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# M01#26

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Re: M01#26 [#permalink]  05 May 2011, 05:41

1. Not sufficient
1*prime =prime
2*prime = not prime

2. Not sufficient

Same examples from 1 can be applied here.

1*prime =prime
2*prime = not prime

Together it's still not sufficient.
Considering Product of two integers also multiple of prime

1*prime =prime
2*prime = not prime

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Re: M01#26 [#permalink]  05 May 2011, 06:17
Bunuel wrote:
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;

Really!!!!
What if a=1.5 and b=1.5; 'a' is divisible by 'b' but 'a' and 'b' are not integers. Can someone clear my doubt because it's highly unlikely that Bunuel will respond?
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Re: M01#26 [#permalink]  06 May 2011, 00:10
E for me

Question: If x is an integer, is x a prime number?

Statement1: x is a multiple of a prime number --> Insufficient
Let's pick x = 2 and 4
If x = 2, 2 is a multiple of 2 (2 x 1), and 2 is a prime number Ans --> Yes
If x = 4, 4 is a multiple of 2 (2 x 2), but 4 is NOT a prime number Ans --> No

Statement2: x is a product of two integers --> Insufficient
Let's pick x =2 and 4 again
2 = 2 x 1 , and 2 is a prime number Ans --> Yes
4 = 4 x 1 , but 4 is NOT a prime number Ans --> No

If we take statement#1&#2 together, the given information is still insufficient to determine whether x is a prime number.
Let's try x = 2, 4 again
2 is a multiple of a prime number and 2 is a product of two integers (2 x 1 = 2) Ans --> Yes (2 is a prime number)
4 is a multiple of a prime number (2) and 4 is a product of two integers (4 x 1 = 4) Ans --> No (4 is NOT a prime number)
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Re: M01#26 [#permalink]  08 May 2011, 03:33
A....is x a prime number....so according to choice A x is not a prime no and from choice b there can be no conclusion.
so correct choice is A
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Re: M01#26 [#permalink]  07 Nov 2011, 10:31
mehtakaustubh wrote:
A....is x a prime number....so according to choice A x is not a prime no and from choice b there can be no conclusion.
so correct choice is A

No.
The answer is E. Because based on the S1 you can reach to for example 3, 6, 9, ...
3 is prime but the others are not.
So A is insufficient
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Re: M01#26 [#permalink]  10 May 2012, 12:56
seofah 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

Source: GMAT Club Tests - hardest GMAT questions

Statement 1: insufficient
Why?
2 is a prime number.
2 x 1 = 2 (and thus a prime number)
but 2 x 2 = 4 (not a prime number)
Conclusion: insufficient

Statement 2: insufficient
Why?
2 x 1 = 2 (and thus a prime number)
but 2 x 2 = 4 (not a prime number)
Conclusion: insufficient

Statements 1 & 2: insufficient
Why?
Same explanation as above. Even with the two statements together, I didn't notice anything new or special from it that I can form. Thus, the same two explanations from above can be used.

Conclusion: None of the statements are sufficient to solve the mystery!
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Re: M01#26 [#permalink]  20 May 2012, 18:28
Why not C
1. multiple of prime.. ok. 3*2... any thing not sufficient
2. product of 2 integer. 3*1, 4*1 no sufficient.

from both,Hello but see, if product of 2 integer, one of them must be 1.
from a. product of a prime. so samalest prime is 2.
so it may me 2*1. 3*1, 5*1.. hense prime.
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Re: M01#26 [#permalink]  10 May 2013, 04:47
Expert's post
fluke wrote:
Bunuel wrote:
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;

Really!!!!
What if a=1.5 and b=1.5; 'a' is divisible by 'b' but 'a' and 'b' are not integers. Can someone clear my doubt because it's highly unlikely that Bunuel will respond?

Yes.

Every GMAT divisibility question will tell you in advance that any unknowns represent positive integers, which means that ALL GMAT divisibility questions are limited to positive integers only.

Thus 1.5 is divisible by 1.5 makes no sense as far as GMAT is concerned.
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Re: M01#26 [#permalink]  12 May 2013, 03:11
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.

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

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Re: M01#26 [#permalink]  12 May 2013, 03:28
Expert's post
WannabeTitan wrote:
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.

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.

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Re: M01#26 [#permalink]  12 May 2013, 03:53
Bunuel wrote:
WannabeTitan wrote:
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.

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..
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Re: M01#26 [#permalink]  12 May 2013, 05:53
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Expert's post
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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Re: M01#26 [#permalink]  25 Apr 2014, 13:08
Statement 1 is clearly trying to get us to think about multiples of a number. Let us remember that a multiple of a number, in this case a prime number, is the product of itself and any integer. Therefore, we can try to prove that this statement is not sufficient by using the following examples:

1x2 = 2 is a prime number.
2x2 = 4 is not a prime number.

Therefore, statement 1 is not sufficient since two examples that satisfy the condition presented by the statement provide two different answers.

Statement 2 is just another way to present statement 1. We could argue that statement 1 is a particular or specific case of statement 2. Therefore statement is even less specific and more general. Therefore, we could use any two integers or even use the same examples we used in the previous statement. Consequently, statement 2 is not sufficient.

Since both statements roughly present the same information, I would say that neither statement nor the combination of them will be sufficient.

E
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Re: M01#26 [#permalink]  04 May 2014, 12:31
we can solve this question very easily.
consider few prime numbers 2, 3, ....
statement 1 says x is a multiple of prime numbers= so if we take 2 as no then its multiple are 2,4,6 ,8....
is 3 then 3,6,9,12....
So this this statement doesn't give a concrete ans.
Statement 2 says x is a product of two integers
as we know product of two integers are never prime except the number and 1.
so this statement doesn't give a concrete explanation.
Now on combining statement 1 and statement 2 we do not get any concrete answer so E is the correct ans.
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Re: M01#26   [#permalink] 04 May 2014, 12:31

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# M01#26

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