Circle and ratios

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Circle and ratios

by Gmatasap » Sat May 28, 2016 8:45 am
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In the diagram above, points A, O, and B lie on the diameter of the large circle and D and d are diameters of two smaller circles. If the sum of the areas of the two smaller circles is 5/8 of the large circle's area. What is the ratio of D to d?

A.3:2
B.5:3
C.2:1
D.3:1
E.4:1

Question source Manhattan Test prep OA-D.
Can any one explain the answers.

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by GMATGuruNY » Sat May 28, 2016 8:57 am
Gmatasap wrote:Image

In the diagram above, points A, O, and B lie on the diameter of the large circle and D and d are diameters of two smaller circles. If the sum of the areas of the two smaller circles is 5/8 of the large circle's area. What is the ratio of D to d?

A.3:2
B.5:3
C.2:1
D.3:1
E.4:1
We can PLUG IN THE ANSWERS, which represent the ratio of D to d.
When the correct answer choice is plugged in, (area of left inner circle + area of right inner circle)/(area of outer circle) = 5/8.

D: D/d = 3/1.
Let D=6 and d=2, with the result that the diameter of the outer circle = 6+2 = 8.
Since the radius of left inner circle = 3, the area of the left inner circle = 9Ï€.
Since the radius of right inner circle = 1, the area of the right inner circle = π.
Since the radius of the other circle = 4, the area of the outer circle = 16Ï€.
Resulting ratio:
(area of left inner circle + area of right inner circle)/(area of outer circle) = (9π + π)/16π = 10π/16π = 5/8.
Success!

The correct answer is D.
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by Gmatasap » Sat May 28, 2016 9:07 am
Thanks for the solution. But, Would it be possible to plug-in the answers to find the correct solution within 2 minutes?
Solving the question would require even more time. May be, plugging in the answers is the only plausible option.

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by [email protected] » Sat May 28, 2016 2:50 pm
Hi gmatasap,

Assuming that you spend the full 75 minutes, the AVERAGE amount of time that you'll spend on questions in the Quant section will be about 2 minutes per question, but spending 2 minutes per question should NOT be your goal (your goal should be to deal with each question in the most efficient way possible, even if that means dumping it). To that end, some questions will require 3 minutes of work on your part - multi-shape Geometry questions often fall into that category. Keeping that in mind, could you have approached this prompt using what Mitch showed you and done so in 3 minutes? While there are a number of little math 'steps' involved, is any of them that difficult?

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by Gmatasap » Sat May 28, 2016 8:09 pm
Dear Rich,
Thank you for your response. I actually have experienced the problem, I grow impatient if i take any where near 2 minutes to solve a problem, and at the end of the test I always end up with nearly 10 minutes to spare. Could you please roughly mention the time I could allot to each of the chapters in Quant.

Your response could actually increase my score by 20- 30 points.

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by [email protected] » Sun May 29, 2016 10:55 am
Hi gmatasap,

Rather than think in terms of how much time you should study each Quant 'category', let's take a practical look at your last CAT. If you finished any section 5-10 minutes early, then that is almost certainly NOT a good thing. 75 minutes is the perfect amount of time to work through all of the prompts at a reasonable pace, take notes, think critically and make a reasonable attempt at answering every question.... but ONLY if you use most (if not all) of that time.

Since you're focused on the Quant section, after reviewing the section on the last CAT that you took, how many questions did you get wrong....
1) Because of a silly/little mistake?
2) Because there was some math that you just didn't know how to do?
3) Because the question was too hard?

Be honest with your assessment. Which of those 3 categories was the most frequent reason for why you got questions wrong? Now, assuming you had spent just a little more time on each of those questions that you got wrong, how many of them would you likely have gotten correct?

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