Set S consists of n distinct positive integers, none of which is great

Question

Set S consists of n distinct positive integers, none of which is greater than 12. What is the greatest possible value of n if no two integers in S have a common factor greater than 1?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 11

gmatophobia · Answer

As no two integers in S have a common factor greater than 1, the set as all co-prime numbers. All the prime numbers can be the member of the set, also 1 can be the member of the set

S = { 1, 2, 3, 5, 7, 11 }

n = 6

Option C

scrantonstrangler · Answer

Take all numbers from (1-12)
{1,2,3,4,5,6,7,8,9,10,11,12)

From here start taking numbers that are co-primes.

Eg: {1,2,3,5,7,11}

Mahim27 · Answer

Hello folks

Quick question - Why is 0 not included in the set of n numbers?

Bunuel · Answer

Because 0 is not a positive integer.

Set S consists of n distinct  positive  integers, none of which is greater than 12. What is the greatest possible value of n if no two integers in S have a common factor greater than 1?

ZERO:

1. Zero is an  INTEGER .

2. Zero is an  EVEN  integer.

3. Zero is  neither positive nor negative  (the only one of this kind)

4. Zero is  divisible by EVERY integer except 0 itself  ( \frac{x}{0} = 0 , so 0 is a divisible by every number, x).

5. Zero is a  multiple of EVERY integer  ( x*0 = 0 , so 0 is a multiple of any number, x)

6. Zero is  NOT a prime number  (neither is 1 by the way; the smallest prime number is 2).

7. Division by zero is NOT allowed:  anything/0 is undefined .

8. Any non-zero number  to the power of 0 equals 1  ( x^0 = 1 )

9.  0^0  case is  NOT tested on the GMAT .

10. If the exponent n is positive (n > 0),  0^n = 0 .

11. If the exponent n is negative (n < 0),  0^n  is undefined, because  0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0} , which is undefined.  You CANNOT take 0 to the negative power .

12.  0! = 1! = 1 .

Set S consists of n distinct positive integers, none of which is great

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Set S consists of n distinct positive integers, none of which is great

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