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If the number of factors of a positive integer, P, that are in the for
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28 Nov 2023, 06:50
28 Nov 2023, 06:50
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Difficulty:
95%
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Question Stats:
19% (03:11) correct
81%
(02:21)
wrong
based on 21
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If the number of factors of a positive integer, P, that are in the form 5k is 30, and P=56^a* P1^b*P2^c, where 5, P1, P2 are distinct prime factors and a,b & c are positive integers, then what is the value of a+b+c?
1) The total number of factors of P is even
2) O is divisible by 125, but not divisible by 625
a) Statement 1) ALONE is sufficient but statement
2) ALONE isn't sufficient b) Statement 2) ALONE is sufficient but statement 1) ALONE isn't sufficient
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE isn't sufficient
d) EACH statement ALONE is sufficient
e) Statement 1) and 2) TOGETHER aren't sufficient
1) The total number of factors of P is even
2) O is divisible by 125, but not divisible by 625
a) Statement 1) ALONE is sufficient but statement
2) ALONE isn't sufficient b) Statement 2) ALONE is sufficient but statement 1) ALONE isn't sufficient
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE isn't sufficient
d) EACH statement ALONE is sufficient
e) Statement 1) and 2) TOGETHER aren't sufficient
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Joined: 30 Nov 2023
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Concentration: General Management, Leadership
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WE:Engineering (Manufacturing)
Re: If the number of factors of a positive integer, P, that are in the for
[#permalink]
04 Dec 2023, 02:01
04 Dec 2023, 02:01
can someone elloborate the solution?
Re: If the number of factors of a positive integer, P, that are in the for
[#permalink]
30 Jul 2024, 17:19
30 Jul 2024, 17:19
I think there are typos in the question.
Typo 1. P=56^a* P1^b*P2^c, where 5, P1, P2 are distinct prime factor
Since the underlined portion is given in the question,
P is I guess, 5^a*P1^b*P2^c (assuming this for solving the question)
From this total no of factors of P in the form 5k is given,
a cant be 0
So, (a)*(b+1)*(c+1) = 30
Statement (1), No of factors of P is even,
It can be understood, amonghts a, b or c, one or all are odd numbers.
Not sufficient to get a+b+c
Statement (2)
Typo 2. O is divisible by 125. From where O is coming, shouldn't it be P?
If O is P and it is divisible by 125 but not 625, then, P must have 5^3
i.e. a is 3
if a is 3,
(b+1)*(c+1) = 10
b+1 and c+1 can be 5 or 2
Note: It cant be 10 or 1 as it is given a,b,c are positive integers
and b+1 or c+1 = 1 will give either b or c as 0
Hence a+b+c = 5+2+3 = 10
Correct Option: B
Typo 1. P=56^a* P1^b*P2^c, where 5, P1, P2 are distinct prime factor
Since the underlined portion is given in the question,
P is I guess, 5^a*P1^b*P2^c (assuming this for solving the question)
From this total no of factors of P in the form 5k is given,
a cant be 0
So, (a)*(b+1)*(c+1) = 30
Statement (1), No of factors of P is even,
It can be understood, amonghts a, b or c, one or all are odd numbers.
Not sufficient to get a+b+c
Statement (2)
Typo 2. O is divisible by 125. From where O is coming, shouldn't it be P?
If O is P and it is divisible by 125 but not 625, then, P must have 5^3
i.e. a is 3
if a is 3,
(b+1)*(c+1) = 10
b+1 and c+1 can be 5 or 2
Note: It cant be 10 or 1 as it is given a,b,c are positive integers
and b+1 or c+1 = 1 will give either b or c as 0
Hence a+b+c = 5+2+3 = 10
Correct Option: B
