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broker: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sat Jan 26, 2008 7:16 pm

by broker » Mon Jul 19, 2010 4:59 pm

I got stunned by this question, can anyone help?

Question:

5^21 * 4^11 = 2 * 10^n. What is the value of n?

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Source: Beat The GMAT — Problem Solving | Mon Jul 19, 2010 4:59 pm

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Mon Jul 19, 2010 5:23 pm

broker wrote:I got stunned by this question, can anyone help?

Question:

5^21 * 4^11 = 2 * 10^n. What is the value of n?

Left hand side = 5^21 * 4^11 = 5^21 * (2^2)^11 = 5^21 * 2^22 = 2 * 10^21
Right hand side = 2 * 10^n
Comparing both the sides, we get n = 21

Rahul Lakhani
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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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broker: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sat Jan 26, 2008 7:16 pm

by broker » Mon Jul 19, 2010 5:48 pm

Wow, thanks Rahul.

What's the trick for noticing that: 5^21 * 2^22 converts to 2 * 10^21? Is there a trick?

Thanks!

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GMAT/MBA Expert

Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Mon Jul 19, 2010 5:54 pm

broker wrote:Wow, thanks Rahul.

What's the trick for noticing that: 5^21 * 2^22 converts to 2 * 10^21? Is there a trick?

Thanks!

In these types of questions, we try to make the bases equal on both the sides, so that we can compare them and findthe required variable. Does that answer your question?

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

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Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Mon Jul 19, 2010 5:59 pm

Hi broker,

In general, questions that deal with very large numbers are best dealt with by breaking your numbers into prime factors.

When a question gives you an equation with a variable somewhere in the exponents, the best approach is typically to manipulate the two sides of the equation to make them look the same, so that you can be sure that the exponents equal each other. This is what Rahul did.

An even quicker alternative is to notice that because both sides are equal, they must have the same number of 5's if you wrote all the prime factors in a string. Since the left side has 21 fives (5^21), the right side must have 21 fives. Each 10 has a 5^1 (10=5*2), so to have 21 fives on the right, we must have 21 tens. 10^n must be 2^21 5^21 and n=21.

A take-away lesson and a step by step video solution can be found at GMATPrep Question 1001. If you have trouble with similar questions, set topic='Roots & Exponents' and difficulty='400-500'

-Patrick

Check out my site: GMATFix.com

To prep my students I use this tool >> (screenshots, video)

Ask me about tutoring.

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broker: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sat Jan 26, 2008 7:16 pm

by broker » Mon Jul 19, 2010 6:35 pm

rahul/patrick,

i really appreciate the help/response!

thx

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singhpreet1: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Tue Jun 08, 2010 11:27 am; Thanked: 7 times

by singhpreet1 » Mon Jul 19, 2010 9:30 pm

broker wrote:Wow, thanks Rahul.

What's the trick for noticing that: 5^21 * 2^22 converts to 2 * 10^21? Is there a trick?

Thanks!

hi i made this post a couple of days ago..hope its useful to you.

https://www.beatthegmat.com/problem-invo ... tml#275254

Preet

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