Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 21 Jul 2019, 12:17

### 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

# #p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 29 Apr 2015
Posts: 830
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?  [#permalink]

### Show Tags

09 Aug 2015, 01:50
1
4
00:00

Difficulty:

35% (medium)

Question Stats:

75% (01:55) correct 25% (02:06) wrong based on 75 sessions

### HideShow timer Statistics

#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?

A. –108
B. –44
C. 10
D. 16
E. 18

How do you guys solve such questions other than with Plugging In the AC? I am curious to know your preffered approach. Thanks. It took me 3 minutes 17 seconds with plugging in.

_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.
Intern
Joined: 19 May 2015
Posts: 7
Re: #p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?  [#permalink]

### Show Tags

09 Aug 2015, 02:03
2
1
#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?

My approach took 1:36 and it could have taken less.

if #p=2*p-20 (as noted in Question Stem) =>

#(#(#p))=2(2(2*p-20)-20)-20=

2(4*p-40-20)-20=

8*p-80-40-20=

8*p-140

we know that it equals 4, so 8*p-140=4 =>

8*p=144 => p=18

CEO
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: #p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?  [#permalink]

### Show Tags

09 Aug 2015, 04:48
1
reto wrote:
#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?

A. –108
B. –44
C. 10
D. 16
E. 18

How do you guys solve such questions other than with Plugging In the AC? I am curious to know your preffered approach. Thanks. It took me 3 minutes 17 seconds with plugging in.

Should be straightforward even without plugging in.

Lets use algebra for this:

#p = 2p-20 --->#(#p) = 2(2p-20)-20 = 4p-60 and thus #(4p-60) = 2(4p-60)-20 = 8p-140 = 4 ---> 8p= 144 ---> p = 16, D is the correct answer. Close to 1.5 minutes. Although this is more straightforward approach, you just need to be careful with your algebra all throughout.
Intern
Joined: 21 Jan 2013
Posts: 7
Re: #p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?  [#permalink]

### Show Tags

20 Dec 2018, 16:14
Could someone help explain in more detail how to solve this? Thanks!

reto wrote:
#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?

A. –108
B. –44
C. 10
D. 16
E. 18

How do you guys solve such questions other than with Plugging In the AC? I am curious to know your preffered approach. Thanks. It took me 3 minutes 17 seconds with plugging in.
Senior Manager
Joined: 15 Feb 2018
Posts: 258
Re: #p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?  [#permalink]

### Show Tags

25 Dec 2018, 18:20
chowarth

Apply from the inside and move out.
#p=2p-20

#(#(#p))=4?
#[#(2p-20)]=4
#[2(2p-20)-20]=4
#[4p-40-20]=4
2[4p-40-20]-20=4
8p-80-40-20=4
8p=144
p=18
Intern
Joined: 03 Jan 2017
Posts: 20
Location: India
Concentration: Finance, Economics
Re: #p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?  [#permalink]

### Show Tags

24 Jan 2019, 11:24
just looking at the ans option we can eliminate and b since adding negative and negative will give the bigger negative.
C will give 0 in the 1st substitution. no need to even calculate that.
Between D and E you only need to solve either one if D checks out its the ans if it does not E is the ans. should take less than 30 sec.
Intern
Joined: 12 Sep 2018
Posts: 28
#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?  [#permalink]

### Show Tags

13 Feb 2019, 03:39
Another fast approach is to 'undo' the function # (apply the inverse function #^(-1)):

if #p= 2p-20
p=(#p+20)/2=#p/2+10

Now, we have #(#(#p))=4; therefore, we need to apply the inverse function 3 times:

4/2+10=12
12/2+10=16
16/2+10=18
#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?   [#permalink] 13 Feb 2019, 03:39
Display posts from previous: Sort by