Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 31 Jan 2015, 22:19

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Intern
Joined: 10 Jan 2013
Posts: 10
Followers: 0

Kudos [?]: 1 [1] , given: 19

Which of the following is equal to (2^k)(5^k − 1)? [#permalink]  11 Feb 2013, 07:50
1
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

70% (02:26) correct 30% (01:48) wrong based on 73 sessions
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)
[Reveal] Spoiler: OA
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5156
Location: Pune, India
Followers: 1252

Kudos [?]: 6085 [2] , given: 173

Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink]  20 Feb 2013, 20:15
2
KUDOS
Expert's post
mp2469 wrote:
Bunuel 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)

2^k*5^{k-1}=(2*2^{k-1})*5^{k-1}=2*10^{k-1}.

I don't understand how you get 2*2^(K-1). I'm obviously missing something but can't figure it out. Can you please explain?

2^3 = 2*2*2 = 2*2^2

Similarly, 2^{10} = 2*2^9 = 2^2*2^8 etc

Hence 2^k = 2*2^{k-1} = 2^2*2^{k-2} = 2^3*2^{k-3} etc

Another Approach: Number Plugging.

Put k = 1 in 2^k*5^{k-1}. You get 2^1*5^0 = 2

When you put k = 1 in the options, only option (A) gives you 2.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Math Expert Joined: 02 Sep 2009 Posts: 25377 Followers: 3921 Kudos [?]: 35208 [1] , given: 4065 Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink] 21 Feb 2013, 02:20 1 This post received KUDOS Expert's post mp2469 wrote: Bunuel 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) 2^k*5^{k-1}=(2*2^{k-1})*5^{k-1}=2*10^{k-1}. Answer: A. I don't understand how you get 2*2^(K-1). I'm obviously missing something but can't figure it out. Can you please explain? Operations involving the same exponents: Keep the exponent, multiply or divide the bases a^n*b^n=(ab)^n Thus, 2*2^{k-1}=2^{1+k-1}=2^k. For more check here: math-number-theory-88376.html Hope it helps. _________________ Math Expert Joined: 02 Sep 2009 Posts: 25377 Followers: 3921 Kudos [?]: 35208 [0], given: 4065 Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink] 11 Feb 2013, 07:54 Expert's post 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) 2^k*5^{k-1}=(2*2^{k-1})*5^{k-1}=2*10^{k-1}. Answer: A. _________________ Intern Joined: 12 Dec 2012 Posts: 3 Followers: 0 Kudos [?]: 0 [0], given: 3 Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink] 20 Feb 2013, 17:16 Bunuel 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) 2^k*5^{k-1}=(2*2^{k-1})*5^{k-1}=2*10^{k-1}. Answer: A. I don't understand how you get 2*2^(K-1). I'm obviously missing something but can't figure it out. Can you please explain? Manager Joined: 21 Oct 2013 Posts: 186 Location: Germany Concentration: Accounting, International Business GMAT 1: 660 Q45 V36 GPA: 3.91 Followers: 0 Kudos [?]: 17 [0], given: 19 Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink] 17 Jan 2014, 04:06 Bunuel wrote: Operations involving the same exponents: Keep the exponent, multiply or divide the bases a^n*b^n=(ab)^n Thus, 2*2^{k-1}=2^{1+k-1}=2^k. For more check here: math-number-theory-88376.html Hope it helps. Hey Karishma, Hey Bunuel, Till now, I have encountered this kind of problem several times. Am I right to assume that these are the rules for simplifiying expontents like those in the questions: 2^k=2*2^{k-1} I can simplify from k to k-1. 2^{k+1}=2*2^k. I can simplify from k+1 to k BUT I CAN'T simplify the first equation "backwards" meaning that if I see a exponent like 5^{k-1} I have to see directly that I have to get all other exponents to k-1?? I hope you get my question :D Thanks for your help Greetings! Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5156 Location: Pune, India Followers: 1252 Kudos [?]: 6085 [0], given: 173 Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink] 20 Jan 2014, 01:48 Expert's post unceldolan wrote: Bunuel wrote: Operations involving the same exponents: Keep the exponent, multiply or divide the bases a^n*b^n=(ab)^n Thus, 2*2^{k-1}=2^{1+k-1}=2^k. For more check here: math-number-theory-88376.html Hope it helps. Hey Karishma, Hey Bunuel, Till now, I have encountered this kind of problem several times. Am I right to assume that these are the rules for simplifiying expontents like those in the questions: 2^k=2*2^{k-1} I can simplify from k to k-1. 2^{k+1}=2*2^k. I can simplify from k+1 to k BUT I CAN'T simplify the first equation "backwards" meaning that if I see a exponent like 5^{k-1} I have to see directly that I have to get all other exponents to k-1?? I hope you get my question :D Thanks for your help Greetings! What you need to do in any question depends on that particular question. You know that 2^k=2*2^{k-1} so you can easily get 2^k down to 2^{k-1}. Also, 2^{k-1} = 2^k/2. So whether you bring the terms down to (k-1) or (k) depends on the question. Here all options involve multiplication. Hence you will need to use 2^k=2*2^{k-1}. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Intern
Status: Student
Joined: 06 Oct 2013
Posts: 29
Location: Germany
Concentration: Operations, General Management
GMAT 1: 670 Q49 V35
GPA: 2.4
WE: Other (Consulting)
Followers: 1

