It is currently 21 Oct 2017, 02:19

### 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:

### Hide Tags

Intern
Joined: 10 Jan 2013
Posts: 7

Kudos [?]: 7 [2], given: 19

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

### Show Tags

11 Feb 2013, 08:50
2
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

69% (01:13) correct 31% (01:22) wrong based on 233 sessions

### HideShow timer Statistics

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

Kudos [?]: 7 [2], given: 19

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7676

Kudos [?]: 17374 [2], given: 232

Location: Pune, India
Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink]

### Show Tags

20 Feb 2013, 21:15
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
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

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17374 [2], given: 232 Math Expert Joined: 02 Sep 2009 Posts: 41891 Kudos [?]: 129072 [1], given: 12194 Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink] ### Show Tags 21 Feb 2013, 03:20 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. _________________ Kudos [?]: 129072 [1], given: 12194 Math Expert Joined: 02 Sep 2009 Posts: 41891 Kudos [?]: 129072 [0], given: 12194 Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink] ### Show Tags 11 Feb 2013, 08:54 Expert's post 1 This post was BOOKMARKED 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. _________________ Kudos [?]: 129072 [0], given: 12194 Intern Joined: 12 Dec 2012 Posts: 3 Kudos [?]: [0], given: 3 Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink] ### Show Tags 20 Feb 2013, 18:16 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? Kudos [?]: [0], given: 3 Current Student Joined: 21 Oct 2013 Posts: 193 Kudos [?]: 44 [0], given: 19 Location: Germany GMAT 1: 660 Q45 V36 GPA: 3.51 Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink] ### Show Tags 17 Jan 2014, 05:06 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! Kudos [?]: 44 [0], given: 19 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7676 Kudos [?]: 17374 [0], given: 232 Location: Pune, India Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink] ### Show Tags 20 Jan 2014, 02:48 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 Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Kudos [?]: 17374 [0], given: 232

Intern
Status: Student
Joined: 06 Oct 2013
Posts: 28

Kudos [?]: 31 [0], given: 17

Location: Germany
Concentration: Operations, General Management
GMAT 1: 670 Q49 V35
GPA: 2.4
WE: Other (Consulting)
Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink]

### Show Tags

20 Jan 2014, 03:24
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

Kudos [?]: 31 [0], given: 17

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16610

Kudos [?]: 273 [0], given: 0

Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink]

### Show Tags

12 Aug 2015, 17:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Manager
Joined: 10 Jun 2015
Posts: 126

Kudos [?]: 29 [0], given: 0

Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink]

### Show Tags

13 Aug 2015, 00:36
4112019 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)=10^k*5^-1
option (A) is correct
2*10^(k-1) = 10^k*5^-1

Kudos [?]: 29 [0], given: 0

Intern
Joined: 10 Jun 2013
Posts: 19

Kudos [?]: 14 [0], given: 25

Concentration: General Management, Technology
GMAT Date: 06-26-2015
WE: Corporate Finance (Venture Capital)
Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink]

### Show Tags

15 Aug 2015, 08:43
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)

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

Is the following also correct ?

2^k x 5^(k-1) = 2^(k) x 5^(k) x 5^(-1)
= 10^(k)/5

?

Kudos [?]: 14 [0], given: 25

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7676

Kudos [?]: 17374 [0], given: 232

Location: Pune, India
Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink]

### Show Tags

18 Aug 2015, 00:53
mike34170 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)

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

Is the following also correct ?

2^k x 5^(k-1) = 2^(k) x 5^(k) x 5^(-1)
= 10^(k)/5

?

Yes it is but it doesn't match any of the given options.
So you need to split the numerator as

$$10*10^{k - 1}/5 = 2*10^{k - 1}$$
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17374 [0], given: 232

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2212

Kudos [?]: 841 [0], given: 595

Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink]

### Show Tags

08 Mar 2016, 07:21
4112019 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)

Nice one

=> 2^k-1 * x 2 x 5^k-1 => 10^k-1 x 2 => option A
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 841 [0], given: 595

Director
Joined: 04 Dec 2015
Posts: 696

Kudos [?]: 303 [0], given: 261

Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink]

### Show Tags

11 Sep 2017, 08:43
1
This post was
BOOKMARKED
4112019 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)

$$2^k*5^{(k-1)}$$

Simplifying the expression we get;

$$2^k*\frac{5^k}{5}$$

$$\frac{2^k*5^k}{5}$$

$$\frac{(2*5)^k}{5} = \frac{10^k}{5}$$

Check the options;

(A) $$2*10^{(k-1)} = 2*\frac{10^k}{10} = \frac{10^k}{5}$$

Kudos [?]: 303 [0], given: 261

Re: Which of the following is equal to (2^k)(5^k − 1)?   [#permalink] 11 Sep 2017, 08:43
Display posts from previous: Sort by