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If a is divisible by 6!, then a/5 must be [#permalink]
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06 Dec 2016, 07:31
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Re: If a is divisible by 6!, then a/5 must be [#permalink]
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06 Dec 2016, 07:55
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Bunuel wrote: If a is divisible by 6!, then a/5 must be
I. a prime number II. divisible by 3 III. a multiple of 5
A. None B. II only C. III only D. I and II only E. I, II, and III Least value of a = 720 Now, a/5 = 144 ( Divisible by 3 ) Let value of a = 1440 Now, a/5 = 288 ( Divisible by 3 ) Answer will be (B) Only II...
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Re: If a is divisible by 6!, then a/5 must be [#permalink]
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18 Apr 2017, 05:23
Abhishek009 wrote: Bunuel wrote: If a is divisible by 6!, then a/5 must be
I. a prime number II. divisible by 3 III. a multiple of 5
A. None B. II only C. III only D. I and II only E. I, II, and III Least value of a = 720 Now, a/5 = 144 ( Divisible by 3 ) Let value of a = 1440 Now, a/5 = 288 ( Divisible by 3 ) Answer will be (B) Only II...
Hi tell me one thing since least value of a is 720 so it should be multiple of 5 as well Please explain Abhishek009
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Re: If a is divisible by 6!, then a/5 must be [#permalink]
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18 Apr 2017, 05:27
ehsan090 wrote: Abhishek009 wrote: Bunuel wrote: If a is divisible by 6!, then a/5 must be
I. a prime number II. divisible by 3 III. a multiple of 5
A. None B. II only C. III only D. I and II only E. I, II, and III Least value of a = 720 Now, a/5 = 144 ( Divisible by 3 ) Let value of a = 1440 Now, a/5 = 288 ( Divisible by 3 ) Answer will be (B) Only II...
Hi tell me one thing since least value of a is 720 so it should be multiple of 5 as well Please explain Abhishek009The least value of a is 6! = 720, but we are asked about a/5, not a. The least value of a/5 is 6!/5 = 144. Hope it's clear.
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Re: If a is divisible by 6!, then a/5 must be [#permalink]
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18 Apr 2017, 05:42
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Hi ehsan090 It is not necessary to compute this value 720 at all here. Its good to remember factorials upto 6. But i did not depend on my knowledge to remember that 6! is 720.
Simply put let a=6!(smallest value)
So we are asked about a/5
Statement 1=> a/5 will never be a prime.There would be a lot of other integers in the numerator> 2,3,4 etc. Hence this is false Statement 2 => a/5 will take aways the five from 6! But three would always be there in the numerator. Hence this is always true.
Statement 2 => a/5 may or may not contain 5. Example if a=6! then a/5 will be 1*2*3*4*6. We don't have any five here. Hence this statement may or may be true.
((This statement can be true if a was say 6!*5 ))
Smash that B.
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Re: If a is divisible by 6!, then a/5 must be [#permalink]
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18 Apr 2017, 07:13
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a is divisible by 6! i.e. a is divisible by 1*2*3*4*5*6 So least value of a is 6!= 1*2*3*4*5*6 a/5= 1*2*3*4*6 a has at least 2 prime nos. (2 and 3). So a is not a prime no. As a has 3 as its prime factor, it is divisible by 3. We just eliminated 5 and we are not sure if there is any other 5 or a multiple of 5 in the factors of a. So choice 3 is also not true as this is a MUST BE question.
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Re: If a is divisible by 6!, then a/5 must be [#permalink]
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24 Apr 2017, 16:54
Bunuel wrote: If a is divisible by 6!, then a/5 must be
I. a prime number II. divisible by 3 III. a multiple of 5
A. None B. II only C. III only D. I and II only E. I, II, and III Since 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720, we see that a = 720k for some positive integer k, and hence a/5 = 720k/5 = 144k. Furthermore, since 144 is a multiple of 3, 144k will be always divisible by 3 for all values of k. However, since 144 is not a multiple of 5, 144k will only be a multiple of 5 for some values of k. Last but not least, since 144 is not a prime number, 144k will never be a prime number for any values of k. Answer: B
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Re: If a is divisible by 6!, then a/5 must be [#permalink]
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25 Apr 2017, 13:09
If a is divisible by 6!, the lowest value of is 6!. a/5 removes a factor of 5. So, if a=6x5x4x3x2, then a/5 is not divisible by 5. In addition, it's clear that a/5 is not a prime. Lastly, dividing by 5 does not remove the factor of 3. So we know that II is true.



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Re: If a is divisible by 6!, then a/5 must be [#permalink]
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03 Dec 2017, 08:22




Re: If a is divisible by 6!, then a/5 must be
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