HELP: Difficult % and Geometry Questions

jaffershah · July 31, 2010, 3:56pm

If a is 60 percent more than b, b is 50 percent less than c, and c is 50 percent more than d, what percent of a is d?

A. 6 2/3%
B. 40%
C. 60%
D. 83 1/3%<—Answer
E. 160%

PLEASE EXPLAIN how to reach this answer. I’ve set up the problem several times and tried plugging in.

And another question, a geometry one.

I can’t draw the figure, but it’s one big circle, with 3 smaller circles along the bigger circle’s diameter. The 3 smaller circles inside the bigger one are 1/2 the preceding one. The shaded in area is the area uncovered by the 3 smaller circles.

In the figure above segment WZ(the diameter) contains the centers of four circles(3 smaller one’s and the entire thing is 1 large circle). If WX is 1/2 of XY, and XY is 1/2 of YZ, what is the ratio of the area of the shaded region to the sum of the areas of the three smaller circles?

WZ is the diameter of the big circle, it looks like this. W—X------Y------------Z
The answer is 4/3, I can’t figure out how to reach this answer either.

If you need further clarification on this question please ask.

314159265 · July 31, 2010, 4:08pm

For the first one, you set up 3 equations based on the info given. These are the three equations:

a=1.6b
b=0.5c
c=1.5d

Now, you need to get a=(something)*d. So, plug in 1.5d for c in the 2nd equation:

b=0.5(1.5d)

b=.75d

Now plug that into the first equation for b:

a=1.6(.75d)

a=1.2d=(6/5)d

Now, the question asks, “what percent of a is d?”

So, you need to solve for d:

a=(6/5)d

(5/6)a=d

Convert 5/6 to a percent and you get D. 83 1/3%

antonioray · July 31, 2010, 4:13pm

disclaimer: this might not be the most efficent way

diameter of left small =1, radius= .5, area = .25pi
diamter of middle small= 2, radius=1 a= pi
diameter of right small = 4, radius =2 a=4pi

sum of their areas = 5.25 pi

the diameter of the big circle =4+2+1, r of big circle = 3.5 area of big circle= 12.25pi
area of shaded area = 12.25pi-5.25pi, or 7pi

7:5.25 = 4/3

jaffershah · July 31, 2010, 4:20pm

I don’t understand how you translated the question into the 3 equations.

I thought that the equations were:
a=b+.6
b=c-.5
c=d+.5

For ex, it says a is 60 percent more than b, doesn’t that mean a=60/100+b

I think this is where I made my mistake. Can you please explain?

jaffershah · July 31, 2010, 4:22pm

THANKS(for both fast/simple replies)!! Both questions make sense now.

jaffershah · July 31, 2010, 4:23pm

btw, anto I was surprised at how fast you deciphered that mess of a question i tried to explain, hah.

314159265 · July 31, 2010, 7:00pm

When it says “a is 60 percent more than b,” it’s saying that a=b+.6b=1.6b

The “60 percent” is not “60 percent of 1,” it’s “60 percent of b.”

I hopes that makes sense.

HELP: Difficult % and Geometry Questions

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