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nitred
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If x is the smallest positive integer that is not prime and not a fact 04 Mar 2017, 08:54
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Difficulty:

65% (hard)

Question Stats:

50% (01:56) correct 50% (01:16) wrong based on 6 sessions

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If x is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of x?



A. 51
B. 54
C. 72
D. 162
E. 50!+2



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vitaliyGMAT
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If x is the smallest positive integer that is not prime and not a fact 04 Mar 2017, 09:44
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nitred
If x is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of x?



A. 51
B. 54
C. 72
D. 162
E. 50!+2
Show more

Hi

Smallest prime, which is not a factor of 50! is 53, smallest composite number not a factor of 50! is 2*53 = 106.

Sum of all factors of 106:

(2^2 - 1) * (53^2 - 1) / 52 = 3*54 = 162

Answer D
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If x is the smallest positive integer that is not prime and not a fact 04 Mar 2017, 09:50
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Quote:
Hi

Smallest prime, which is not a factor of 50! is 53, smallest composite number not a factor of 50! is 2*53 = 106.

Sum of all factors of 106:

(2^2 - 1) * (53^2 - 1) / 52 = 3*54 = 162

Answer D
Show more

Isn't x = 51 ?

51 is not a prime number and it is not a factor of 50!.
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If x is the smallest positive integer that is not prime and not a fact 04 Mar 2017, 10:21
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nitred
Quote:
Hi

Smallest prime, which is not a factor of 50! is 53, smallest composite number not a factor of 50! is 2*53 = 106.

Sum of all factors of 106:

(2^2 - 1) * (53^2 - 1) / 52 = 3*54 = 162

Answer D

Isn't x = 51 ?

51 is not a prime number and it is not a factor of 50!.
Show more

Hi

51 = 3*17 and both are factors of 50! It should be min prime greater than 50 times smallest prime - 2.
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If x is the smallest positive integer that is not prime and not a fact 04 Mar 2017, 12:18
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Hi Vitaliy,

Can you explain the logic here:
Smallest prime, which is not a factor of 50! is 53, smallest composite number not a factor of 50! is 2*53 = 106.

I understand the rest (i.e. how to sum the factors).

Thanks!
-Max
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vitaliyGMAT
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If x is the smallest positive integer that is not prime and not a fact 04 Mar 2017, 12:39
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mbah191
Hi Vitaliy,

Can you explain the logic here:
Smallest prime, which is not a factor of 50! is 53, smallest composite number not a factor of 50! is 2*53 = 106.

I understand the rest (i.e. how to sum the factors).

Thanks!
-Max
Show more

Hi Max

50! = 1*2*3* ... 48*49*50 ie it has all primes from 2, 3, 5, ... to ... , 43, 47. All other numbers in 50! are just combinations of those primes. Hence we need to take least prime which is not in that list - 53 and make our number non-prime by multiplying it by another smallest prime - 2. We can multiply by 3 etc but in this case our number won't be the least possible.
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If x is the smallest positive integer that is not prime and not a fact 04 Mar 2017, 21:45
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nitred
Quote:
Hi

Smallest prime, which is not a factor of 50! is 53, smallest composite number not a factor of 50! is 2*53 = 106.

Sum of all factors of 106:

(2^2 - 1) * (53^2 - 1) / 52 = 3*54 = 162

Answer D

Isn't x = 51 ?

51 is not a prime number and it is not a factor of 50!.

Hi

51 = 3*17 and both are factors of 50! It should be min prime greater than 50 times smallest prime - 2.
Show more



I was just considering 50!/51, since there is no 51 explicitly in the expansion of 50!, I thought x = 51.

But since 51 = 3*17, both of which are contained in the expansion of 50!, we indeed have a 51 in 50!. Hence x = 51 is not correct.

Finally understood :-D
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If x is the smallest positive integer that is not prime and not a fact 05 Mar 2017, 03:34
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nitred
If x is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of x?



A. 51
B. 54
C. 72
D. 162
E. 50!+2
Show more

This question is discussed here: if-x-is-the-smallest-positive-integer-that-is-not-prime-and-157021.html

TOPIC LOCKED AND MOVED TO THE ARCHIVE.



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