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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 Source: GMAT Club Tests  hardest GMAT questions



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18 Feb 2009, 21:04
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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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Re: M01#26 [#permalink]
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31 Oct 2009, 06:51
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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.
Answer is A. 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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Re: M01#26 [#permalink]
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07 Jan 2011, 03:41
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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Re: M01#26 [#permalink]
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12 May 2013, 06:53
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 coprime 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) Nonprime numbers : 14 = 7 * 2
Not sufficient
Hence, the answer is (a)
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. Answer: E. 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_numberYou 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: mathnumbertheory88376.htmlHope it helps.
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Re: M1  26 [#permalink]
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05 Feb 2009, 20:05
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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Re: M1  26 [#permalink]
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11 Feb 2009, 11:13
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
My answer A



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Re: M1  26 [#permalink]
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19 Feb 2009, 21:05
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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Re: M01#26 [#permalink]
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31 Oct 2009, 06:27
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.
Answer is A.



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Re: M01#26 [#permalink]
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15 Nov 2009, 06:12
(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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Re: M1  26 [#permalink]
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30 Jan 2010, 13:07
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!!!! Thus A is the answer!
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Re: M01#26 [#permalink]
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30 Jan 2010, 13:15
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! Please discuss!
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Re: M01#26 [#permalink]
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30 Jan 2010, 13:28
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! Please discuss! 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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Re: M01#26 [#permalink]
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06 Feb 2010, 15:21
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! Please discuss! 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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Re: M01#26 [#permalink]
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11 Feb 2010, 10:42
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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Re: M01#26 [#permalink]
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03 May 2010, 05:57
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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Re: M01#26 [#permalink]
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03 May 2010, 10:02
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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Re: M01#26 [#permalink]
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06 Jan 2011, 19:50
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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Re: M01#26 [#permalink]
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08 Jan 2011, 21:12
Answer is E. 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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Re: M01#26 [#permalink]
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08 Jan 2011, 21:20
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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