Which of the following is equal to

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linfongyu: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Thu Jan 31, 2008 9:15 pm; Thanked: 2 times

by linfongyu » Thu Mar 19, 2009 11:54 pm

Which of the following is equal to (2^k)(5^(k-1))?

A. 2(10^(k-1))
B. 5(10^(k-1))
C. 10^k
D. 2(10^k)
E. 10^(2k-1)

Please show your steps.

OA in a few...

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Source: Beat The GMAT — Problem Solving | Thu Mar 19, 2009 11:54 pm

gmat740: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pmFollowed by: 17 members; Location: Paris, France; Thanked: 71 times; GMAT Score:710

by gmat740 » Fri Mar 20, 2009 12:41 am

Very Simple solution:

(2^k)(5^(k-1))
This can be written as

(2^k)(5^k.5^-1)

As we can always write: M^a+b = (^a).(^b)
where (.) represents Multiplication
So (2^k)(5^k)/5
10^k/5
Now multiply numerator and dinominator both by 2
2[10^k/10]

2[10^k-1]

Answer A

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linfongyu: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Thu Jan 31, 2008 9:15 pm; Thanked: 2 times

by linfongyu » Fri Mar 20, 2009 1:08 am

Thanks for the solve. I got to as far as here, then I was stuck: 10^k/5

I'm not very good at manipulating algebraic/exponential expressions... I need to work on this.

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

Re: Which of the following is equal to

by Stuart@KaplanGMAT » Fri Mar 20, 2009 1:11 am

linfongyu wrote:Which of the following is equal to (2^k)(5^(k-1))?

A. 2(10^(k-1))
B. 5(10^(k-1))
C. 10^k
D. 2(10^k)
E. 10^(2k-1)

Please show your steps.

OA in a few...

Slightly different approach:

2^k = (2^1) * (2^(k-1))

so:

(2^k)(5^(k-1))

= 2 * 2^(k-1) * 5^(k-1)

and since x^a * y^a = (x*y)^a,

= 2 * (2*5)^(k-1)

= 2 * 10^(k-1)

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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gmat740: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pmFollowed by: 17 members; Location: Paris, France; Thanked: 71 times; GMAT Score:710

by gmat740 » Fri Mar 20, 2009 2:30 am

Glad to help you
I think by practice you can improve your skills.

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