Math CHALLENGE...Post the hardest math SAT I questions you can find..

Test Preparation
121

<p>In how many zeroes does 99! end?</p>

<p>19
9 from 10, 20, 30, ...
10 from 5, 15, 25, ... (there are plenty of 2s to go with it)</p>

<p>"The smallest angle of n-sided convex polygon is 120 degrees.
Its angle measurements follow the pattern 120,125,130,135, ... degrees.
Find n."</p>

<p>Hmm...an n-sided polygon has 180*(n - 2) internal degrees...the pattern must end before or at 175...
Series:
120 + 125 =
245 + 130 =
375 + 135 =
510 + 140 =
650 + 145 =
795 + 150 =
940 + 155 =
1095 + 160 =
1255 + 165 =
1420 + 170 =
1590 + 175 =
1765</p>

<p>But none of these are divisible by 180...what am I doing wrong?</p>

122

<p>I always liked the shape of a nonagon</p>

<p>n=9</p>

<p>What was wrong
120 + 125 =
245 + 130 =
375 + 135 =
510 + 140 =
650 + 145 =
795 + 150 = <======= 945
940 + 155 = <======
1095 + 160 =
1255 + 165 =</p>

123

<p>a1, a2,a3, ..., a19 are the first 19 terms of an arithmetic sequense.
Find their sum, if a4 + a8 + a12 + a16 = 224.</p>

124

<p>What is the last digit of the 2005 digit number
122333444455555666666...... ?</p>

<p>1-9 make 45 digits
10-99 make 90 * 109 > 2005 digits, so we'll worry about those</p>

<p>1-9 = 45
f(10) = 45 + 20 = 65
f(11) = 65 + 22 = 87
f(n) = 45 + 2(10 + 11 + ... + n) = 45 + 2 * (n * (n + 1) / 2 - 45) = n(n - 1) - 45
use a graphing calculator to find the largest value of n such that f(n) < 2005
f(44) = 1935</p>

<p>then add an even number of digits using 45, so the number ends in 5</p>

125

<p>gcf101's 101st post is #123.
Not intended, honest!</p>

126

<p>a1, a2,a3, ..., a19 are the first 19 terms of an arithmetic sequense.
Find their sum, if a4 + a8 + a12 + a16 = 224.</p>

<p>a1 is 2, a19 is 110. Sum is 1064</p>

127

<p>oops lol I need to be more careful...but then again, I don't have a calculator with me, so...</p>

<p>a1, a2,a3, ..., a19 are the fiirst 19 terms of an arithmetic sequense.
Find their sum, if a4 + a8 + a12 + a16 = 224.</p>

<p>Let a1 = A
a4 = A + 3
(A + 3) + (A + 7) + (A + 11) + (A + 15) = 224
4A + 36 = 224
A + 9 = 56
A = 47</p>

<p>the sum = 47 + 48 + ... + (47 + 18) = 47 + 48 + ... + 65 = 19 * (47 + 65) / 2 = 1064</p>

<p>OR more generally,
a1 = A
a4 = A + 3B (B real)
4A + 36B = 224
A + 9B = 56
A = 56 - 9B
sum = A + (A + B) + (A + 2B) + ... + (A + 18B) = 19A + (9 * 19) B
= 19(56 - 9B) + 9 * 19B
= 19 * 56
= 1064</p>

<p>well, what do you know...SAT tactic: always input nice numbers, like B = 1 :)</p>

128

<p>All you really needed was this: </p>

<p>As soon as you see that the sequence has 19 numbers, you know that that number 10 is also the average. </p>

<p>The average of the given 4 numbers totaling 224 is 56.<br>
So, number ten is 56.<br>
Total is 56 * 19 or 1064. :)</p>

129

<p>tanonev, watch for traps,
i.e. 5*20 = 100.</p>

130

<p>If in a right triangle legs' medians are sqrt(52) and sqrt(73),
what is its hypotenuse?
Shortcut, please.</p>

131

<p>If distances from a point inside an equalateral triangle to its sides are 3, 4, and 5, what's its height?</p>

132

<p>"If in a right triangle legs' medians are sqrt(52) and sqrt(73),
what is its hypotenuse?
Shortcut, please."</p>

<p>Hypo is 10. How's that for a shortcut.</p>

<p>Label triangle a b c
Need to add sqrt(52)^2 = b^2 + (A/2)^4
and sqrt(73)^2 = a^2 + (b/2)^2</p>

<p>125 = 5/4 (a^2 + b^2)
or 100 = c^2
or c = 10. </p>

<p>A shortcut would have been to visualize the triangle and see that 8^2 + 3^2 = 73 and that 4^2 + 6^2 = 52. That makes for a perfect 6,8, 10 triangle.</p>

133

<p>"tanonev, watch for traps,
i.e. 5*20 = 100."</p>

<p>your example is bad, but I see what you mean
5, 10, 15, ... contribute 19 5's + an extra one each for 25, 50, and 75
a total of 22 5's are in 99!
there are more than 22 2's, so there are 22 10's</p>

<p>Therefore, there are 22 zeroes</p>

134

<p>If I gave a good example, the answer would be right there.
You did good!</p>

135

<p>Thanks :) My turn!!!</p>

<p>Draw a line from (0, 0) to (0, 1) and from (0, 0) to (0, -1). Now, from each of the endpoints, (0, 1) and (0, -1), draw 2 lines from the point that are perpendicular to the previous line and that extend out 1/2 unit.
From each of those endpoints (there should be four of them), draw lines extending out 1/4 unit. Then 1/8 unit, and so on.
ex.
|
|</p>

<p>__
∙|
∙|
‾‾</p>

<p>|--|
∙∙|
∙∙|
|--|</p>

<p>(pardon my ASCII art; the dots are just space fillers)</p>

<p>What is the area of the bounding rectangle of this figure?</p>

136

<p>In how many zeroes does 99! end?</p>

<p>answer 22</p>

137

<p>Just reading this thread alone looks like it could bump anyone's score by about 100+ points. :P I'll have to read through it tomorrow.</p>

138

<p>Find 1 + 1/4 + 1/16 + ...</p>

139

<p>Each face of each of three identical cubes is painted one of 6 colors; no two faces of any of the cubes are painted the same color.</p>

<p>In how many different ways can you stack these three cubes together?
(stacks are not considered different if they can be turned one into another by rotation in space)</p>

140

<p>Posts
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97 (just kidding)
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