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# What is the value of the integer p ?

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Math Expert
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What is the value of the integer p ?  [#permalink]

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14 Jun 2012, 03:04
2
4
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Difficulty:

5% (low)

Question Stats:

83% (00:37) correct 17% (00:44) wrong based on 1324 sessions

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What is the value of the integer p ?

(1) Each of the integers 2, 3, and 5 is a factor of p.
(2) Each of the integers 2, 5, and 7 is a factor of p.

Diagnostic Test
Question: 26
Page: 25
Difficulty: 550

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Re: What is the value of the integer p ?  [#permalink]

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14 Jun 2012, 03:04
2
SOLUTION

What is the value of the integer p ?

(1) Each of the integers 2, 3, and 5 is a factor of p. We don't know whether these are the only factors of p. Not sufficient.
(2) Each of the integers 2, 5, and 7 is a factor of p. We don't know whether these are the only factors of p. Not sufficient.

(1)+(2) 2, 3, 5, and 7 are factors of p, but again we don't know whether these are the only factors of p. For example p could be 2*3*5*7 or 2*3*5*7*11 or 2^2*3*5*7 etc... Not sufficient.

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Re: What is the value of the integer p ?  [#permalink]

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Updated on: 14 Jun 2012, 04:41
Hi,

Difficulty level: 550 (It's an easy one.)

Using (1)
Each of the integers 2, 3, and 5 is a factor of p.
Possible values of p = 2*3*5 or $$2^2*3*5*11$$. Insufficient.

Using (2)
Each of the integers 2, 5, and 7 is a factor of p.
Possible values of p = 2*5*7 or $$2*5^2*7*11$$. Insufficient.

Combining both (1) & (2),
Possible values of p = 2*3*5*7 or $$2*3^3*5^2*7*11$$. Insufficient.

Regards,

Originally posted by cyberjadugar on 14 Jun 2012, 04:23.
Last edited by cyberjadugar on 14 Jun 2012, 04:41, edited 1 time in total.
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Re: What is the value of the integer p ?  [#permalink]

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14 Jun 2012, 04:26
Hi,

Using (1)
Each of the integers 2, 3, and 5 is a factor of p.
Possible values of p = 2*3*5 or $$2^2*3*5*11$$. Insufficient.

Using (2)
Each of the integers 2, 5, and 7 is a factor of p.
Possible values of p = 2*5*7 or $$2*5^2*7*11$$. Insufficient.

Combining both (1) & (2),
Possible values of p = 2*3*5*7 or $$2*3^3*5^2*7*11$$. Insufficient.

Regards,

A little note: the possible values of p are not limited to just 2 values.
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Re: What is the value of the integer p ?  [#permalink]

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14 Jun 2012, 04:29
Hi,

Using (1)
Each of the integers 2, 3, and 5 is a factor of p.
Possible values of p = 2*3*5 or $$2^2*3*5*11$$. Insufficient.

Using (2)
Each of the integers 2, 5, and 7 is a factor of p.
Possible values of p = 2*5*7 or $$2*5^2*7*11$$. Insufficient.

Combining both (1) & (2),
Possible values of p = 2*3*5*7 or $$2*3^3*5^2*7*11$$. Insufficient.

Regards,

Also, can you please share you view on the difficulty level of this question. Thank you.
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Re: What is the value of the integer p ?  [#permalink]

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14 Jun 2012, 04:33
Bunuel wrote:
Hi,

Using (1)
Each of the integers 2, 3, and 5 is a factor of p.
Possible values of p = 2*3*5 or $$2^2*3*5*11$$. Insufficient.

Using (2)
Each of the integers 2, 5, and 7 is a factor of p.
Possible values of p = 2*5*7 or $$2*5^2*7*11$$. Insufficient.

Combining both (1) & (2),
Possible values of p = 2*3*5*7 or $$2*3^3*5^2*7*11$$. Insufficient.

