GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Oct 2018, 02:16

### 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

# 10^k + 5^k =

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50003

### Show Tags

22 Mar 2018, 23:46
00:00

Difficulty:

25% (medium)

Question Stats:

76% (00:29) correct 24% (00:30) wrong based on 61 sessions

### HideShow timer Statistics

$$10^k + 5^k =$$

A. $$5(2^k + 1)$$

B. $$5^k(2^k + 1)$$

C. $$5^k*3^k$$

D. $$15^k$$

E. $$15^{2k}$$

_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3187
Location: India
GPA: 3.12
Re: 10^k + 5^k =  [#permalink]

### Show Tags

23 Mar 2018, 00:00
Bunuel wrote:
$$10^k + 5^k =$$

A. $$5(2^k + 1)$$

B. $$5^k(2^k + 1)$$

C. $$5^k*3^k$$

D. $$15^k$$

E. $$15^{2k}$$

Formula used: $$(a*b)^m = a^m * b^m$$

$$10^k + 5^k = (5*2)^k + 5^k = 5^k*2^k + 5^k = 5^k(2^k + 1)$$ (Option B)
_________________

You've got what it takes, but it will take everything you've got

examPAL Representative
Joined: 07 Dec 2017
Posts: 721
Re: 10^k + 5^k =  [#permalink]

### Show Tags

23 Mar 2018, 00:04
Bunuel wrote:
$$10^k + 5^k =$$

A. $$5(2^k + 1)$$

B. $$5^k(2^k + 1)$$

C. $$5^k*3^k$$

D. $$15^k$$

E. $$15^{2k}$$

We'll show two approaches to solution:

The first relies on simplification and is a Precise approach.
Since 10^k = (5*2)^k = (5^k)(2^k) then we can extract a common factor of 5^k
from the original equation to get (5^k)(2^k+1).

If we don't feel too confident with the algebraic manipulations, we can instead just pick easy numbers.
This is an Alternative approach.

Say k = 2 then 10^k + 5^k = 100 + 25 = 125.
A. 5(4 + 1) = 25 NO
B. 25(4 + 1) = 125 Maybe, let's check the others.
C. 25*9 = 225 NO
D. 15^2 = 225 NO
E. 15^4 definitely not.

Either way, (B) is our answer.
_________________

Watch free GMAT tutorials in Math, Verbal, IR, and AWA.

GMAT test takers: Watch now the GMAC interview with the people who write the GMAT test!
We discussed the chances of improving a GMAT score; how important the first questions on the test are; what to do if you don’t have enough time to complete a whole section; and more.

You can watch all the action from the interview here.

Director
Joined: 21 May 2013
Posts: 651
Re: 10^k + 5^k =  [#permalink]

### Show Tags

23 Mar 2018, 05:39
Bunuel wrote:
$$10^k + 5^k =$$

A. $$5(2^k + 1)$$

B. $$5^k(2^k + 1)$$

C. $$5^k*3^k$$

D. $$15^k$$

E. $$15^{2k}$$

=5^k(2^k+1)
Manager
Joined: 28 Jan 2018
Posts: 54
Location: Netherlands
Concentration: Finance
GMAT 1: 710 Q50 V36
GPA: 3

### Show Tags

23 Mar 2018, 09:54
Bunuel wrote:
$$10^k + 5^k =$$

A. $$5(2^k + 1)$$

B. $$5^k(2^k + 1)$$

C. $$5^k*3^k$$

D. $$15^k$$

E. $$15^{2k}$$

Key formula to use: $$(a*b)^{m} = a^{m} * b^{m}$$

$$10^{k} + 5^{k} = 2^{k}*5^{k} + 5^{k} = 5^{k}*(2^{k} + 1) (B)$$
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: 10^k + 5^k =  [#permalink]

### Show Tags

26 Mar 2018, 17:35
Bunuel wrote:
$$10^k + 5^k =$$

A. $$5(2^k + 1)$$

B. $$5^k(2^k + 1)$$

C. $$5^k*3^k$$

D. $$15^k$$

E. $$15^{2k}$$

10^k + 5^k = 2^k * 5^k + 5^k = 5^k(2^k + 1)

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: 10^k + 5^k = &nbs [#permalink] 26 Mar 2018, 17:35
Display posts from previous: Sort by