<p>It was “distinct pair of integers” I am 1000000000000000% sure</p>
<p>How many distinct pairs of integers m+n = mn: 1</p>
<p>Guys, what is the conclusion on this one?</p>
<p>Well, no one is completely sure.</p>
<p>My view: Distinct means the numbers cannot be the same, and the only pairs of integers that would work in this scenario are [0,0] and [2,2]. Therefore, the answer would be 0.</p>
<p>If the ACT wanted the numbers to be the same, they would have said, “how many numbers are equal when added and multiplied”…or something of that sort.</p>
<p>I say 0 distinct pair to me means m can not equal n.</p>
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<p>@Brownguy09 do you remember which one is J, which one is K??</p>
<p>It can’t be 0 and 0 because the question said the integers had to be positive</p>
<p>Dear everyone,
I had a lot of time to think it over, and it was definitely 1 for m + n = mn</p>
<p>Sorry,
Nynjal</p>
<p>I think set and pair do not mean the same think. if they sad set it would mean (x,y) and (y,x) are only counted As one. It says pair, so i take that to mean you can not have (x,x)</p>
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<p>When we say 0 we do not mean 0 was the number. We mean there is no pairs</p>
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<p>@Astoria no one said it was 0 and 0…</p>
<p>The issue is whether or not m and n had to be different numbers</p>
<p>There are no pair. lol should have proof read</p>
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<p>Wait, did it ask how many distinct pairs?</p>
<p>If so, I would think that it means that 3,2 is distinct from 2,2 which is distinct from 1,7 etc… as in you can have m and n as the same number, but they reach pair must be distinct—as in each pair can only be counted once.</p>
<p>IS this |x^2-a^2| J OR K?</p>
<p>I am certain the wording was “distinct pairs of positive integers” because I had 2, then changed to 1 when I realized 0 was not positive.</p>
<p>It was If Kathy worked saturday, she DID NOT work friday.</p>
<p>Question almost word for word:
How many distinct pairs of positive integers (m,n) exist such that m + n = mn
distinct PAIRS, I was on this problem for a good 3 minutes, I know what it was.
(2,2) is no different when x and y are reversed so it is only one distinct pair. They did not ask for different integers, but they had to be positive. (2,2) is the pair which satisfies the problem. Now, I don’t know how to break it down any more…</p>
<p>(2, 2) and (0, 0) and an infinitely many number of decimal values are the only possibilities.</p>
<p>But it had to be positive and be an integer, so (2, 2) is the only valid result. The argument is simply about how ACT worded it. A lot of people thought the m and n had to be different values, so they put 0.</p>
<p>I was dumb on the other hand and put 2 because I didn’t notice it said ‘positive integers’.</p>
<p>@zz862013</p>
<p>It was -(x^2-a^2) I beleive</p>
<p>@GoldenMonkey- that was what I put as well, but I think I misread the graph on accident. Most people said that the graph had a ‘W’ shape, so the answer would be |x^2-a^2|.</p>
<p>Overall, I think I got 4-5 wrong (which is not good)
1.) Overlapping circles.
2.) Baseball averages
3.) The ‘W’ shaped graph
4.) Radius of the points on a circle (I did the diameter)
5.) Possibly the m+n=mn, depending on what is the right answer.</p>
<p>That’s (5 wrong) anywhere from a 31 (based on a scale where 60 is 36, and each decrease in scaled score equals a decrease in raw score) to a 34 (based on the 2012-2013 ACT prep provided on the ACT site, which was the best curve I’ve seen so far).</p>
<p>Ouch…</p>
<p>Guys, I asked my friend about this question a little bit ago. I asked “what is the answer for the x+y=xy question” and he/she said he/she put 0. Then, I asked if he/she remembered exactly what the question asked and he/she said “how many distinct PAIRS…”. I didn’t mention anything about pairs to him/her and he/she doesn’t read CC. I really doubt that he/she would say “pairs” completely by chance considering that he/she hasn’t read the stuff on here which might mix up his/her memory.</p>
<p>So, really, it comes down to whether or not (a,b) = (2,2) is a distinct pair. I would say it is. (3,2) and (2,3) would be distinct pairs as well since they are distinct in that their “a” values and “b” values are not equal to each other which is also why (2,2) is only counted as 1 distinct pair; you can’t reverse it.</p>