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

 It is currently 15 Nov 2018, 16:03

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

November 17, 2018

November 17, 2018

07:00 AM PST

09:00 AM PST

Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### GMATbuster's Weekly GMAT Quant Quiz # 9

November 17, 2018

November 17, 2018

09:00 AM PST

11:00 AM PST

Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

# What is y in terms of x ?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 22 Jun 2017
Posts: 72
Location: Brazil
GMAT 1: 600 Q48 V25
GPA: 3.5
WE: Engineering (Energy and Utilities)
What is y in terms of x ?  [#permalink]

### Show Tags

08 May 2018, 14:54
1
1
2
00:00

Difficulty:

5% (low)

Question Stats:

90% (01:29) correct 10% (02:27) wrong based on 72 sessions

### HideShow timer Statistics

If $$5^x$$ – 5^(x–3) = (124)$$(5^y)$$, what is y in terms of x ?

A) x

B) x – 6

C) x – 3

D) 2x + 3

E) 2x + 6
RC Moderator
Joined: 24 Aug 2016
Posts: 520
Concentration: Entrepreneurship, Operations
GMAT 1: 630 Q48 V28
GMAT 2: 540 Q49 V16
Re: What is y in terms of x ?  [#permalink]

### Show Tags

08 May 2018, 15:15
1
1
FillFM wrote:
If $$5^x$$ – 5^(x–3) = (124)$$(5^y)$$, what is y in terms of x ?

A) x

B) x – 6

C) x – 3

D) 2x + 3

E) 2x + 6

$$5^x$$ – 5^(x–3) = (124)$$(5^y)$$
or $$5^x$$ – $$\frac{5^x}{5^3}$$ = $$(125-1)$$$$(5^y)$$
or $$\frac{(5^x*5^3-5^x)}{5^3}$$ = $$(5^3-1)$$$$(5^y)$$
or $$5^x*(5^3-1)$$ = $$(5^3-1)$$$$(5^y)(5^3)$$
or $$5^x$$ = 5^(y+3)
==> $$x=y+3$$
==>$$y=x-3$$ ..................Thus the answer is option C.
_________________

Please let me know if I am going in wrong direction.
Thanks in appreciation.

Manager
Joined: 03 Oct 2016
Posts: 128
Re: What is y in terms of x ?  [#permalink]

### Show Tags

08 May 2018, 17:58
1
FillFM wrote:
If $$5^x$$ – 5^(x–3) = (124)$$(5^y)$$, what is y in terms of x ?

A) x
B) x – 6
C) x – 3
D) 2x + 3
E) 2x + 6

$$5^x$$ – 5^(x-3) = (124)$$(5^y)$$
$$5^x$$ * (1 - 5^-3) = (124)$$(5^y)$$ ---- Take out $$5^x$$ common.
$$5^x$$ * $$\frac{(125 - 1)}{125}$$ = (124)$$(5^y)$$
$$5^x$$ * $$\frac{124}{125}$$ = (124)$$(5^y)$$
$$5^x$$ * $$\frac{1}{125}$$ = $$(5^y)$$ --- Striking out 124.
$$5^x$$ = 5^(y+3)

x=y+3 -> y= x- 3

_________________

Non-Allergic To Kudos

Senior Manager
Joined: 29 Dec 2017
Posts: 389
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33
GMAT 2: 690 Q47 V37
GMAT 3: 710 Q50 V37
GPA: 3.25
WE: Marketing (Telecommunications)
Re: What is y in terms of x ?  [#permalink]

### Show Tags

08 May 2018, 18:39
1
FillFM wrote:
If $$5^x$$ – 5^(x–3) = (124)$$(5^y)$$, what is y in terms of x ?

The shortest way is to substitute a real number for x. Let's say x =3, then $$5^3$$ – 5^(3–3) = (124)$$(5^y)$$
and it gives us that y = 0

