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20 Dec 2021, 07:00
Kudos
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C
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Difficulty:
65%
(hard)
Question Stats:
51% (01:33) correct
49%
(01:33)
wrong
based on 307
sessions
History
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Time
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Not Attempted Yet
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.
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.
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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
20 Dec 2021, 07:20
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Bunuel
(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
20 Dec 2021, 07:32
Kudos
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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.
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.
