<p>From earlier this year…</p>
<p>18."
The graph of y=f(x) where f is a function is shown above. Which of the following is the graph of y=f(x-2)
"</p>
<p>Rather than give the graphs let me say the main graph has a point at (6,8). It seems to me that the answer would be the graph through (4,8).</p>
<p>Instead the answer goes through (8,8). Why?</p>
<p>The function actually shifts the other direction. A little counter-intuitive at first, but it can be proven that if k > 0 and f(x): R → R, then f(x-k) is obtained by shifting f(x) k units to the right.</p>
<p>The penny has dropped. </p>
<p>g(8)=y(6)= 8.</p>
<p>Really counter intuitive for me. Glad they don’t seem to ask the question this way frequently.</p>
<p>Thanks rspence</p>
<p>Can a line intersect another line and be not perpendicular to it?</p>
<p>@maraudersmap Yes of course.</p>
<p>Another SAT-level problem (slightly trickier):</p>
<p>A triangle has integer side lengths, and has perimeter 15. How many non-congruent triangles satisfy the above constraints?</p>
<p>3?
…</p>
<p>^More than three.</p>
<p>@Neatoburrito – were you assuming that the sides all had to be different? Because if that were the case, I believe 3 would have been right…</p>
<p>Something about playing with this question reminded me of solving KenKen puzzles…</p>
<p>^The triangle could be isosceles (or equilateral). For the SAT math sections, the questions themselves are almost always to be interpreted literally (e.g. don’t assume side lengths are different).</p>
<p>Here’s a hint and a bump:</p>
<p>When you solve a KenKen, you often have to consider all of the ways to make numbers add up to a desired total, constrained by other things in the puzzle. This time, you need the integers to add up to 15. But you are constrained by the triangle inequality. The two smaller sides have to add to more than the larger. That puts a limit on how big your biggest side can be…for example, it can’t be 10, because the remaining sides would only add up to 5…</p>
<p>Can someone help me with this?</p>
<p>In the xy-plane, line L passes through the origin and is perpendicular to the line 4x+y=k, where k is a constant. If the two lines intersect at the point (t, t+1), what is the value of t?</p>
<p>A. -4/3
B. -5/4
C. 3/4
D. 5/4
E. 4/3</p>
<p>maraudersmap:
Find the slope of line L is perpendicular to:
y = -4x + k
Slope is -4 and the y-intercept is (0, k)
Since line L is perpendicular, the slope is the negative reciprocal of -4, so it is 1/4
Because it passes through the origin, its y-intercept is zero.
The equation for line L is therefore y=x/4</p>
<p>Plug in the values of the intersection point for the equation for line L:
t+1 = t/4
4t + 4 = t
3t = -4
t = -4/3
(ans)</p>
<p>Note that “k” was never used and was likely put there to confuse you!</p>
<p>Here’s a math question that I made up:
How many ways can you flip a penny 10 times and get:
a) 2 heads in a row (ex THHTTTTTTT, TTTHHTTTTT
b) 2 heads, a tail, and a head? (in that order) (ex. TTHHTHTTTH)</p>
<p>a) I see a solution but it involves creating a recursive function which I don’t want to evaluate ~10 times right now. I’ll see if there’s a simpler solution…</p>
<p>b) looks like it can be done directly, but you have to take into account two HHTH’s occurring within the string, as well as HHTHHTH and HHTHHTHHTH (the latter are easy to count though). </p>
<p>Here’s one that I made up:
John picks two (not necessarily distinct) integers at random from the set {1,2,3,…,20}. He adds the product of these two integers with the sum of these two integers. For which of the following numbers is it impossible for John to obtain as a final result?
A) 23
B) 48
C) 83
D) 91
E) 131</p>
<p>Is the answer C)83 ?</p>
<p>C)83
The two numbers are 3,20</p>
<p>D) 91. If the two numbers are a and b, we can write ab+a+b=(a+1)(b+1)-1. Setting this equal to 91, we get (a+1)(b+1)=92, which is impossible since the only factor pairs of 92 are (1,92), (2,46), an (4,23), all of which have a factor greater than 21.</p>
<p>Yup, it’s D) 91.</p>
<p>Here’s a problem:
How many positive integers n produce a remainder of 9 when 2009 is divided by n and n > 9?</p>
<p>@JackTC nice problem…already solved it, don’t want to spoil the answer/solution though.</p>
<p>I saw this problem once:
A square pyramid and a tetrahedron have all of their edges equal to 1. A triangular face of the tetrahedron is glued to a triangular face of the pyramid. How many faces does the resulting solid have?</p>