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20 May 2017, 06:20
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
46% (01:11) correct
54%
(01:08)
wrong
based on 145
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Is Integer x a prime number?
1) x has only one odd factor
2) x has only one even factor
Source: www.GMATinsight.com
1) x has only one odd factor
2) x has only one even factor
Source: www.GMATinsight.com
20 May 2017, 07:11
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A prime number always has only 2 factors: 1 and itself. Also there is only one even prime number: 2. Rest all prime numbers are odd: 3, 5, 7, 11, 13, ....
Statement 1. x has only 1 odd factor.
x can be equal to 1 (which has only one factor 1)
or x could be 2 (1 odd factor 1)
or x could be 4 (1 odd factor 1)
or x could be 8... Basically x could be any number of the form 2^n where n is a non negative integer
In this case, x could be prime (if it is 2) or it might not be prime (if it is 1 or 4 or 8 or 16..etc)
so Insufficient.
Statement 2. x has only 1 even factor.
First of all, x must be even (if it has an even factor). Now, any even number is a multiple of 2.
Multiples of 2: 2, 4, 6, 8, 10,...
Out of these, '2' has only 1 even factor (which is 2)
But for any other value, there will be at least two even factors: first is 2 and second will be the number itself.
So we can deduce that if x has only 1 even factor, it can only take a value of '2' and nothing else.
And '2' is a prime number.
So the information is Sufficient to answer the question.
Hence B
Statement 1. x has only 1 odd factor.
x can be equal to 1 (which has only one factor 1)
or x could be 2 (1 odd factor 1)
or x could be 4 (1 odd factor 1)
or x could be 8... Basically x could be any number of the form 2^n where n is a non negative integer
In this case, x could be prime (if it is 2) or it might not be prime (if it is 1 or 4 or 8 or 16..etc)
so Insufficient.
Statement 2. x has only 1 even factor.
First of all, x must be even (if it has an even factor). Now, any even number is a multiple of 2.
Multiples of 2: 2, 4, 6, 8, 10,...
Out of these, '2' has only 1 even factor (which is 2)
But for any other value, there will be at least two even factors: first is 2 and second will be the number itself.
So we can deduce that if x has only 1 even factor, it can only take a value of '2' and nothing else.
And '2' is a prime number.
So the information is Sufficient to answer the question.
Hence B
20 May 2017, 09:40
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GMATinsight
I like this problem! It's a little unusual - I haven't seen many GMAT problems that talk about 'odd factors' and 'even factors'. However, you can work it out using only basic math and what you know about the definition of factors. I'd say you could definitely see something like this on the GMAT.
I'd probably start by 'translating' the question and the statements. That's a good place to start with number properties problems (problems that ask about issues like primes, factors, divisibility, etc.) You really want to focus in on what each piece of the problem is trying to say. When the question asks 'is x a prime number?' it's asking something like "is x 2, 3, 5, 7, 11, 13, ...?, or is it a different number instead?" Briefly remind yourself that 1 isn't prime - that's often relevant in these problems!
Statement 1 says that x only has one odd factor. What kinds of numbers only have one odd factor? Well, 1 is an odd number, and it's a factor of everything. So, every number has at least one odd factor! The trick is to find a number that has only one odd factor. That means it doesn't have any other odd factors, besides 1.
This should make you think about 2, because it's a special number - it's the only even prime. x could equal 2, since it doesn't have any odd factors other than 1. That would mean the answer to the question was 'yes'.
What other numbers have no odd factors (besides 1)? Okay, that would have to be a number that's only divisible by 2, 4, 8, etc. (It couldn't be divisible by 6, because then it would be divisible by 3! Likewise, it couldn't be divisible by 10, because then it would be divisible by 5). The simplest number to look at first is 4, which fits. It also isn't prime, so the answer is 'no'.
We got a 'yes' and a 'no', so 1 is insufficient.
Statement 2 is trickier. We know that 1 has to be a factor, since it's a factor of every number. We also know that 2 has to be a factor. Think about it this way: if a number has an even factor, it's definitely divisible by 2. So 2 must be the only even factor of the number. What kinds of numbers fit that?
The number 2 works, and it's prime.
Bigger numbers, like 4 or 6, don't work. The problem is, every number is a factor of itself. So, 4 has two different even factors, 2 and 4. 6 does as well (2 and 6). That means no even number other than 2 will fit the statement. (2) is sufficient.
