218. If the integer x is greater than 1, does x = 2?
A) x is evenly divisible by exactly two positive integers.
B) The sum of any two distinct positive factors of x is odd.
Solution:
[spoiler](A) This tells us that x is prime (it's actually the definition of a prime number)
So, x could equal 2, but it could also equal 3, 5, 7 etc --> INSUFFICIENT
(B) Factor sum is odd. So, x could equal 2 (1+2=3) or x could equal 4 (1+2+4=7)--> INSUFFICIENT
(A&B): (A) tells us that x is a prime number. Now most prime numbers (except 2) are odd, which means the two factors will be odd (1 and the prime number itself), so the sum of the factors will always be even (e.g., x=7 --> factors are 1 and 7 --> sum=8)
However, the two factors of 2 (1 and 2) add to be an odd number (3). So, x must equal 2, which means(A)&(B) are sufficient.
Answer = C[/spoiler]
pl explain ..why/how B is not sufficient.
B..says The sum of any two distinct positive factors of x is odd.
while explanation says- b is insufficient because B) Factor sum is odd. So, x could equal 2 (1+2=3) or x could equal 4 (1+2+4=7)--> INSUFFICIENT
is it satisfy the condition : sum of any two distinct positive factors of x is odd...??
1+2=3 odd.... ok
1+4=5 odd ... ok.
2+4=6...even no...
why it is 1+2+4=7..odd... why summimg all three...??
pl explain.
thanks.
A) x is evenly divisible by exactly two positive integers.
B) The sum of any two distinct positive factors of x is odd.
Solution:
[spoiler](A) This tells us that x is prime (it's actually the definition of a prime number)
So, x could equal 2, but it could also equal 3, 5, 7 etc --> INSUFFICIENT
(B) Factor sum is odd. So, x could equal 2 (1+2=3) or x could equal 4 (1+2+4=7)--> INSUFFICIENT
(A&B): (A) tells us that x is a prime number. Now most prime numbers (except 2) are odd, which means the two factors will be odd (1 and the prime number itself), so the sum of the factors will always be even (e.g., x=7 --> factors are 1 and 7 --> sum=8)
However, the two factors of 2 (1 and 2) add to be an odd number (3). So, x must equal 2, which means(A)&(B) are sufficient.
Answer = C[/spoiler]
pl explain ..why/how B is not sufficient.
B..says The sum of any two distinct positive factors of x is odd.
while explanation says- b is insufficient because B) Factor sum is odd. So, x could equal 2 (1+2=3) or x could equal 4 (1+2+4=7)--> INSUFFICIENT
is it satisfy the condition : sum of any two distinct positive factors of x is odd...??
1+2=3 odd.... ok
1+4=5 odd ... ok.
2+4=6...even no...
why it is 1+2+4=7..odd... why summimg all three...??
pl explain.
thanks.
