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# M01#26

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05 Feb 2009, 15:32
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If $$x$$ is an integer, is $$x$$ a prime number?

1. $$x$$ is a multiple of a prime number
2. $$x$$ is a product of two integers

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18 Feb 2009, 20:04
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If x is an integer, is x a prime number?

1) x is a multiple of a prime number
2)x is a product of two integers

1 is not suff - x is multiple of prime number so x could be 3,6,9.... Now when x=3 x is prime else not.
2 is not suff - x could be product of any integers i.e. 2 and 3.

1+2 is also not suff - if x=3, x is product of two integers 1 and 3 but when x = 6, x is product of two integers 2 and 3. So still we do not know the exact value of x. Hence E is correct.
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31 Oct 2009, 05:51
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Paris92978 wrote:
Can we revisit this one?

Statement (1) says that x is a multiple of a prime number. Well, that immediately tells us that x is not a prime number because we can factor the a multiple. So now choices B, C, and E are eliminated.

Statement (2) says that x is a product of two integers. Well, we could look at the case of 2 * 3 = 6 but more importantly there is the case of 1 * any prime number. With the case of the 1 * prime number, choice D is eliminated.

As far as I know, the general rule is that a number is a multiple of itself.

so 7*1 = 7 which is the first multiple of 7.

If one were to keep this rule in mind, then statement (1) would prove insufficient.

Thus, IMO, the correct answer is E.
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07 Jan 2011, 02:41
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Wayxi wrote:
1. x is a multiple of a prime number.

I don't understand why this answer can't be A.

This means that x is a multiple of a prime. The primes are 2, 3, 5, 7, 11. So any multiples of these numbers are NOT prime. Therefore we know X is definately NOT PRIME.

How can a number be considered a multiple of itself ?
i.e. 3 is a multiple of 3, 5 is a multple of 5 etc...

On the GMAT when we are told that $$a$$ is divisible by $$b$$ (or which is the same: "$$a$$ is multiple of $$b$$", or "$$b$$ is a factor of $$a$$"), we can say that:
1. $$a$$ is an integer;
2. $$b$$ is an integer;
3. $$\frac{a}{b}=integer$$.

So "$$a$$ is multiple of $$b$$" means that $$\frac{a}{b}=integer$$ --> the least positive multiple of an integer $$b$$ is $$b$$ itself as $$\frac{b}{b}=integer$$: 3 is a multiple of 3, 5 is a multiple of 5, ... (it's the same as the greatest factor of a positive integer is this integer itself.)

Hope it's clear.
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12 May 2013, 05:53
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WannabeTitan wrote:
Bunuel wrote:
WannabeTitan wrote:

Agree with you Paris.. just putting in a bit more inputs..

Case 1: X is a multiple of a prime number
-> A number having any factor other than itself and 1 is not a prime no. For example: 6 (1, 2, 3,6) is not a prime no.
Please note, that "1" is not a prime number, but rather a co-prime no... so don;t confuse yourself by saying that 7 = 1*7 is a possibility in above case.

Option A is sufficient

Case 2: X is a product of two integers
-> Here there can be two type of number:
(i) Prime numbers. Eg. 7 = 1* 7
(ii) Non-prime numbers : 14 = 7 * 2

Not sufficient

The correct answer s E, not A.

If x is an integer, then is x a prime number?

(1) x is a multiple of a prime number --> if x=2 then the answer is Yes, but if x=4 then the answer is NO. Not sufficient.

(2) x is a product of two integers --> the same here: if x=1*2=2 then the asnwer is Yes, but if x=1*4=4 then the answer is NO. Not sufficient.

(1)+(2) The same xample: if x=2 then the asnwer is Yes, but if x=4 then the answer is NO. Not sufficient.

Bunuel I guess you didn't read the "Please note..." line i mentioned just after the case 1 in my explanation.. In order to emphasize my point that "One" is not a prime number I provide you the following links..

http://primes.utm.edu/notes/faq/one.html
http://en.wikipedia.org/wiki/Prime_number

You will find the common definition of Prime Number as -> "Any number greater than 1 but divisible only by itself and 1 is called a prime number..

Thank you for the links. I do know that 1 is not a prime number, but this has nothing to do with the question.

(1) says that "x is a multiple of a prime number". Notice that the least positive multiple of a positive integer is this integer itself. For example, 3 is a multiple of 3. Now, if x=2=prime, then it is a multiple of prime number 2, so in this case we have an YES answer to the question but if x=4 the we have a NO answer to the question. Therefore, the first statement is not sufficient.

(2) says that "x is a product of two integers". If x=2=1*2=prime then the answer is YES, but if x=1*4=4 then the answer is NO. So, this statement is also not sufficient.

