Processing math: 100%

Last visit was: 16 Apr 2025, 14:11 It is currently 16 Apr 2025, 14:11
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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
Your Progress

every week, we’ll send you an estimated GRE 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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

If 14/6^-2 * 45 = 2^x*3^4*35

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 31581
Own Kudos [?]: 37783 [0]
Given Kudos: 26238
Send PM
If 14/6^-2 * 45 = 2^x*3^4*35 [#permalink] New post   21 May 2019, 11:21
Expert Reply
00:00
A
B
C
D
E

Question Stats:

97% (01:28) correct 2% (06:06) wrong based on 37 sessions

Show timer Statistics

If 146−2∗45=2x∗34∗35 , what is the value of x ?

A. -2

B. 1

C. 2

D. 3

E. 4
ShowHide Answer
Official Answer
D
User avatar
B
MyGuruStefan
GRE Prep Club Tests Editor
Joined: 13 May 2019
Affiliations: Partner at MyGuru LLC.
Posts: 186
Own Kudos [?]: 336 [0]
Given Kudos: 5
Location: United States
GMAT 1: 770 Q51 V44
GRE 1: Q169 V168
WE:Education (Education)
Send PM
Re: If 14/6^-2 * 45 = 2^x*3^4*35 [#permalink] New post   21 May 2019, 18:16
1
Expert Reply
Quote:
If 146−2∗45=2x∗34∗35 , what is the value of x ?

With textbook arithmetic work step by step and eliminate fractions first. In this case, if there is a negative exponent in a denominator, you can simply move the base to the numerator and make the negative exponent positive.

Therefore, 6^2 * 14 * 45 = 2^x * 3^4 * 35.

Now, break the left side compound product into prime factors to determine the number of factors of 2.

So, 2^2 * 2 * 7 means that the left hand side of the equation includes 2^3 which means on the right hand side of the equation x = 3. Select Choice D.
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12358 [0]
Given Kudos: 136
Send PM

Top Member of the Month
Re: If 14/6^-2 * 45 = 2^x*3^4*35 [#permalink] New post   23 May 2019, 07:37
2
Carcass wrote:
If 146−2∗45=2x∗34∗35 , what is the value of x ?

A. -2

B. 1

C. 2

D. 3

E. 4


6−2=162=136

So, 146−2=(141)(136)=(141)(361)=(14)(36)

So, 146−2∗45=(14)(36)(45)

Our equation becomes: (14)(36)(45)=(2x)(34)(35)

Find the prime factorization of remaining values: (2)(7)(2)(2)(3)(3)(3)(3)(5)=(2x)(34)(5)(7)

Rearrange: (2)(2)(2)(3)(3)(3)(3)(5)(7)=(2x)(34)(5)(7)

Rewrite as powers: (23)(34)(5)(7)=(2x)(34)(5)(7)

We can see that x = 3

Answer: D

Cheers,
Brent
Prep Club for GRE Bot
gmatclubot
Re: If 14/6^-2 * 45 = 2^x*3^4*35 [#permalink]
23 May 2019, 07:37
Moderators:
adewale223
GRE Instructor
108 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1131 posts
VibhuAnurag
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact