<p>Hey guys, I was wondering, how do you solve this problem?</p>
<p>On the number line above, the tick marks are equally spaced. Which of the lettered points represents Y ?</p>
<p>(A) A<br>
(B) B<br>
(C) C<br>
(D) D<br>
(E) E</p>
<p>x+y/2 is the average of x + y. So x and y have be equally far apart from the average. x is 4 units away, so y has to be too. Therefore the answer is E.</p>
<p>((x+y)/2 + x) / 2 = y</p>
<p>Here, I am just taking the average of x and (x+y)/2 to get y, because y is midway between these two points.</p>
<p>Then I would solve for y in terms of x:</p>
<p>2x+x+y=2y
3x+y=2y
2y=3x
y=3/2x</p>
<p>To make our calculation as painless as possible, choose a value that you can easier work with 3/2. Pick 2. If x is 2, then y is 3. Looking back at the number line, x is 2, then 3 more tick marks is the letter C.</p>
<p>hotctyplaya, that is true. I didn't even see that. But what is wrong with my explanation?</p>
<p>Oh I see my mistake. My equation was wrong.</p>
<p>Thanks guys</p>
<p>Hey 1 more question.....</p>
<p>Let the function s be defined so that s(x) is the area of a semicircle with diameter x. If s(6) + s(8) = s(b) what is the value of b?</p>
<p>Is there a quick shortcut way in doing this problem???</p>
<p>Thanks</p>
<p>is b = 5? ...........</p>
<p>No.... B=10</p>
<p>yea thats rigt.. my answer was radius. </p>
<p>so basically</p>
<p>6/2 = 3 = radius
8/2 = 4</p>
<p>calculate area using (pie r^2)/2 ( area for semi circle ) using 3 and 4 </p>
<p>and add the area. you should get total = 25pie/2 which is same as </p>
<p>(5)^2 pie / 2 . so radius = 5 * 2 = 10 = diameter.</p>
<p>btw what prep book are you using?</p>
<p>Online course for CB. Thanks for explanation. It is alot simplier than i was doing it.</p>
<p>Sorry, but here is one more. Is there a simply way to do this??
Besides guess and check</p>
<p>If a and b are integers such that a + b < 1000 and a/b= .625 what is the greatest possible value of b?</p>
<p>
<p>Is there a quick shortcut way in doing this problem???
There is: </p>
<p>s(6) = Pi 3^2 /2
s(8) = Pi 4^2 /2
s(b) = Pi (b/2)^2 /2</p>
<p>Pi 3^2 /2 + Pi 4^2 /2 = Pi (b/2)^2 /2
3^2 + 4^2 = (b/2)^2
That's the Pi. theorem for the triangle 3-4-5
b/2 = 5
b=10</p>
<p>whats teh ans?</p>
<p>(Reply to post#13)</p>
<p>If a/b = 0.625, then a = 0.625 b</p>
<p>a + b = 1.625 b < 1000, so b < 1000/1.625 or b < 615.38
Largest integer value for b is 615 .</p>
<p>For the original problem, why can’t you solve the first equation by setting (x+y) equal to average of x and (x+y)/2?</p>
<p>@ miaomiao4: You can, but it would not be the fastest way to get the answer.</p>
<p>Solving that equation would give us:</p>
<p>x + y = (x + ((x + y)/2))/2</p>
<p>2x + 2y = x + ((x + y)/2)
x + 2y = (x + y)/2
2x +4y = x + y
x + 3y = 0
x = -3y</p>
<p>It would be faster to use this equation:</p>
<p>x + 2 = x + y
y = 2</p>
<p>We would then need to figure out what 0 is, either way. This can be found by realizing that (x + y)/2 is halfway between x + y and 0. This puts 0 at point D and Y at point E.</p>