What is the value of the integer p ?

A little note: the possible values of p are not limited to just 2 values.

Hi,

As long as a DS question is having a unique answer we can go with the Answer choice.

But in case there are two or more values which fulfill same criteria, there is no need to list all. If we have only one more case, we can say that answer from the given statement is not unique, and thus the choice is insufficient to get the answer.

Regards,

Since there are infinitely many values of p possible, then you simply won't be able to list them all. I just wanted to make it clear that there are more values of p possible than listed in your solution. Otherwise your reasoning is correct.

Hope it's clear.

What is the value of the integer p ?


1) This tells us that 2,3,5 are factors of p, so p could be = 2*3*5 or p = 2*3*5*a or p = 2*3*5 *a*b etc.
basically since we do not know the definite number of factors that p has,
hence p could have many more factors besides 2,3,5
Hence,the statement is insufficient and answer choices A & D are eliminated.

2) This tells us that 2,3,7 are factors of p,so p could be = 2*3*7 or p = 2*3*7*a or p = 2*3*5*d*a etc.
we do not know the definite number of factors that p has so p could could have more factors as well
Hence,the statement is insufficient and answer choice B is eliminated.

When we look at both the statements together,p has 2,3,5,7 as factors but then again we have no way of finding out
whether these 4 numbers are the only factors that p has.Hence both statements combined are insufficient and E is the answer.

What is the value of the integer p ?

(1) Each of the integers 2, 3, and 5 is a factor of p.
LCM OF 2,3&5=30; p= multiple of 30 such as, 30,60,90...not sufficient
(2) Each of the integers 2, 5, and 7 is a factor of p.
LCM of 2,5,&7=70;p=multiples of 70 such that 70,140,210 etc...not sufficient
from (i) and (ii)
LCM of 30,70=10;p=10,20,....not sufficient
not sufficient

Here is a visual that should help.

ASIDE:
For questions involving factors (aka "divisors"), we can say:
If k is a divisor of N, then k is "hiding" within the prime factorization of N
Consider these examples:
3 is a divisor of 24 because 24 = (2)(2)(2)(3), and we can clearly see the 3 hiding in the prime factorization.
Likewise, 5 is a divisor of 70 because 70 = (2)(5)(7)
And 8 is a divisor of 112 because 112 = (2)(2)(2)(2)(7)
And 15 is a divisor of 630 because 630 = (2)(3)(3)(5)(7)

Conversely, we can say that, if k is "hiding" within the prime factorization of N, then N is a multiple of k
Examples:
24 = (2)(2)(2)(3) <--> 24 is a multiple of 3
(2)(5)(7) <--> 70 is a multiple of 5
330 = (2)(3)(5)(11) <--> 330 is a multiple of 6

----NOW ONTO THE QUESTION-------------
Target question: What is the value of the integer p ?

Statement 1: Each of the integers 2, 3, and 5 is a factor of p.
So, p = (2)(3)(5)(possibly other primes)
This tells us that p is a multiple of 30.
There are infinitely many values of p that satisfy statement 1.
For example, p could equal 30 or p could equal 60 (etc)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Each of the integers 2, 5, and 7 is a factor of p.
So, p = (2)(5)(7)(possibly other primes)
This tells us that p is a multiple of 70.
There are infinitely many values of p that satisfy statement 2.
For example, p could equal 70 or p could equal 140 (etc)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that p = (2)(3)(5)(possibly other primes)
Statement 2 tells us that p = (2)(5)(7)(possibly other primes)
When we COMBINE the statements, we can conclude that p = (2)(3)(5)(7)(possibly other primes)
In other words, p is a multiple of 210.
There are infinitely many values of p that satisfy this condition.
For example, p could equal 210 or p could equal 420 (etc)
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

RELATED VIDEO

1. 2,3,5 are factors of P but we do not know how many times they are occurring. Like P=2*3*5 or P=2^2*3^3*5^5 or can be anything. Also, we do not know whether 2,3,5 are only factors of P -INSUFFICIENT
2. 2,5,7 are factors of P but we do not know how many times they are occurring. Like P=2*5*7 or P=2^2*5^3*7^5 or can be anything. Also, we do not know whether 2,7,5 are only factors of P- INSUFFICIENT
Hence Answer: E

Statement One Alone:

Each of the integers 2, 3, and 5 is a factor of p.

We see that p could be 2 x 3 x 5 = 30, or p could be any multiple of 30. Statement one alone is not sufficient.

Statement Two Alone:

Each of the integers 2, 5, and 7 is a factor of p.

We see that p could be 2 x 5 x 7 = 70, or p could be any multiple of 70. Statement two alone is not sufficient.

Statements One and Two Together:

With two statements together, p could be 2 x 3 x 5 x 7 = 210, or p could be any multiple of 210. The two statements together are still not sufficient to answer the question.

Answer: E

thevenus
LCM of 30,70 = 10
This is not correct. LCM of 30,70 is 210
What you have done is actually HCF because HCF of 30,70 is 10
I mention this to avoid confusion for beginners.

Bunuel
How would you solve it if the statements were as follow:
(1) 2,3, and 5 are the only factors of P
(2) 2,5 and 7 are the only factors of P

Please help!

This would be a flawed question.

First of all, if 2, 3, and 5 are factors of p, then so are 1, 2*3, 2*5, 3*5, and 2*3*5. So, it makes no sense to say that 2, 3, and 5 are the ONLY factors of p. Similarly, if 2, 5 and 7 are factors of p, then so are 1, 2*5, 2*7, 5*7, and 2*5*7, are the ONLY factors of p.

If you meant to say that

(1) 2, 3 and 5 are the only PRIME factors of p
(2) 2, 5 and 7 are the only PRIME factors of p

Then we'd still have a flawed question because two statements cannot contradict each other and here they clearly are.

And finally, if (1) were "2, 3 and 5 are the only PRIME factors of p" and (2) were some non-contradictory statement, then (1) would still not be sufficient, because we would not know the powers of these primes to get the exact value of p.

Hope it's clear.