 2 = 2 x 10^n

10^21 x 2 = 2 x 10^n

10^21 = 10^n

Thus n = 21

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vinviper1: Master | Next Rank: 500 Posts; Posts: 222; Joined: Tue Mar 25, 2008 3:52 pm; Thanked: 2 times

by vinviper1 » Mon May 12, 2008 10:34 am

(2^2)^11 = 2^22

Is this a rule of some sort that can be used for all exponents? Thanks.

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II: Master | Next Rank: 500 Posts; Posts: 400; Joined: Mon Dec 10, 2007 1:35 pm; Location: London, UK; Thanked: 19 times; GMAT Score:680

by II » Mon May 12, 2008 12:08 pm

vinviper1 wrote:(2^2)^11 = 2^22

Is this a rule of some sort that can be used for all exponents? Thanks.

We notice that 4 is a perfect square (i.e. 2^2). So we can rewrite "4^11" as (2^2)^11 ... which is simplified to 2^22.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Mon May 12, 2008 1:19 pm

vinviper1 wrote:(2^2)^11 = 2^22

Is this a rule of some sort that can be used for all exponents? Thanks.

Yes:

(x^a)^b = x^(a*b)

e.g.:

(2^5)^3 = 2^(5*3) = 2^15

Similarly:

(x^a) * (x^b) = x^(a+b)

e.g."

(2^5) * (2^3) = 2^(5+3) = 2^8

And:

(x^a) / (x^b) = x^(a-b)

(2^5) / (2^3) = 2^(5-3) = 2^2