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

 It is currently 18 Sep 2018, 13:01

### 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

# If x = a^5 and y = a^6, a is not equal to 0, which of the following is

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49206
If x = a^5 and y = a^6, a is not equal to 0, which of the following is  [#permalink]

### Show Tags

18 Jul 2018, 00:45
00:00

Difficulty:

15% (low)

Question Stats:

78% (00:55) correct 23% (01:02) wrong based on 40 sessions

### HideShow timer Statistics

If $$x = a^5$$ and $$y = a^6$$,a is not equal to 0, which of the following is equivalent to $$a^{13}$$?

A. $$xy$$

B. $$x^2 y$$

C. $$\frac{x^3}{y}$$

D. $$\frac{x^4}{y}$$

E. $$\frac{y^3}{x}$$

_________________
SC Moderator
Joined: 30 Jan 2015
Posts: 593
Location: India
Concentration: Operations, Marketing
GPA: 3.5
Re: If x = a^5 and y = a^6, a is not equal to 0, which of the following is  [#permalink]

### Show Tags

18 Jul 2018, 00:58
Bunuel wrote:
If $$x = a^5$$ and $$y = a^6$$,a is not equal to 0, which of the following is equivalent to $$a^{13}$$?

+1 for E.

x = a^5
y = a^6
a^13 = ?

Now,plug in the values from option i.e 6*3 - 5 = 18 - 5 = 13
y^3 = a^18

and,
y^3 / x
= a^18 / a^5 = a^13

Hence, E.
_________________

The few, the fearless !

Thanks

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1985
Re: If x = a^5 and y = a^6, a is not equal to 0, which of the following is  [#permalink]

### Show Tags

18 Jul 2018, 05:26

Solution

Given:

• $$x=a^5$$
• $$y=a^6$$

To find:

• Among the given options, which is equal to$$a^{13}$$

Approach and Working:

Let’s check every option one by one.

A. $$xy= a^5 * a^6= a^11$$
B. $$x^2y= a^{10}*a^6=a=^{16}$$
C. $$\frac{x^3}{y}= \frac{a^{15}}{a^6}= a^9$$
D. $$\frac{x^4}{y}= \frac{a^{20}}{a^6}= a^{14}$$

Only one option is remaining so that has to be the answer ?
However, let’s calculate it.

E. $$\frac{y^3}{x}= \frac{a^{18}}{a^5}= a^{13}$$

Hence, the correct answer is option E.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

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

BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 3128
Location: India
GPA: 3.12
If x = a^5 and y = a^6, a is not equal to 0, which of the following is  [#permalink]

### Show Tags

18 Jul 2018, 08:30
Given that: x = $$a^5$$ and y = $$a^6$$

Common rules in exponents
$$(a^m)^n = a^{m*n}$$ | $$a^m * a^n = a^{m + n}$$ | $$\frac{1}{a^n} = a^{- n}$$

We need to find which of the answer options is equal to a^{13}.

A. $$xy = a^{5+6} = a^{11}$$
B. $$x^2*y = a^{5*2}*a^6 = a^{16}$$
C. $$\frac{x^3}{y} = a^{5*3}*a^{-6} = a^{9}$$
D. $$\frac{x^4}{y} = a^{5*4}*a^{-6} = a^{14}$$

E. $$\frac{y^3}{x} = a^{6*3}*a^{-5} = a^{13}$$ (Option E)
_________________

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

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3484
Location: United States (CA)
Re: If x = a^5 and y = a^6, a is not equal to 0, which of the following is  [#permalink]

### Show Tags

22 Jul 2018, 18:06
Bunuel wrote:
If $$x = a^5$$ and $$y = a^6$$,a is not equal to 0, which of the following is equivalent to $$a^{13}$$?

A. $$xy$$

B. $$x^2 y$$

C. $$\frac{x^3}{y}$$

D. $$\frac{x^4}{y}$$

E. $$\frac{y^3}{x}$$

Let’s check each given choice:

A) xy

xy = (a^5)(a^6) = a^11

A is not correct.

B) x^2y

x^2y = (a^5)^2(a^6) = (a^10)(a^6) = a^16

B is not correct.

C) x^3/y

x^3/y = (a^5)^3/(a^6) = (a^15)/(a^6) = a^9

C is not correct.

D) x^4/y

x^4/y = (a^5)^4/(a^6) = (a^20)/(a^6) = a^14

D is not correct either. So the right answer must be E, but let’s verify it anyway.

E) y^3/x

y^3/x = (a^6)^3/(a^5) = (a^18)/(a^5) = a^13

_________________

Scott Woodbury-Stewart
Founder and CEO

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

Re: If x = a^5 and y = a^6, a is not equal to 0, which of the following is &nbs [#permalink] 22 Jul 2018, 18:06
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.