Regards,

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,
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Re: What is the value of the integer p ?  [#permalink]

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14 Jun 2012, 04:39
Bunuel wrote:
Hi,

Using (1)
Each of the integers 2, 3, and 5 is a factor of p.
Possible values of p = 2*3*5 or $$2^2*3*5*11$$. Insufficient.

Using (2)
Each of the integers 2, 5, and 7 is a factor of p.
Possible values of p = 2*5*7 or $$2*5^2*7*11$$. Insufficient.

Combining both (1) & (2),
Possible values of p = 2*3*5*7 or $$2*3^3*5^2*7*11$$. Insufficient.

Regards,

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.
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Re: What is the value of the integer p ?  [#permalink]

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14 Jun 2012, 04:55
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.
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Re: What is the value of the integer p ?  [#permalink]

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14 Jun 2012, 08:00
integer p = ?
st.1 ) p = 2*3*5*n - NS
st.2) p = 2*5*7*n -NS

1+2 , p = 2*3*5*7*n -NS

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Re: What is the value of the integer p ?  [#permalink]

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16 Jun 2012, 04:27
Difficulty level: 600 or below

Statement 1: Int 2, 3 and 5 are the factors of P. P might have other factors too therefore might give value of 30 or multiple of it or something else.

Statement 2: Int 2, 5 and 7 are the factors of P. Similar reasoning. Multiple values are possible.

Together: Same reasoning. put together P can have factors of Int 2, 3, 5 and 7 and some other number too. There are multiple values possible.

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Re: What is the value of the integer p ?  [#permalink]

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23 Jul 2012, 07:41
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
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Re: What is the value of the integer p ?  [#permalink]

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27 Mar 2016, 19:49
Here is a visual that should help.
Attachments

Screen Shot 2016-03-27 at 7.48.34 PM.png [ 97.51 KiB | Viewed 13819 times ]

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Re: What is the value of the integer p ?  [#permalink]

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03 Dec 2016, 19:58
Here we need the value of integer p
Lets use test cases
Statement 1
p=30
p=60
Not sufficient
Statement 2
p=70
p=140
not sufficient
Statement 1 and 2
p=210
p=420
Clearly not sufficient
Hence E

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What is the value of the integer p ?  [#permalink]

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12 Jul 2017, 08:10
Bunuel wrote:
What is the value of the integer p ?

(1) Each of the integers 2, 3, and 5 is a factor of p.
(2) Each of the integers 2, 5, and 7 is a factor of p.

Diagnostic Test
Question: 26
Page: 25
Difficulty: 550

Statement 1:
2,3,5 is a factor of p
i.e. 30 is a factor of p
i.e. p is a multiple of 30.
There are numerous multiples of 30. Insufficient.

Statement 2:
2,5,7 is a factor of p
i.e. 70 is a factor of p
ie. p is a multiple of 70
There are numerous multiples of 70.

Statement 1 and 2:
2,3,5,7 is a factor of p. Similarly, there are numerous numbers.

Hence, Ans is E
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Re: What is the value of the integer p ?  [#permalink]

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24 Aug 2017, 11:30
Top Contributor
Bunuel wrote:
What is the value of the integer p ?

(1) Each of the integers 2, 3, and 5 is a factor of p.
(2) Each of the integers 2, 5, and 7 is a factor of p.

Diagnostic Test
Question: 26
Page: 25
Difficulty: 550

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

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Re: What is the value of the integer p ?  [#permalink]

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25 Dec 2017, 21:38
Bunuel wrote:
What is the value of the integer p ?

(1) Each of the integers 2, 3, and 5 is a factor of p.
(2) Each of the integers 2, 5, and 7 is a factor of p.

Diagnostic Test
Question: 26
Page: 25
Difficulty: 550

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
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Re: What is the value of the integer p ?  [#permalink]

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18 May 2018, 11:34
Bunuel wrote:
What is the value of the integer p ?

(1) Each of the integers 2, 3, and 5 is a factor of p.
(2) Each of the integers 2, 5, and 7 is a factor of p.

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.

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Re: What is the value of the integer p ? &nbs [#permalink] 18 May 2018, 11:34
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