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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]

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17 Jun 2006, 10:59
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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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Jun 2013, 05:49, edited 1 time in total.
Edited the question and added the OA
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Re: DS - Fractional part in cube [#permalink]

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17 Jun 2006, 12:57
jaynayak wrote:
What fractional part of the total surface area of cube C is red?
(1) Each of 3 faces of C is exactly red.
(2) Each of 3 faces of C is entirely white.

E.
1. doesnot tell about the other 3 faces.
2. doesnot tell about other colors including red.
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17 Jun 2006, 13:23
Why can't the answer be A? Stmt 1 says that 3 of the 6 faces are red which indicates that 1/2 of the total surface area is red
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17 Jun 2006, 20:46
Am I missing something? Seems a straight C to me. Both statements together define the color of all possible faces of the cube. so fraction red = 1/2
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18 Jun 2006, 03:13
Thanks guys It is preety straight if you dont think that every question in GMAT is crooked.

OA: C
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18 Jun 2006, 10:25
It can't be (C), I agree with ns.

Let's look at the concepts and wording.

A cube has 6 surface squares. So we need to know how many are red, the rest don't matter because we are looking at a fraction.

So when (A) says "3 are exactly red", that's all we need! Whether the rest are white, blue or alien green don't batter. We know exactly 3 are red (=> none other are red), so the fraction is 3/6 -> 1/2

(A)
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Re: DS - Fractional part in cube [#permalink]

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24 Feb 2011, 13:38
yep, I also think that 1st statement is suff. to answer the question. But the OA is C, no? So how is it possible?
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Re: DS - Fractional part in cube [#permalink]

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24 Feb 2011, 13:49
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banksy wrote:
yep, I also think that 1st statement is suff. to answer the question. But the OA is C, no? So how is it possible?

What does "exactly red" exactly mean in the 1st statement?

Is there some way to be "not exactly red"...

If the question said;
(1) Each of 3 faces of C is entirely red.
(2) Each of 3 faces of C is entirely white.

Then C would be the answer. Here's how;

(1) We know about the 3 faces of the cube. We don't know anything about the other 3. Each of those faces could be partially red or not red at all. Not Sufficient.

(2) We don't know about the other 3 faces. They could be all red or all green. Not Sufficient.

Combining both;
3 Red faces and 3 white faces;
Fraction of red = 1/2.
Sufficient.

Ans: "C"
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Re: DS - Fractional part in cube [#permalink]

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24 Feb 2011, 13:59
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banksy wrote:
yep, I also think that 1st statement is suff. to answer the question. But the OA is C, no? So how is it possible?

There is a typo in the first post. Question should read:

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.

(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.

Hope it's clear.
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Re: DS - Fractional part in cube [#permalink]

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24 Feb 2011, 14:03
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Bunuel wrote:
banksy wrote:
yep, I also think that 1st statement is suff. to answer the question. But the OA is C, no? So how is it possible?

There is a typo in the first post. Question should read:

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.

(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.

Hope it's clear.

Now, it's making complete sense. Thanks for the clarification, Bunuel.
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Re: DS - Fractional part in cube [#permalink]

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13 Apr 2011, 00:01
Bunuel wrote:

(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.

Hope it's clear.

How to understand (1) Each of 3faces of C is exactly 1/2 red--->means 1/2 of 3 faces is red. and then where 1.5/6 = 1/4 come from?
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Re: DS - Fractional part in cube [#permalink]

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13 Apr 2011, 00:37
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.

Ok I have another explanation.

1/2 is obvious from 2). ----> cube is half white. remaining is 1/2 cube
The remaining half of half cube is red. i.e. 1/2 of 1/2 is red. Hence 1/4 of the whole cube is red.

Another way
------------
3 faces white ---->Remaining is 3/6 cube or 1/2 cube
From 1) 3 faces are half red. Hence 3 * 1/2 are red.

3/2 = 1.5 faces of the whole cube (6 faces) are red. Fraction is 1.5/6 = 1/4

yvonne0923 wrote:

How to understand (1) Each of 3faces of C is exactly 1/2 red--->means 1/2 of 3 faces is red. and then where 1.5/6 = 1/4 come from?

Last edited by gmat1220 on 13 Apr 2011, 00:44, edited 1 time in total.
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Re: DS - Fractional part in cube [#permalink]

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13 Apr 2011, 00:53
yvonne0923 wrote:
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.

How to understand (1) Each of 3faces of C is exactly 1/2 red--->means 1/2 of 3 faces is red. and then where 1.5/6 = 1/4 come from?

How many faces does a cube have?
"6"

We need to consider both statements as true.
(1) Each of 3 faces of C is exactly 1/2 red.
Out of the 6 faces of a cube, 3 faces are exactly half red. We don't know anything about the other 3 faces of the cube. Thus, we wouldn't know what fractional part would be red.
Not Sufficient.

(2) Each of 3 faces of C is entirely white.
Out of the 6 faces of a cube, 3 faces are entirely white. We don't know anything about the other 3 faces of the cube. They could be all red or not red at all.
Not Sufficient.

Combining both and accepting both the statements as true:

3 faces are half red and the other 3 faces are entirely white. So, how much red for 6 faces?
3 are entirely white. Red=0 out of 3
3 faces are half red. Red=3/2 = 1.5 out of 3.
Fractional part which is red= 1.5/(3+3)=1.5/6=1/4=25%
Sufficient.

Ans: "C"
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Re: DS - Fractional part in cube [#permalink]

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14 Apr 2011, 06:24
1. Not sufficient.
We don't know anything about other 3 sides. Could be more Red in those faces.

2.Not sufficient.
We don't know anything about other 3 sides. May/may not have Red in those faces.

Together we know about all 6 faces and all the faces where it's Red.

Sufficient . Answer is C.

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Re: DS - Fractional part in cube [#permalink]

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30 Apr 2011, 09:36
Bunuel wrote:
banksy wrote:
yep, I also think that 1st statement is suff. to answer the question. But the OA is C, no? So how is it possible?

There is a typo in the first post. Question should read:

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.

(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.

Hope it's clear.

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

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02 Dec 2013, 03:45
I also think that c is the answer- I solved like this-

1) Not sufficient as we do not know about other sides (they can be red too)
2) Not sufficient as we do not know about other three sides
combined we can calculate and hence answer should be C
Re: What fractional part of the total surface area of cube C is   [#permalink] 02 Dec 2013, 03:45
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# What fractional part of the total surface area of cube C is

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