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

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

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New post 09 Aug 2015, 01:50
1
4
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

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

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#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.

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

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New post 09 Aug 2015, 02:03
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#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

Correct Answer E.
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Re: #p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?  [#permalink]

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New post 09 Aug 2015, 04:48
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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.
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Re: #p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?  [#permalink]

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New post 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.
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Re: #p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?  [#permalink]

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New post 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
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Re: #p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?  [#permalink]

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

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New post 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
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#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=4?   [#permalink] 13 Feb 2019, 03:39
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