A) x = 3
B) x – 6 = 3-6=-3
C) x – 3 = 0 - correct
D) 2x + 3 = 9
E) 2x + 6 = 12

VP
Joined: 09 Mar 2016
Posts: 1069
Re: What is y in terms of x ?  [#permalink]

### Show Tags

29 May 2018, 11:50
seed wrote:
FillFM wrote:
If $$5^x$$ – 5^(x–3) = (124)$$(5^y)$$, what is y in terms of x ?

A) x
B) x – 6
C) x – 3
D) 2x + 3
E) 2x + 6

$$5^x$$ – 5^(x-3) = (124)$$(5^y)$$
$$5^x$$ * (1 - 5^-3) = (124)$$(5^y)$$ ---- Take out $$5^x$$ common.
$$5^x$$ * $$\frac{(125 - 1)}{125}$$ = (124)$$(5^y)$$
$$5^x$$ * $$\frac{124}{125}$$ = (124)$$(5^y)$$
$$5^x$$ * $$\frac{1}{125}$$ = $$(5^y)$$ --- Striking out 124.
$$5^x$$ = 5^(y+3)

x=y+3 -> y= x- 3

Hi pushpitkc

cab you expain based on which rule do we take out $$5^x$$ common

i mean if it were like this (2x+7x) i understand we take out common x --> x(2+7)

but in this case $$5^x$$ – $$5^{x-3}$$ = $$(124)$$$$(5^y)$$ how can we take common $$5^x$$ it is not even in the brackets and there is only only one $$5^x$$

Also how after this $$5^x$$ * $$\frac{1}{125}$$ = $$(5^y)$$ --- Striking out 124.

we get this $$5^x$$ = 5^(y+3)

thanks for your great help
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3307
Location: India
GPA: 3.12
What is y in terms of x ?  [#permalink]

### Show Tags

29 May 2018, 12:36
1
dave13 wrote:

Hi pushpitkc

cab you expain based on which rule do we take out $$5^x$$ common

i mean if it were like this (2x+7x) i understand we take out common x --> x(2+7)

but in this case $$5^x$$ – $$5^{x-3}$$ = $$(124)$$$$(5^y)$$ how can we take common $$5^x$$ it is not even in the brackets and there is only only one $$5^x$$

Also how after this $$5^x$$ * $$\frac{1}{125}$$ = $$(5^y)$$ --- Striking out 124.

we get this $$5^x$$ = 5^(y+3)

thanks for your great help

Hey dave13

The first step is to understand what happens to $$5^{x-3}$$.

$$5^{x+(-3)} = 5^{x}*5^{-3} = 5^{x}*\frac{1}{5^3} = 5^{x}*\frac{1}{125}$$

Now, $$5^x - 5^{x-3}$$ = $$5^x – 5^{x}*\frac{1}{125}$$ = $$5^x(1 - \frac{1}{125}) = \frac{124}{125} * 5^x$$

Now, since we have $$124$$ on both sides, we will finally get $$5^x = 5^y*125 = 5^y*5^3 = 5^{y+3}$$

Hope this helps you.
_________________

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

Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: What is y in terms of x ?  [#permalink]

### Show Tags

14 Jul 2018, 18:13
FillFM wrote:
If $$5^x$$ – 5^(x–3) = (124)$$(5^y)$$, what is y in terms of x ?

A) x

B) x – 6

C) x – 3

D) 2x + 3

E) 2x + 6

5^x - 5^(x - 3) = (124)(5^y)

We see that 5^(x - 3) is common to both terms on the left side of the equation, so we factor it out:

5^(x - 3)(5^3 - 1) = (124)(5^y)

5^(x - 3)(124) = (124)(5^y)

5^(x - 3) = 5^y

Recall that when the bases are equal, we can equate the exponents:

x - 3 = y

_________________

Jeffery Miller
Head of GMAT Instruction

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

Re: What is y in terms of x ? &nbs [#permalink] 14 Jul 2018, 18:13
Display posts from previous: Sort by

# What is y in terms of x ?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.