GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If the diameter (d ) of a circle is an integer and 6 cm ≤ d
[#permalink]
04 Feb 2018, 15:35
04 Feb 2018, 15:35
Expert Reply
00:00
Question Stats:
61% (00:44) correct
38% (00:46) wrong based on 31 sessions
Hide Show timer Statistics
If the diameter (d) of a circle is an integer and \(6 cm\) \(\leq\) \(d\) \(\leq\) \(10 cm\), which could be the area of the circle?
A. \(36\pi cm^2\)
B. \(25\pi cm^2\)
C. \(14\pi cm^2\)
D. \(6\pi cm^2\)
E. \(3\pi cm^2\)
Kudo for the right solution and explanation
Sherpa Prep Representative
Joined: 15 Jan 2018
Posts: 147
Given Kudos: 0
Re: If the diameter (d ) of a circle is an integer and 6 cm ≤ d
[#permalink]
04 Feb 2018, 19:14
04 Feb 2018, 19:14
2
Expert Reply
Firstly, let me just remark that problems by McGraw-Hill are generally terrible. So don't take them as a very accurate gauge of how the GRE works.
This one is not too bad though. When we find the area of circles, we don't really care about diameters; we care about radii. We could quickly eliminate 3 answer choices by thinking along these lines: If the diameter is an integer, then the radius must also be an integer, or end in .5. For example, if the diameter was 10, the radius must be 5, but if the diameter was 9, the radius would be 4.5. So the area, which is πr^2, should either be a perfect square (if the radius was an integer) or end in .25 (if the radius ended in .5). C, D, and E fulfill neither of those categories. So it's either A or B.
We've also been told that 6 ≤ d ≤ 10. We still don't care about d, so I'd replace it with 2r and we'd get 6 ≤ 2r ≤ 10. Dividing all three parts gets us 3 ≤ r ≤ 5. So the radius must be 3, 4, or 5, and the areas could be 9π, 16π, or 25π. So it's B.
This one is not too bad though. When we find the area of circles, we don't really care about diameters; we care about radii. We could quickly eliminate 3 answer choices by thinking along these lines: If the diameter is an integer, then the radius must also be an integer, or end in .5. For example, if the diameter was 10, the radius must be 5, but if the diameter was 9, the radius would be 4.5. So the area, which is πr^2, should either be a perfect square (if the radius was an integer) or end in .25 (if the radius ended in .5). C, D, and E fulfill neither of those categories. So it's either A or B.
We've also been told that 6 ≤ d ≤ 10. We still don't care about d, so I'd replace it with 2r and we'd get 6 ≤ 2r ≤ 10. Dividing all three parts gets us 3 ≤ r ≤ 5. So the radius must be 3, 4, or 5, and the areas could be 9π, 16π, or 25π. So it's B.
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: If the diameter (d ) of a circle is an integer and 6 cm ≤ d
[#permalink]
10 Dec 2021, 09:59
10 Dec 2021, 09:59
1
Length of Diameter (d) of a circle with radius, r = 2r
\(6 cm\) \(\leq\) \(d\) \(\leq\) \(10 cm\)
=> \(6 cm\) \(\leq\) \(2r\) \(\leq\) \(10 cm\)
Divide all the sides by 2 we get
\(3 cm\) \(\leq\) \(r\) \(\leq\) \(5 cm\)
Now, the diameter is an integer => radius will also be an integer
=> r can be 3cm , 4cm or 5cm
And, we know that Area of Circle with radius r = \(\pi r^2\)
=> For r = 3 cm, Area = \(\pi 3^2 cm^2\) = \(9 \pi cm^2\)
=> For r = 4 cm, Area = \(\pi 4^2 cm^2\) = \(16 \pi cm^2\)
=> For r = 5 cm, Area = \(\pi 5^2 cm^2\) = \(25 \pi cm^2\)
Only possible value in the answer choices is \(25 \pi cm^2\)
So, Answer will be B
Hope it helps!
Watch the following video to Learn Basics of Circles
\(6 cm\) \(\leq\) \(d\) \(\leq\) \(10 cm\)
=> \(6 cm\) \(\leq\) \(2r\) \(\leq\) \(10 cm\)
Divide all the sides by 2 we get
\(3 cm\) \(\leq\) \(r\) \(\leq\) \(5 cm\)
Now, the diameter is an integer => radius will also be an integer
=> r can be 3cm , 4cm or 5cm
And, we know that Area of Circle with radius r = \(\pi r^2\)
=> For r = 3 cm, Area = \(\pi 3^2 cm^2\) = \(9 \pi cm^2\)
=> For r = 4 cm, Area = \(\pi 4^2 cm^2\) = \(16 \pi cm^2\)
=> For r = 5 cm, Area = \(\pi 5^2 cm^2\) = \(25 \pi cm^2\)
Only possible value in the answer choices is \(25 \pi cm^2\)
So, Answer will be B
Hope it helps!
Watch the following video to Learn Basics of Circles