When combining, we still could have an YES answer (if for example x=2=prime) as well as a NO answer (if for example x=4). Thus the answer to the question is E.

For more on check number theory chapter of our math book: math-number-theory-88376.html

Hope it helps.
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05 Feb 2009, 19:05
botirvoy wrote:
If x is an integer, is x a prime number?

1) x is a multiple of a prime number
2)x is a product of two integers

The question is unclear particularly statement 1. I am assuming x could be a multiple of itself or something else.

1: x could be that prime number or a multiple of a prime number.

If x is a multiple of only itself and 1, it is a prime.
If x is a multiple of integers other than 1 and itself, x is not a prime..

not suff...

2: x is a prime if x is a product of 2 integers i.e x and 1. suff.

B.
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11 Feb 2009, 10:13
Ok, first I do not think 1 is a prime number, you could check it out in materials but as far as I know it is not a prime number.

Back to the question

1. Multiple of a prime number : so it could be divided by itself, 1 and the prime number that make it => it is not a prime number

2. Product of 2 integer: 1 is also an integer, so if the number = 1 * an integer, it could be prime ( 1* 2 or 1*3) or could not an integer( 1*6) => stmt 2 not suff

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19 Feb 2009, 20:05
tzvister wrote:
I don't see how B is suff - as X could be a product of 2 and 3 = 6 which is not a prime.

Not suff

Thats 3 integers. if x is a multiple of 2 integers, then x must be a prime.

Suppose:
x = 2. it is a multiple of 1 and 2 i.e 2 integers.
x = 3. it is a multiple of 1 and 3 i.e. 2 integers.
x = 4. it is a multiple of 1, 2 and 4 i.e. 3 integers.
x = 5. it is a multiple of 1 and 5 i.e. 2integers.
x = 6. it is a multiple of 1, 2, 3 and 6 i.e. 4 integers.

x = 10. it is not a multiple of 2 and 5 rather its a multiple of 1, 2, 5, and 10.

Now I realize x could be -2. If so, x is a multi of either -2 and 1 or -1 and 2. If x = -2, x is not a prime.

So I think it should be C. From 1 and 2, x is a product of a prime and it is a product of 2 integers. In that case, x is a prime as it is multiple of a prime and 1..
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31 Oct 2009, 05:27
Can we revisit this one?

Statement (1) says that x is a multiple of a prime number. Well, that immediately tells us that x is not a prime number because we can factor the a multiple. So now choices B, C, and E are eliminated.

Statement (2) says that x is a product of two integers. Well, we could look at the case of 2 * 3 = 6 but more importantly there is the case of 1 * any prime number. With the case of the 1 * prime number, choice D is eliminated.

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15 Nov 2009, 05:12
(1) Insufficient
2 * 3 = 6 – not a prime
1 * 3 = 3 – a prime
(2) Insufficient
2*3*3 = 18 – not a prime
1*3 = 3 – a prime
(1) and (2)
2*3*3 = 18 – not a prime
1*3 = 3 – a prime
Thus, insufficient E

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30 Jan 2010, 12:07
GMAT TIGER wrote:
botirvoy wrote:
If x is an integer, is x a prime number?

1) x is a multiple of a prime number
2)x is a product of two integers

The question is unclear particularly statement 1. I am assuming x could be a multiple of itself or something else.

1: x could be that prime number or a multiple of a prime number.

If x is a multiple of only itself and 1, it is a prime.
If x is a multiple of integers other than 1 and itself, x is not a prime..

not suff...

2: x is a prime if x is a product of 2 integers i.e x and 1. suff.

B.

I don't agree on the the answer

Statement 2. Why don't we consider product of 2 integers as ANY Integer?
( the statement doesn't specify whether the integers are prime or not prime,
for example: X can be a product of 1*2 ( then yes prime)
but X can be a product of 2*3 ( thus not prime)

and statement 1 is enough as if X is multiple of prime numbers ( 2, 3, 5, ...)
thus X is not prime because it will include 1* PRIME1*PRIME2 and thus has more than 2 factors!!!!

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30 Jan 2010, 12:15
Prometoh wrote:
(1) Insufficient
2 * 3 = 6 – not a prime
1 * 3 = 3 – a prime
(2) Insufficient
2*3*3 = 18 – not a prime
1*3 = 3 – a prime
(1) and (2)
2*3*3 = 18 – not a prime
1*3 = 3 – a prime
Thus, insufficient E

I have a question?!!!
the statement 1 says- x is a multiple of prime numbers!!!!
1- is not a prime number , it is a FACTOR of prime number. the smalles prime number is 2 thus the combination of 1*3 will not hold true!

