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Two circular road signs are to be painted yellow. If the rad

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skamal7
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Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   19 Jun 2013, 07:48
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Two circular road signs are to be painted yellow. If the radius of the larger sign is twice that of the smaller sign, how many times more paint is needed to paint the larger sign (assuming that a given amount of paint covers the same area on both signs)?

A. 2
B. 3
C. 4
D. 3 /2
E. 3/5
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C
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   05 Jan 2018, 23:53
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prateekbhatt
Let the radius of smaller circle be r

Let the radius of bigger circle be 2r

Now if the to complete the bigger circle the entire diameter will be 4 times that of the smaller circle. hence its 4.

Hi,
I also followed the same approach but since in the question it was asked that how many times more paint is needed to paint the larger sign..
I subtracted the larger circle with that of the smaller circle. so the answer I got was 4-1 =3.

I feel for the answer to be 4 the question, the word more should have been omitted would have been something like
the paint on the larger cirlce would be how many times that of the smaller circle

Can somebody clear this doubt?
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prateekbhatt
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   19 Jun 2013, 09:33
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Let the radius of smaller circle be r

Let the radius of bigger circle be 2r

Now if the to complete the bigger circle the entire diameter will be 4 times that of the smaller circle. hence its 4.
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   19 Jun 2013, 09:42
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Here dont we need to find the circumference of the circle..Why we need to calculate the area?pls clarify?
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   19 Jun 2013, 09:52
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skamal7
Here dont we need to find the circumference of the circle..Why we need to calculate the area?pls clarify?

Two circular road signs are to be painted yellow. If the radius of the larger sign is twice that of the smaller sign, how many times more paint is needed to paint the larger sign (assuming that a given amount of paint covers the same area on both signs)

How many times more paint need means to cover the entire area, thus we just need to know area.
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   19 Jun 2013, 09:56
thanks!it helped!
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   08 Jun 2015, 10:19
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Dear skamal

You see you need to understand the difference between circumference and area visually first.
if you draw a circle on paper then:-
the boundary of circle called circumference . it formula is 2*pie*radius

the space covered inside the closed boundary and also the space covered by the drawing of boundary(how so ever small it is) is called area..

Now you need to draw sign.
Unless stated otherwise, you can safely assume that you draw fully filled circle and not a empty circle.

Hope it helps
Kudos please if you like it. :)
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   08 Jun 2015, 10:48
In this case we want to find how much more paint is needed for the larger sign.

We need to use the formula of calculating the area to get our answer, this is
r^2 * pi

r(larger sign) = r(smaller sign) * 2

So plugging that into the formula gives us

(r(smaller sign) * 2 ) ^ 2 * pi =
r(smaller sign) * 4 * pi

Hence we need 4 times more paint for the larger sign than the smaller sign.

Answer C
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   17 Jan 2018, 13:02
suramya26
prateekbhatt
Let the radius of smaller circle be r

Let the radius of bigger circle be 2r

Now if the to complete the bigger circle the entire diameter will be 4 times that of the smaller circle. hence its 4.

Hi,
I also followed the same approach but since in the question it was asked that how many times more paint is needed to paint the larger sign..
I subtracted the larger circle with that of the smaller circle. so the answer I got was 4-1 =3.

I feel for the answer to be 4 the question, the word more should have been omitted would have been something like
the paint on the larger cirlce would be how many times that of the smaller circle

Can somebody clear this doubt?


Hi I have the same doubt as well. Can some body please explain why the answer is not 3.
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   24 Jan 2018, 08:59
I had the same query as Suramya and Cool Naren. could someone explain why the answer is 4 and not 3?
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   14 Jan 2019, 07:35
Bunuel
Hi, the answer is stated as 4 on the forum whereas I think it is 3 because of the word "more". Why is it 4?
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   14 Jan 2019, 09:23
BatuhanKavlak
Bunuel
Hi, the answer is stated as 4 on the forum whereas I think it is 3 because of the word "more". Why is it 4?

Please read this part of the question stem carefully -

Quote:
...........how many times more paint is needed to paint the larger sign..............
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   21 Jan 2019, 14:40
The language of this question doesn’t make any sense. It is ambiguous imo. As per the question stem, the answer could be 3 as well.

Please help!

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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   28 Feb 2020, 08:23
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skamal7
Two circular road signs are to be painted yellow. If the radius of the larger sign is twice that of the smaller sign, how many times more paint is needed to paint the larger sign (assuming that a given amount of paint covers the same area on both signs)?