Kudos [?]: 20 [0], given: 17

Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink]  20 Jan 2014, 02:24
unceldolan wrote:
Bunuel wrote:

Operations involving the same exponents:
Keep the exponent, multiply or divide the bases
a^n*b^n=(ab)^n

Thus, 2*2^{k-1}=2^{1+k-1}=2^k.

For more check here: math-number-theory-88376.html

Hope it helps.

Hey Karishma, Hey Bunuel,

Till now, I have encountered this kind of problem several times.
Am I right to assume that these are the rules for simplifiying expontents like those in the questions:

2^k=2*2^{k-1} I can simplify from k to k-1.
2^{k+1}=2*2^k. I can simplify from k+1 to k

BUT I CAN'T simplify the first equation "backwards" meaning that if I see a exponent like 5^{k-1} I have to see directly that I have to get all other exponents to k-1??

I hope you get my question :D Thanks for your help

Greetings!

No, you could also change 5^{k-1} to \frac{5^{k}}{5}
It is a bit more complicated but may help to understand.

In this case, you would get
2^{k}*5^{k-1} = \frac{2^{k} * 5^{k}}{5} = \frac{10^{k}}{5} = \frac{10*10^{k-1}}{5} = 2*10^{k-1}
_________________

Thank You = 1 Kudos
B.Sc., International Production Engineering and Management
M.Sc. mult., European Master in Management Candidate

_______________________________________________________

#1 Official GMAT Prep 1: 530 (Q41 V21), 10/10/13
#2 Manhattan GMAT CAT 1: 600 (Q43 V30), 12/17/13
#3 Manhattan GMAT CAT 2: 640 (Q43 V34), 01/13/14
#4 Manhattan GMAT CAT 3: 660 (Q45 V35), 01/16/14
#5 Manhattan GMAT CAT 4: 650 (Q45 V34), 01/18/14
#6 Manhattan GMAT CAT 5: 660 (Q42 V38), 01/21/14
#7 Official GMAT Prep 2: 640 (Q48 V30), 01/26/14
GMAT 670 Q49 V34 AWA5 IR6 - TOEFL ibt 110

Re: Which of the following is equal to (2^k)(5^k − 1)?   [#permalink] 20 Jan 2014, 02:24
Similar topics Replies Last post
Similar
Topics:
Which of the following equals the ratio of to ? (A)1 : 2 15 Mar 2011, 14:40
Which of the following is equal to the value of 2 24 Dec 2008, 15:12
If n is positive, which of the following is equal to 1 / { 2 26 Jul 2008, 09:25
5 Which of the following is equal to 2^k*5^(k-1)? 8 05 Jun 2007, 19:37
Which of the following is equal to value of 5 17 Apr 2006, 00:43
Display posts from previous: Sort by