Can someone please walk me through the logic in statement 2.
If the integer n is greater than 1, is n equal to 2?
1. n has exactly two positive factors
2. The difference of any two distinct positive factors of n is odd.
OA = B
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- force5
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hi tonebeeze
stmnt 1 (insuff) eg 2,3,5 etc)
stmnt 2 (sufficient) - 2 ( has only 2 factors 1 and 2 and the difference between 2 and 1 = odd number
3( has factors 1 and 3 the diff will always be even)
4 ( has factors 1,2,4) difference between any 2 distinct factors is not odd.
5 (1 and 5 ) will always be even.
hence you see that the diff between factors is odd only in the case of 2.
hence B
stmnt 1 (insuff) eg 2,3,5 etc)
stmnt 2 (sufficient) - 2 ( has only 2 factors 1 and 2 and the difference between 2 and 1 = odd number
3( has factors 1 and 3 the diff will always be even)
4 ( has factors 1,2,4) difference between any 2 distinct factors is not odd.
5 (1 and 5 ) will always be even.
hence you see that the diff between factors is odd only in the case of 2.
hence B
- GMATGuruNY
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Statement 1: n has exactly 2 positive factors.tonebeeze wrote:Can someone please walk me through the logic in statement 2.
If the integer n is greater than 1, is n equal to 2?
1. n has exactly two positive factors
2. The difference of any two distinct positive factors of n is odd.
OA = B
In other words, n can be any prime number.
Insufficient.
Statement 2: The difference of any two distinct positive factors of n is odd.
Thus, n cannot have two odd factors, since odd-odd = even.
Thus, n cannot have two even factors, since even-even = even.
Thus, n must have exactly one odd factor and exactly one even factor.
Only n=2 has exactly one odd factor (1) and exactly one even factor (2).
Sufficient.
The correct answer is B.
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Hi,tonebeeze wrote:Can someone please walk me through the logic in statement 2.
If the integer n is greater than 1, is n equal to 2?
1. n has exactly two positive factors
2. The difference of any two distinct positive factors of n is odd.
first off, it's important to understand exactly what (2) says - I've seen many people get this question wrong because they misinterpret (2).
This means that if you take any two distinct factors of n, you'll get an odd difference. How is this possible? Only in 1 case: n must have exactly 1 even factor and exactly 1 odd factor.The difference of any two distinct positive factors of n is odd.
Let's examine why this conclusion holds:
if n had two odd factors, then if we took the difference between those two factors we'd get an even result and violate the condition;
if n had two even factors, then if we took the difference between those two factors we'd get an even result and violate the condition; and
if n has more than two factors, then we'll always have at least two evens or at least two odds in the mix, leading to a violation of the condition.
Since 2 is the only number that has exactly 1 even factor and exactly 1 odd factor, (2) gives us a definite "yes" answer and is sufficient.
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