A. 2
B. 3
C. 4
D. 3 /2
E. 3/5

We can let the area of the smaller sign = πr^2. The radius of the larger sign is twice that of the smaller sign, so its radius is 2r. Thus, the area of the larger sign is:

π(2r)^2 = π4r^2 = 4πr^2

Thus, we see that 4 times as much paint would be needed.

Answer: D
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Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   03 Apr 2020, 00:05
Dear Bunuel VeritasKarishma chetan2u GMATGuruNY IanStewart DmitryFarber RonPurewal ccooley MathRevolution,

Why the correct answer isn't choice B.?

The question says: how many times MORE paint...
So, it should be 4 - 1 times. We have to minus one (the current amount) because the question asks for MORE paint.

Why is this thinking wrong?
(Many posters above have the very same query but IMO has not been addressed yet)
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   04 Apr 2020, 07:21
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varotkorn

Why the correct answer isn't choice B.?

The question says: how many times MORE paint...
So, it should be 4 - 1 times. We have to minus one (the current amount) because the question asks for MORE paint.

Why is this thinking wrong?

I answered this question in another thread, so I'll just quote myself here:

IanStewart
No, that's not the case. I understand why many people think this, when they compare this wording with the wording we use with percentages -- because "400% greater" does not mean the same thing as "400% of", it might seem that "4 times more" should mean a different thing than "4 times as many". But "4 times more" and "4 times as many" mean the same thing, just because of idiomatic usage in English. The Merriam-Webster dictionary, quoted here, says this:

The fact is that "five times more" and "five times as much" are idiomatic phrases which have - and are understood to have - exactly the same meaning. The "ambiguity" of _times more_ is imaginary: in the world of actual speech and writing, the meaning of _times more_ is clear and unequivocal. It is an idiom that has existed in our language for more than four centuries

The quote above applies to similar phrases, like "five times greater" (as the longer quote at the link makes clear). Even if this meaning might seem illogical to some (because of the analogy with how we discuss percentages), it's an idiom, and idioms don't always obey logic. If you read "x is five times greater than y" or "x is five times more than y", or "x is greater than y by a factor of 5", those phrases all mean "x = 5y".
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   04 Apr 2020, 07:33
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Dear Bunuel VeritasKarishma chetan2u GMATGuruNY IanStewart DmitryFarber RonPurewal ccooley MathRevolution,

Why the correct answer isn't choice B.?

The question says: how many times MORE paint...
So, it should be 4 - 1 times. We have to minus one (the current amount) because the question asks for MORE paint.

Why is this thinking wrong?
(Many posters above have the very same query but IMO has not been addressed yet)

Hi,

As also explained above by Ian, we use 'how many times more' to mean ' how many times'?

For example, if John has $10 while Brian has $50, then we would say that five times more money. Although just five times the money that John has clears the ambiguity.

Having said that, I don't remember any question in official questions that uses the phrase 'how many times more'. It is generally how many times x...
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   04 Apr 2020, 23:11
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Ian is right that in daily usage, "5 times more" may be used to mean "5 times as much," but this question is still a dud. Since we are asking for the actual amount of paint used on the larger sign, there is absolutely zero justification for using the word "more" in the question, unless we count a desire for concision. A clearer rewording might look like "The amount of paint required to paint the larger sign is how many times the amount of paint required to paint the smaller sign?" I suppose that is a lot of trouble to go to just to ask an area question.

Another solution would be to get rid of 3 as an answer so that anyone who reads it differently will have a chance to figure out the intended meaning without missing the question. As it is, the question is unnecessarily imprecise and confusing.
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   06 Apr 2020, 01:48
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varotkorn
Dear Bunuel VeritasKarishma chetan2u GMATGuruNY IanStewart DmitryFarber RonPurewal ccooley MathRevolution,

Why the correct answer isn't choice B.?

The question says: how many times MORE paint...
So, it should be 4 - 1 times. We have to minus one (the current amount) because the question asks for MORE paint.

Why is this thinking wrong?
(Many posters above have the very same query but IMO has not been addressed yet)

Yes, technically you are correct, colloquially, the answer is.
Usually, "how many times" is considered same as "how many times more". Hopefully, GMAT will not put you in a spot regarding this distinction.
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink] Two circular road signs are to be painted yellow. If the rad   09 Sep 2023, 21:44
Hi! This may be a silly question but just wanted to understand further. I completely understand the explanations given.
My query was if the answer would be 3 (and not 4) what would the question read as?
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Re: Two circular road signs are to be painted yellow. If the rad [#permalink]
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