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Hope this helps.
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The stem can be rephrased as: Is x prime? With this information we can start looking at the statements:

Statement 1: This is obviously not enough, as there is an infinite number of primes greater than 19!. E.G. 19!+1. As consecutive integers are mutually co-prime, 19!+1 must be a prime number.

Statement 2: Sufficient. This statement explicitly excluded 19!+1, so we need to check if any value x is co-prime with 19!, in which case x would be prime, since 19! contains all factors<=19.

Because of the same reason, we do not need to actively check all values x <=19! + 19, for which x cannot be prime. One example for this: x=19! + 19:
\(x=19! + 19=18!*19+19=(18!+1)*19\) Therefore, x=19!+19 cannot be prime. The same goes for all other x<=19!+19

Now we need to exclude x=19!+20, x=19!+21 and x=19!+22. Since all of the summands added to 19! are non-prime numbers with factors between 1 and 19, they share factors as 19!. Therefore statement 2 is sufficient to conclude that x cannot be prime.

Answer B.

19!+1 is not a prime no. it is divisible by 71. though, the highlighted portion is correct.

In deed, you are right. Thanks for the heads up. The conclusion stays valid though. For the numbers 2 to 22, it can easily be determined that they are not prime, so statement 2 is still sufficient.

Why are you saying that we are looking for a prime number? For instance 6 has a factor greater than 1 and less than 6..

Dear gmatmania,

You are right, actually the stem translates to "Is x NOT a prime number?" not "Is x a prime number?" as I have written mistakenly. For your example, as 6 does have factors greater than 1 and smaller than itself, it is not a prime.

However, this doesn't have an impact on the strategy for this question, or even its outcome. As this is a DS question, the question is "Do the statements provide another information to conclude that x is NOT a prime?", which is equivalent to "Do the statements provide enough information to conclude that x is a prime?"

Hope that helps.

I can'understand what kind of number are19!+2 and 19!+22 without calculating them.. I can't understand statement 2

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If all summands of a sum are divisible by a factor, then the sim is also divisible by that factor.

Take for example 19!+6. 19! Is divisible by 6, as 6 is one of its factors and 6 is of course divisible by 6, the sum 19!+6 is also divisible by 6 and therefore no prime number.

With that approach, you can conclude that all numbers from 19!+2 to 19!+22 are not prime numbers, as they all have at least one factor other than 1 and itself.

Will i have to consider only integers between 19! +2 and 19!+22? Can i consider 19!+2.1?

Thank you!

Posted from my mobile device

The question stem says that x is a positive integer.

Happy to help. If this is helpful to you, please consider giving me Kudos.

lets consider a simple example lets say we have 5!+2. now 5! = 1*2*3*4*5. thus 5!+2= 1*2*3*4*5 +2 = 2(1*3*4*5 +1). now since the whole expression is a multiple of 2. thus 5!+2 is not a prime number. you can apply the same analogy for 19!+2.

also, for 19!+22. we know that 19! contains both 11 and 2. hence we can easily take out 22 as common factor. thus 19!+22 will not be a prime




NO. since x is an integer. therefore fractional values are not allowed.

i hope it helps.

Dear pepo,

Please do not start a new thread for a problem already posted. Please search extensively before beginning a brand new thread for a math question, because most GMAT practice math questions in existence have already been posted. You can find this one here:
dose-positive-integer-x-have-a-factor-f-such-that-1-f-x-190858.html
I will ask Bunuel to merge these topics.

Mike
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Let us take statement 2 First
We had enough explanation for statements such as 19! +2<=x<=19! +22.

x will always have a factor (other than 1 and itself). In other words x is NOT prime.

[say x = 19!+2 --> we can take 2 out. This means that x is divisible by 2. Similarly we can take out 3, 4, 5, .......upto 19. Bottomline: x is composite number]

B is sufficient.

Statement 1

x > 19!

x can be a prime number. In such a case we do not have any factor f.

Or it can be a composite number. In which case there will be some f

Not sufficient.

B is the answer.

I do not understand the question and the answers mentioned, can someone explain ?