Statement 1:
a^2+b^2+c^2+d^2 = 0.
Since all the terms have an even power, none of them can be -ve. And sum of 4 +ve numbers cannot be 0.
So all the terms, a,b,c and d should be 0. Their product would be =0 (even) Sufficient.
Statement 2:
You can have 4 even numbers, even product
or 4 odd numbers, odd product. A IMO
difficult questions
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Source: Beat The GMAT — Data Sufficiency |
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shankar.ashwin
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shankar.ashwin
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Statement 1:sukh wrote:
If N is a positive integer, is N ! divisible by 66 ?
(1)N! is divisible by 11
(2)N! is divisible by 12
Since 11 is a prime number N should be >11, for it to be divisible by 11. N! would contain (6*11) Hence would be divisible by 66. Sufficient.
Statement 2:
N! is divisible by 12.
N! could be 4! (or) 12!. One case its divisible by 66 and in the other its not. Insuff.
A IMO
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neelgandham
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Is the product abcd even?
(1)a^2 +b^2 +c^2 + d^2 = 0 square of a number is always >0. So, only one case exists - a=b=c=d=0 ! - Sufficient!
(2)a = b = c = d If a = b = c = d = Even, then product abcd is Even; If a = b = c = d = Odd, then product abcd is Odd - Insufficient
IMO A
__________________________________________
If N is a positive integer, is N ! divisible by 66 ? Rephrasing the question, Is N > 11 ?
(1)N! is divisible by 11 => N > 11 - Sufficient
(2)N! is divisible by 12 => N > 4 - Insufficient
IMO A
(1)a^2 +b^2 +c^2 + d^2 = 0 square of a number is always >0. So, only one case exists - a=b=c=d=0 ! - Sufficient!
(2)a = b = c = d If a = b = c = d = Even, then product abcd is Even; If a = b = c = d = Odd, then product abcd is Odd - Insufficient
IMO A
__________________________________________
If N is a positive integer, is N ! divisible by 66 ? Rephrasing the question, Is N > 11 ?
(1)N! is divisible by 11 => N > 11 - Sufficient
(2)N! is divisible by 12 => N > 4 - Insufficient
IMO A
Anil Gandham
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vaibhavgupta
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One of the most basic rules that u keep in ur head is that a square of any non-imaginary i.e. without iota, will always be non negative.sukh wrote:Is the product abcd even? (1)a^2 +b^2 +c^2 + d^2 = 0 (2) a = b = c = d
plz expain in detail
If N is a positive integer, is N ! divisible by 66 ? (1)N! is divisible by 11 (2)N! is divisible by 12
If OA is A, IMO B
If OA is B, IMO C
If OA is C, IMO D
If OA is D, IMO E
If OA is E, IMO A
FML!! :/
If OA is B, IMO C
If OA is C, IMO D
If OA is D, IMO E
If OA is E, IMO A
FML!! :/
