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ARe positive integers...

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ARe positive integers...

by houstonrockets16 » Tue Aug 17, 2010 3:25 pm
Are positive integers p and q both greater than n?

1) p - q is greater than n
2) q > p

Please help. I dont understand why it is this answer.

Answer: [spoiler]C- both statements together are sufficient... why is this it? I don't understand why you need 2 for it to work.
[spoiler][/spoiler][/spoiler]
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by nate » Tue Aug 17, 2010 4:28 pm
Are positive integers p and q both greater than n?

1) p - q is greater than n
2) q > p


1) p-q > n

p=2, q=1 2-1 > n
1 > n (this could be yes or no as n could be anything)

Insufficient.

2) q > p -> no relationship to n, so again insufficient.

Combining 1) and 2)

p - q > n

p > n + q , but p < q from (2)

since both q and p are positive, both of these equations can only be true if n is negative

(p is the smaller number, yet when added to n, p becomes larger then n+q)

- Both is sufficient as p and q are positive, hence is greater than n(negative)
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by uwhusky » Tue Aug 17, 2010 4:33 pm
1) Doesn't tell you the relationship between p/q to n. Assuming p is 4 and q is 2, 4 - 2 > n; 2 > n, both are larger than n. But if p is 10 and q is 2, 10 - 2 > n; 8 > n, then p > n, but q could be less than n (n could be 7).

2) q > p. Insufficient, because it doesn't tell you the relationship between q/p to n.

Together, we know that q > p, so p - q must be a negative number, and this number is larger than n, and therefore n MUST be a negative number. Since the question says p and q are both positive, then they must be larger than n.
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