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30 Jan 2010, 12:28
TIMURgmat wrote:
Prometoh wrote:
(1) Insufficient
2 * 3 = 6 – not a prime
1 * 3 = 3 – a prime
(2) Insufficient
2*3*3 = 18 – not a prime
1*3 = 3 – a prime
(1) and (2)
2*3*3 = 18 – not a prime
1*3 = 3 – a prime
Thus, insufficient E

I have a question?!!!
the statement 1 says- x is a multiple of prime numbers!!!!
1- is not a prime number , it is a FACTOR of prime number. the smalles prime number is 2 thus the combination of 1*3 will not hold true!

Consider the below question from the same test where it;s clearly stated that 1- is not a prime number!

Is the product of x and y a prime number?

1. x^2 = 1
2. y is positive and prime; x is positive but not prime
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06 Feb 2010, 14:21
TIMURgmat wrote:
Prometoh wrote:
(1) Insufficient
2 * 3 = 6 – not a prime
1 * 3 = 3 – a prime
(2) Insufficient
2*3*3 = 18 – not a prime
1*3 = 3 – a prime
(1) and (2)
2*3*3 = 18 – not a prime
1*3 = 3 – a prime
Thus, insufficient E

I have a question?!!!
the statement 1 says- x is a multiple of prime numbers!!!!
1- is not a prime number , it is a FACTOR of prime number. the smalles prime number is 2 thus the combination of 1*3 will not hold true!

Statement 1 says that "x is a multiple of a prime number." This is different from what you have quoted "x is a multiple of prime numbers"

Statement #1: x is a multiple of a prime number.

Consider Prime number 3.
First multiple of 3 = 3
Second multiple of 3 = 6
Third multiple of 3 = 9,etc....

The statement says that: x is a multiple of a prime number.
But now we don't know which multiple they are talking about! First? Second? Third?

If it is the first multiple, then x is a prime number.
If it a the 2nd,3rd, etc, multiple, then no, x is not a prime number.

Hence Statement 1 is insufficient.

I hope this makes sense.

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11 Feb 2010, 09:42
I think so It E

each the statements alone is not suff.

becoz 1 ) x is multiple of prime no .So if x is multiple of prime no 3.So the value of x is going to be 3,6,9,12,15 etc

Where 3 is a prime number and rests are not .So 1 is insuff

2) is absolutely insuff .Becoz two int can be any int.

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03 May 2010, 04:57
I think the best response to the question is option E.
(1) x is a multiple of a prime no: 2 = 2x1; 6=2x3...Insuff
(2) x is a product of two intgs: Again, 2=2x1; also 6 = 2x3 (two integers) so, Insufficient
Considering (1) and (2):
2 = 2x1 is a multiple of a prime no & product of 2 integers...YES, x is prime
-2 = -1 x 2: multiple of a prime(2) & product of 2 integers (2 & -1)...NO, x is not prime
6 = 2x3 is equally a multiple of a prime no and product of 2 integers..NO, x is not prime
Therefore, (1) and (2) combined is out.

Option E seems the best.
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03 May 2010, 09:02
If is an integer, is a prime number?

1. is a multiple of a prime number
2. is a product of two integers

St 1:

x is multiple of prime number (can be 7*1, or 2*3 or 5*6)
so not suff.

St 2:
x is product of two integers(7*1, or 2*3 or 2*5)
not suff.

in either case its not concluding to single value with or without combining both statements & thus its E.

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06 Jan 2011, 18:50
1. x is a multiple of a prime number.

I don't understand why this answer can't be A.

This means that x is a multiple of a prime. The primes are 2, 3, 5, 7, 11. So any multiples of these numbers are NOT prime. Therefore we know X is definately NOT PRIME.

How can a number be considered a multiple of itself ?
i.e. 3 is a multiple of 3, 5 is a multple of 5 etc...

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08 Jan 2011, 20:12

Catch here is to know that every prime number is a multiple of a prime number, that is the same number. 3 is a prime number and it is a multiple of 3 as 3*1=3.

Very good trap question.
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08 Jan 2011, 20:20
Wayxi wrote:
1. x is a multiple of a prime number.

I don't understand why this answer can't be A.

This means that x is a multiple of a prime. The primes are 2, 3, 5, 7, 11. So any multiples of these numbers are NOT prime. Therefore we know X is definately NOT PRIME.

How can a number be considered a multiple of itself ?
i.e. 3 is a multiple of 3, 5 is a multple of 5 etc...

As per definition of a "multiple", any number that allows any other number divide it completely (ie leaving zero as a remainder) is a multiple of that other number. 3, when divided by 3, leaves a remainder of 0, hence 3 is a multiple of 3. This applies to all numbers.

Additional info: 0 is also a multiple of all numbers as 0 when divided by any other number yields a remainder of 0. This is an important number property frequently tested on the GMAT.
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