For all positive integers p, p" = 2p + 1 when p is a prime number and

Question

For all positive integers p, p" = 2p + 1 when p is a prime number and p" = 3p, when p is not a prime number. What is the value of 12" + 29" ?

A. 25"
B. 41"
C. 47"
D. 95"
E. 123"

stne · Answer

12  is non prime, so we use p" = 3p and we get  = 12*3 = 36 
 29  is prime , so we use p" = 2p + 1 and we get  = 2*29 +1 =59

So  36 +59 = 95

Note the answers are given in funtion form and not directy. So we need to convert the options and see which will give  95

Among the options we see only  47   will give the answer.

47  is prime so we use  = 2p + 1 = 2*47 +1 = 95

Ans C

Hope it's clear.

SaquibHGMATWhiz · Answer

Solution:

12''+29''=3	imes 12+2	imes 29+1=36+58+1=36+59=95

Now while choosing the answer option, we have to be smart 
  Checking each option would be very tedious  
 95 is not a multiple of 3 which means it has to be of the form  prime''  
 This narrows down the possible  answer choice to either option B or C  
 upon solving, we get  47''=2	imes 47+1=94+1=95

Hence the right answer is    Option C

bumpbot · Answer

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For all positive integers p, p" = 2p + 1 when p is a prime number and

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GMAT Problem Solving (PS) Questions

For all positive integers p, p" = 2p + 1 when p is a prime number and

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