<li>How many positive integers less than 1001 are divisible by either 2 or 5 or both?</li>
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<p>answer: 600
I got 700. hm…</p>
<li>If a triangle has exactly one of its vertices on a circle, which of the following CANNOT be the number of points that the triangle and circle have in common?</li>
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<p>answer: six
I don’t understand the question. One of the answer choices is five. How can there be five points on a triangle? I think I’m not understanding the picture.</p>
<ol>
<li>1000/2 = 500
1000/5 = 200
You counted the integers that are both multiples of 2 AND 5 twice, so therefore:
1000/(2*5) = 100
500 + 200 - 100 = 600</li>
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<ol>
<li>Approach this problem abstractly (cause I can't draw here. . .)
At most, each line can at most cross a circle twice (common sense) Since a triangle has 3 lines, it can cross the circle six times (therefore, six points that the triangle and circle have in common) However, since one of the vertices is on the circle, two of the six points are fused into a single point, so the maximum is 5. The answer is, therefore, 6 points. </li>
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<p>Imagine a big triangle, and find its center. Imagine a smaller cirlce, and find its center. place the triangle and circle on top of each other, so the centers match. That's six common points.</p>
<p>Thanks fewfdsagdsag!! what did u get on the math section of SATs?</p>
<p>I'm always scoring in the 690ish-730ish... there always seems to be one question in each section where I i) make a stupid mistake or ii) don't know how to do it.</p>
<p>lol. . .I'm a rising junior, so I haven't taken it for real yet. . .
My sophomore math score on the PSAT was 760 (yeah. . .making a stupid mistake really hurts you)</p>