SAT Math Prep problem?!? Algebra again?
If p and n are integers such that p > n > 0 and p^2 - n^2 = 12, which of the following can be the value of p - n?
I. 1
II. 2
III. 4
If p and n are integers such that p > n > 0 and p^2 - n^2 = 12, which of the following can be the value of p - n?
I. 1
II. 2
III. 4
Comments
Hi,
p and n are integers such that p > n > 0 and p² - n² = 12.
p² - n² = 12
(p - n)(p + n) = 12
I. 1
If (p - n) = 1, then p + n = 12 so (p - n)(p + n) = 12
p - n = 1
p + n = 12
----------------
2p = 13
p would not be an integer, so discard this answer.
II. 2
If (p - n) = 2, then p + n = 6 so (p - n)(p + n) = 12
p - n = 2
p + n = 6
----------------
2p = 8
p = 4 and n = 2
This answer works.
III. 4
If (p - n) = 4, then p + n = 3 so (p - n)(p + n) = 12
p - n = 4
p + n = 3
----------------
2p = 7
p would not be an integer, so discard this answer.
Roman numeral II is the only answer. <==ANSWER
I hope that helps!! :-)
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