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Re D0120
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09 Sep 2017, 15:00
I don't agree with the explanation. i think A should be the answer because a set (1,1,c!) will have a median of 1 always na



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09 Sep 2017, 15:07
samism wrote: I don't agree with the explanation. i think A should be the answer because a set (1,1,c!) will have a median of 1 always na You should read solutions and the following discussions more carefully. The question asks whether a, b, and c are consecutive integers. For (1): a=0, b=1 and c=2 gives an YES answer while a=0, b=1 and c=3 gives a NO answer.
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Re: D0120
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13 Mar 2018, 17:48
I got it wrong in the tests due to oversight on my part.
Option 1  The factorial of a number can be odd only if its 0 or 1. This gives a value of b. But C can be any number greater than b.  Not sufficient.
Option 2  c! is a prime number. The only number whose factorial is prime is 2. So we get the value of c as 2. but we do not have value of a and b. Not sufficient.
Considering both the options, we can find that the numbers are consecutive numbers.
Ans: C



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all integers; a<b<c
consec?
1. Median of a! b! c! is odd a=0= 0! = 1 b=1 = 1! = 1 c=2 = 2! = 2 consec
OR
a=0 =0! = 1 b=1 = 1! = 1 c= 6 = 6!= 720
not consec
Therefore statement 1 is insufficient
Statement 2 c! = prime c= 2!
But a can still equal 1 a= 1 b= 1 c=2 =2! thus not consecutive
since the only constraint for a and b is a<b<c then we can make a and b equal anything.
Combining the two statements, combined, a!<b!<c!
A factorial is defined only for nonnegative integer numbers.
Thus 0!<1!<2! is the only possible solution within the constraint.
Sufficient.



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Re D0120
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21 Sep 2019, 00:06
I think this is a highquality question and I agree with explanation. Great question! Tests a mix of multiple basic facts on numbers.



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Re: D0120
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16 Oct 2019, 00:17
Bunuel wrote: Official Solution:
Note that: A. The factorial of a negative number is undefined. B. 0!=1. C. Only two factorials are odd: 0!=1 and 1!=1. D. Factorial of a number which is prime is 2!=2. (1) The median of {a!, b!, c!} is an odd number. This implies that b!=odd. Thus b is 0 or 1. But if b=0, then a is a negative number, so in this case a! is not defined. Therefore a=0 and b=1, so the set is {0!, 1!, c!}={1, 1, c!}. Now, if c=2, then the answer is YES but if c is any other number then the answer is NO. Not sufficient. (2) c! is a prime number. This implies that c=2. Not sufficient. (1)+(2) From above we have that a=0, b=1 and c=2, thus the answer to the question is YES. Sufficient.
Answer: C I don't quite agree with the solution here. Using option (2) , I come up with the number c =2 , since none of the numbers can be negative, we are left with only 0 and 1, here in the problem statement , it is given that a<b<c , hence a has to take 0 and b has to take 1



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Re: D0120
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16 Oct 2019, 00:22
dasoisheretorule wrote: Bunuel wrote: Official Solution:
Note that: A. The factorial of a negative number is undefined. B. 0!=1. C. Only two factorials are odd: 0!=1 and 1!=1. D. Factorial of a number which is prime is 2!=2. (1) The median of {a!, b!, c!} is an odd number. This implies that b!=odd. Thus b is 0 or 1. But if b=0, then a is a negative number, so in this case a! is not defined. Therefore a=0 and b=1, so the set is {0!, 1!, c!}={1, 1, c!}. Now, if c=2, then the answer is YES but if c is any other number then the answer is NO. Not sufficient. (2) c! is a prime number. This implies that c=2. Not sufficient. (1)+(2) From above we have that a=0, b=1 and c=2, thus the answer to the question is YES. Sufficient.
Answer: C I don't quite agree with the solution here. Using option (2) , I come up with the number c =2 , since none of the numbers can be negative, we are left with only 0 and 1, here in the problem statement , it is given that a<b<c , hence a has to take 0 and b has to take 1 I think that's addressed on the previous pages. Please reread. Hope it helps.
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Re: D0120
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16 Oct 2019, 00:29
dasoisheretorule wrote: Bunuel wrote: Official Solution:
Note that: A. The factorial of a negative number is undefined. B. 0!=1. C. Only two factorials are odd: 0!=1 and 1!=1. D. Factorial of a number which is prime is 2!=2. (1) The median of {a!, b!, c!} is an odd number. This implies that b!=odd. Thus b is 0 or 1. But if b=0, then a is a negative number, so in this case a! is not defined. Therefore a=0 and b=1, so the set is {0!, 1!, c!}={1, 1, c!}. Now, if c=2, then the answer is YES but if c is any other number then the answer is NO. Not sufficient. (2) c! is a prime number. This implies that c=2. Not sufficient. (1)+(2) From above we have that a=0, b=1 and c=2, thus the answer to the question is YES. Sufficient.
Answer: C I don't quite agree with the solution here. Using option (2) , I come up with the number c =2 , since none of the numbers can be negative, we are left with only 0 and 1, here in the problem statement , it is given that a<b<c , hence a has to take 0 and b has to take 1 I see my mistake now. Until I use (1) , I can't come up with the information that a and b are also supposed to be within the set of positive integers. Thanks [color=#ff0000]Bunnel [/color]



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Re: D0120
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17 Nov 2019, 06:17
Just a short question: since we know that factorials for negative numbers is undefined should't it be safe to assume that a,b,c are positive ?



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17 Nov 2019, 07:40
alexjsfk wrote: Just a short question: since we know that factorials for negative numbers is undefined should't it be safe to assume that a,b,c are positive ? Your doubt is already addressed on the previous pages. Please reread. Hope it helps.
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Re: D0120
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22 Nov 2019, 16:07
bunuel why not you consider values of negative integer for a? for ex. a=1,2,3.. these numbers also satisfy given condition



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Re: D0120
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22 Nov 2019, 19:16
anubhav31 wrote: bunuel why not you consider values of negative integer for a? for ex. a=1,2,3.. these numbers also satisfy given condition The factorial of a negative number is undefined.
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