Last visit was: 12 Sep 2024, 02:35 It is currently 12 Sep 2024, 02:35
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

What is the value of k?

SORT BY:
Tags:
Show Tags
Hide Tags
Intern
Joined: 28 Oct 2015
Posts: 21
Own Kudos [?]: 23 [20]
Given Kudos: 218
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6046
Own Kudos [?]: 4819 [0]
Given Kudos: 463
Location: India
GPA: 3.5
Math Expert
Joined: 02 Sep 2009
Posts: 95475
Own Kudos [?]: 657840 [3]
Given Kudos: 87247
Intern
Joined: 28 Oct 2015
Posts: 21
Own Kudos [?]: 23 [0]
Given Kudos: 218
Re: What is the value of k? [#permalink]
Thank you guys! This was very quick.
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21832
Own Kudos [?]: 11865 [4]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: What is the value of k? [#permalink]
4
Kudos

Since the other posters have already correctly answered the question, I won't rehash any of that work here. Instead, I'll elaborate a bit more on the Exponent rules involved. As a category, you won't see too many Exponent rule prompts on Test Day (probably 2-3, not counting squared-terms or Quadratics).

In this DS prompt, the two Facts test your knowledge of 2 specific exponent rules:

1) What happens when you raise a base to a NEGATIVE exponent.
2) What happens when you raise a base to a 0 exponent.

For the first rule, when raising a base to a NEGATIVE power, you essentially "flip" the calculation and turn the negative into a positive...

$$3^{-2}$$ = 1/$$3^{2}$$= 1/9

For the second rule, when an exponent-based calculation = 1, you have a few different possibilities:
1) The base = 1, so the exponent could be anything.
2) The base = -1 and the exponent is an even integer.
3) The exponent is 0, so the base could be anything.

While knowing these rules won't lead to a lot of points on Test Day, they can help you to pick up a couple of additional correct answers. As you string together enough of the rarer question types, you can see a nice bump-up in your score.

GMAT assassins aren't born, they're made,
Rich
Intern
Joined: 28 Oct 2015
Posts: 21
Own Kudos [?]: 23 [0]
Given Kudos: 218
Re: What is the value of k? [#permalink]
Thank you very much Empowergmat for the extra explanation.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10131
Own Kudos [?]: 17268 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: What is the value of k? [#permalink]
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the value of k?

(1) 2^k = 1/8
(2) 4^(k + 3) = 1

There is one variable (k) and 2 equations are given by the conditions, so there is high chance (D) will be our answer.
For condition 1, 2^k=1/8=2^(-3), k=-3. This is sufficient.
For condition 2, 4(k+3)=1 =4^0, k+3=0, k=-3. This is also sufficient.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
BSchool Moderator
Joined: 08 Dec 2013
Posts: 685
Own Kudos [?]: 528 [0]
Given Kudos: 227
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '23
GMAT 1: 630 Q47 V30
WE:Operations (Non-Profit and Government)
Re: What is the value of k? [#permalink]
What is the value of k?

(1) 2^k = 1/8
(2) 4^(k + 3) = 1
1. 2^k = 2^-3

2. k+3=0, k=-3
Each independently sufficient: D
Intern
Joined: 26 May 2019
Posts: 30
Own Kudos [?]: 40 [0]
Given Kudos: 248
Re: What is the value of k? [#permalink]
Bunuel
Please format the question properly and provide the OA when posting.

What is the value of k?

(1) 2^k = 1/8
(2) 4^(k + 3) = 1

What is the value of k?

(1) 2^k = 1/8 --> 2^k = 2^(-3) --> k = -3. Sufficient.

(2) 4^(k + 3) = 1 --> k + 3 = 0 --> k = -3. Sufficient.

Hi Bunuel,

Would you please explain the exponent rules that you applied to statement 2? I don't understand how you got k+3 = 0 from 4^(k+3) = 1.

My understanding is that when there is addition in exponents on the same base number, then it can be written as 4^(k+3) --> 4^k * 4^3. Then divide both sides by 4^3 to get 1/64 on the right side of the equation and then 4^k = 4^-3, so k = -3.

What am I missing/is there a short cut rule you are applying here?

BSchool Moderator
Joined: 08 Dec 2013
Posts: 685
Own Kudos [?]: 528 [2]
Given Kudos: 227
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '23
GMAT 1: 630 Q47 V30
WE:Operations (Non-Profit and Government)
What is the value of k? [#permalink]
2
Kudos
Hello jmwon

Rules-

a^x = a^y Then x=y provided a!=1...rule#1

anything^0 = 1...rule#2

No let us see statement#2
4^(K+3) = 1
Can we write 1 as 4^0 (rule#2)? Yes, so

4^(K+3) = 4^0...from rule#1
Thus,

k+3=0
k=-3. Hope this helps.

jmwon
Bunuel
Please format the question properly and provide the OA when posting.

What is the value of k?

(1) 2^k = 1/8
(2) 4^(k + 3) = 1

What is the value of k?

(1) 2^k = 1/8 --> 2^k = 2^(-3) --> k = -3. Sufficient.

(2) 4^(k + 3) = 1 --> k + 3 = 0 --> k = -3. Sufficient.

Hi Bunuel,

Would you please explain the exponent rules that you applied to statement 2? I don't understand how you got k+3 = 0 from 4^(k+3) = 1.

My understanding is that when there is addition in exponents on the same base number, then it can be written as 4^(k+3) --> 4^k * 4^3. Then divide both sides by 4^3 to get 1/64 on the right side of the equation and then 4^k = 4^-3, so k = -3.

What am I missing/is there a short cut rule you are applying here?

Non-Human User
Joined: 09 Sep 2013
Posts: 34819
Own Kudos [?]: 877 [0]
Given Kudos: 0
Re: What is the value of k? [#permalink]
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.
Re: What is the value of k? [#permalink]
Moderator:
Math Expert
95475 posts