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# What fractional part of the total surface area of cube C is red?

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What fractional part of the total surface area of cube C is red? [#permalink]

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22 Mar 2008, 01:57
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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/what-fractio ... 96929.html
[Reveal] Spoiler: OA

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Re: What fractional part of the total surface area of cube C is red? [#permalink]

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22 Mar 2008, 02:24
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

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Re: What fractional part of the total surface area of cube C is red? [#permalink]

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22 Mar 2008, 02:58
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)?

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Re: What fractional part of the total surface area of cube C is red? [#permalink]

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22 Mar 2008, 03:31
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)?

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.
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Re: What fractional part of the total surface area of cube C is red? [#permalink]

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22 Mar 2008, 03:39
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.

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: What fractional part of the total surface area of cube C is red? [#permalink]

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22 Mar 2008, 03:49
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.

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: What fractional part of the total surface area of cube C is red? [#permalink]

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22 Mar 2008, 06:54
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: What fractional part of the total surface area of cube C is red? [#permalink]

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22 Mar 2008, 11:00
Sorry, guys, I'm not verbal guru
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Re: What fractional part of the total surface area of cube C is red? [#permalink]

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22 Mar 2008, 19:38
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?

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: What fractional part of the total surface area of cube C is red? [#permalink]

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22 Mar 2008, 21:02
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
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Re: What fractional part of the total surface area of cube C is red? [#permalink]

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22 Mar 2008, 22:00
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

I love this explaination, and the discusion too, you definitely persuded me!
Thank you prasannar!
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Re: What fractional part of the total surface area of cube C is red? [#permalink]

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23 Jan 2011, 09:55
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:
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Re: What fractional part of the total surface area of cube C is red? [#permalink]

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21 Aug 2017, 13:59
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 --> 1/2 of 3 faces out of 6 is red, but we know nothing about the other 3. What if some fraction of the other 3 faces is red also? For example 1/3 of the 4th face is red, 1/4th of the 5th face and 1/10th of the 6th face? Hence statement (1) is not sufficient.

(2) Each of 3 faces of C is entirely white --> 3 faces out of 6 are white, but we know nothing about the other 3. Not sufficient.

(1)+(2) Half of 3 faces is red and other 3 faces are entirely white --> fractional part which is red is 1.5/6=1/4. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/what-fractio ... 96929.html
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Re: What fractional part of the total surface area of cube C is red?   [#permalink] 21 Aug 2017, 13:59
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