12 Days of Christmas GMAT Competition - Day 7: P is a positive integer

Question

12 Days of Christmas GMAT Competition with Lots of Fun

P is a positive integer. How many positive factors does P have?

(1) P/4 is a prime number.
(2) P/8 is not an integer.

Bunuel · Accepted Answer

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Pranayyerra · Answer

(1) P/4 is a prime number.
p/4 can take values 2 3 5 7 11 13 ...
so P can be 8 12 20 28 44 52.....

Number of factors are 4 6 ...
different so not sufficient

(2) P/8 is not an integer.

so P can take values 1 2 3 4 5 6 7 9 10 ... 15 17....
Hence not sufficient as each of them have different factors

combining both we have
p can take 12 20 28 44 52 ..
 
 4*3 4*5 4*7 4*11 4*13....

so number of factors are (2+1) (1+1)

Sufficient 
SO Option C

behlmanmeet · Answer

Question Stem: 
P is a positive integer. How many positive factors does P have?

(1) P/4 is a prime number.
(2) P/8 is not an integer.

Solution:

Statement 1:P/4 is a prime number

P is integer > 0. 
P/4=Prime
P=4*prime
prime=2,3,5,7...etc
P=8,12,20,28...
No. of factors if P=8=2^3=4 factors
No. of factors if P=12=2^2*3=6 factors
No. of factors if P=20=2^2*5=6 factors
No. of factors if P=28=2^2*7=6 factors
Thus, no. of factors of P will be 6 for all other values except 8. 
Statement 1 is not sufficient.

Statement 2: P/8 is not an integer 
 Since P is an integer. P/8 is not equal integer means P is not a multiple of 8 i.e P is not equal to 8,16,24,32,40...
But P can be any other integer, thus we don't have a unique value for any no. of factors of P.
Statement 2 is not sufficient.
 
 Statement 1 + Statement 2:

Now, from 1 we know P will have a unique value for no. of factors for other values except 8, and statement 2 tells us P cannot be 8. Thus, we can find a unique value for no. of factors of P.

Thus, our answer is C.

Boho · Answer

P is a positive integer. How many positive factors does P have?

Statement (1) P/4 is a prime number.
P/4 = 2; P = 8; No of factors =4 
P/4 = 3; P = 12; No of factors =2*3 = 6
P/4 = 5;.... No of factors =2*3 = 6
P/4 =7;.... No of factors =2*3 = 6

Not sufficient

statement (2) P/8 is not an integer.

P = 4; No of factors = 3 
P = 6; No of factors = 4
P= 12; No of factors = 6

Not sufficient

Combined 
P can not be 8

P/4 = 3; P = 12; No of factors =2*3 = 6
P/4 = 5;.... No of factors =2*3 = 6
P/4 =7;.... No of factors =2*3 = 6

sufficient

(C) is correct IMO

sumitkrocks · Answer

P is a positive integer. How many positive factors does P have?

Statement (1) P/4 is a prime number.
P/4 = 2; P = 8; No of factors =4 
P/4 = 3; P = 12; No of factors = 6
For all other possible P values No of factors = 6
Not sufficient

statement (2) P/8 is not an integer.
P = 4; No of factors = 3 
P = 6; No of factors = 4
P= 12; No of factors = 6

Not sufficient

Combined 
P can not be 8

Statement 1 will give unique answer

sufficient

(C) is correct IMO

yashu5279 · Answer

If P/4 is prime --> that number can be 8 ( 4factors) / 4*p that has 3*2 = 6 factors.

if p/8 is not integer, it removes the ambiguity and definitely becomes 6 factors

bumpbot · Answer

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12 Days of Christmas GMAT Competition - Day 7: P is a positive integer

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12 Days of Christmas GMAT Competition - Day 7: P is a positive integer

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