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What fractional part of the total surface area of cube C is

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What fractional part of the total surface area of cube C is [#permalink] New post 22 Mar 2008, 00:57
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16. What fractional part of the total surface area of cube C is red?
(1) Each of 3 faces of C is exactly 1/2 red.
(2) Each of 3 faces of C is entirely white.
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Re: 1000DS: Section 2 Question 16 [#permalink] New post 22 Mar 2008, 01:24
We need to know all the faces to conclude the fraction part.

Stmt -1 -> using this we know nothing about the remaining 3 faces
Stmt-2->We know nothing about the other 3 faces

combining 1&2 -> we know that of the 6 faces, 3 are white and 1.5 is red and 1.5 is another color thus 1/4th is red

so C is the answer
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Re: 1000DS: Section 2 Question 16 [#permalink] New post 22 Mar 2008, 01:58
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Guys, Can you explain wording of "each of 3 faces"?

Is it means that 3 particular faces of cube are exactly 1/2 red (white) or
any 3 faces of cube are exactly 1/2 red (white)?

Please, clarify!
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Re: 1000DS: Section 2 Question 16 [#permalink] New post 22 Mar 2008, 02:31
walker wrote:
Guys, Can you explain wording of "each of 3 faces"?

Is it means that 3 particular faces of cube are exactly 1/2 red (white) or
any 3 faces of cube are exactly 1/2 red (white)?

Please, clarify!



I found I mistake.

"Each of 3 faces" means that 3 faces each have exacltly 1/2 red. So we dont know anything about the other 3 faces. And the same with statement 2

E is my choice. :oops: :oops:
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Re: 1000DS: Section 2 Question 16 [#permalink] New post 22 Mar 2008, 02:39
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sondenso wrote:
"Each of 3 faces" means that 3 faces each have exacltly 1/2 red. So we dont know anything about the other 3 faces. And the same with statement 2

E is my choice. :oops: :oops:


Sondenso, If this meaning is right, we can use following:
1. cube has 6 faces
2. a face can be white or 1/2 red (C)
Therefore, C is correct. 3 faces are white and 3 other faces are 1/2 red and ratio=\frac{3*\frac12}{6}=\frac14
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Re: 1000DS: Section 2 Question 16 [#permalink] New post 22 Mar 2008, 02:49
walker wrote:
sondenso wrote:
"Each of 3 faces" means that 3 faces each have exacltly 1/2 red. So we dont know anything about the other 3 faces. And the same with statement 2

E is my choice. :oops: :oops:


Sondenso, If this meaning is right, we can use following:
1. cube has 6 faces
2. a face can be white or 1/2 red (C)
Therefore, C is correct. 3 faces are white and 3 other faces are 1/2 red and ratio=\frac{3*\frac12}{6}=\frac14



Walker,

The 1 and the 2 combined do not say "the 3 faces...red" and "the other 3 faces...white", so we have 6 faces, how can we know what face? right?
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Re: 1000DS: Section 2 Question 16 [#permalink] New post 22 Mar 2008, 05:54
Sondenso,

The stmt-2 says "Each of 3 faces of C is entirely white" that definitely means the other 3 faces are 1/2 read, isn't it?
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Re: 1000DS: Section 2 Question 16 [#permalink] New post 22 Mar 2008, 10:00
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Sorry, guys, I'm not verbal guru :wink:
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Re: 1000DS: Section 2 Question 16 [#permalink] New post 22 Mar 2008, 18:38
prasannar wrote:
Sondenso,

The stmt-2 says "Each of 3 faces of C is entirely white" that definitely means the other 3 faces are 1/2 read, isn't it?


:-D :-D :-D
prasannar,
I can not understand how "entirely" says that it is "other"? or "entirely" is "other"

@walker, me too. I am not a verbal killer, but...
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Re: 1000DS: Section 2 Question 16 [#permalink] New post 22 Mar 2008, 20:02
Stmt-2 says 3 faces are entirely white, that leaves us with the other 3 faces and we don't know anything about them

Stmt-1 + Stmt-2 -> gives the context that I concluded

Walker and Sondenso don't tease with me with the Verbal Guru stuff :lol:
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Re: 1000DS: Section 2 Question 16 [#permalink] New post 22 Mar 2008, 21:00
prasannar wrote:
Stmt-2 says 3 faces are entirely white, that leaves us with the other 3 faces and we don't know anything about them

Stmt-1 + Stmt-2 -> gives the context that I concluded

Walker and Sondenso don't tease with me with the Verbal Guru stuff :lol:



I love this explaination, and the discusion too, you definitely persuded me! :) :)
Thank you prasannar!
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Re: 1000DS: Section 2 Question 16 [#permalink] New post 23 Jan 2011, 08:55
C per me.

3 of the 6 sides are entirely white -- means definitely not red.
Let's talk about the other 3 sides now. First statement says: 3 of the 6 sides are exactly 1/2 red. Means; they must be talking about the 3 sides which are not entirely white.

Now, if "a" is side:

area of 1 side is a^2.
total area for 6 sides is 6*a^2
area with red will be 3*((a^2)/2). Because half the area of each of the 3 remaining faces is red. (a^2)/2 will be half the area times 3 for three sides.
now, divide:
[3*((a^2)/2)]/[6*a^2]=1/4. We got the answer.
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Re: 1000DS: Section 2 Question 16   [#permalink] 23 Jan 2011, 08:55
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