GMAT Changed on April 16th - Read about the latest changes here

 It is currently 23 Apr 2018, 12:24

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

What is the least integer p for which 27^p > 3^18?

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44635
What is the least integer p for which 27^p > 3^18? [#permalink]

Show Tags

21 Mar 2018, 23:07
00:00

Difficulty:

15% (low)

Question Stats:

81% (00:24) correct 19% (00:14) wrong based on 47 sessions

HideShow timer Statistics

What is the least integer p for which $$27^p > 3^{18}$$?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 18
[Reveal] Spoiler: OA

_________________
Intern
Joined: 14 Mar 2018
Posts: 10
Re: What is the least integer p for which 27^p > 3^18? [#permalink]

Show Tags

21 Mar 2018, 23:11
Bunuel wrote:
What is the least integer p for which $$27^p > 3^{18}$$?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 18

3^3p > 3^18
p>6
p=7
B
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2436
Location: India
GPA: 3.12
What is the least integer p for which 27^p > 3^18? [#permalink]

Show Tags

21 Mar 2018, 23:15
Bunuel wrote:
What is the least integer p for which $$27^p > 3^{18}$$?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 18

$$27^p$$ can be simplified as $$(3^3)^p = 3^{3p}$$ because$$(a^m)^n = a^{m*n}$$

$$3^{3p} > 3^{18}$$ -> $$3p > 18$$ -> $$p > 6$$

Therefore, the least value of p for which $$27^p > 3^{18}$$ is 7 (Option B)
_________________

Stay hungry, Stay foolish

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1007
What is the least integer p for which 27^p > 3^18? [#permalink]

Show Tags

22 Mar 2018, 01:41

Solution

We need to find the smallest integer p for which $$27^p >3^{18}$$.

Working out:

• $$27^p >3^{18}$$

• $$(3^3)^p > 3^{18}$$

• By applying $${(a^m)}^n = a^{m*n}$$, we get $$3^{3p} > 3^{18}$$

• Hence, $$3p> 18$$.
o $$p>6.$$

• Hence, the smallest integer value of $$p$$ greater than $$6$$ is 7.

_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

SVP
Joined: 26 Mar 2013
Posts: 1612
Re: What is the least integer p for which 27^p > 3^18? [#permalink]

Show Tags

23 Mar 2018, 10:16
Bunuel wrote:
What is the least integer p for which $$27^p > 3^{18}$$?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 18

$$27^p > 3^{18}$$

$$3^3p > 3^{18}$$

3p > 18.....p>6

Least integer power is 7

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2273
Re: What is the least integer p for which 27^p > 3^18? [#permalink]

Show Tags

23 Mar 2018, 12:41
Bunuel wrote:
What is the least integer p for which $$27^p > 3^{18}$$?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 18

We first re-express 27 as 3^3, and so 27^p = (3^3)^p = 3^3p. Simplifying the inequality, we have:

27^p > 3^18

3^3p > 3^18

3p > 18

p > 6

The least integer greater than 6 is 7.

_________________

Jeffery Miller

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

Re: What is the least integer p for which 27^p > 3^18?   [#permalink] 23 Mar 2018, 12:41
Display posts from previous: Sort by