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Math Expert V
Joined: 02 Sep 2009
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Every object in a box is either a sphere or a cube, and every object  [#permalink]

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Difficulty:   5% (low)

Question Stats: 82% (01:15) correct 18% (01:13) wrong based on 953 sessions

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Every object in a box is either a sphere or a cube, and every object in the box is either red or green. How many objects are in the box?

(1) There are six cubes and 5 green objects in the box.
(2) There are two red spheres in the box.

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Re: Every object in a box is either a sphere or a cube, and every object  [#permalink]

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As in the attached picture. Total of all objects is (a+b+c+d). We need to find that.

But together also, the statements are NOT sufficient. Hence E answer.
Attachments IMG_20170703_134501-2.jpg [ 46.02 KiB | Viewed 10266 times ]

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Every object in a box is either a sphere or a cube, and every object  [#permalink]

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Every object in a box is either a sphere or a cube,
and every object in the box is either red or green.
How many objects are in the box?

--------Sphere--Cube-----------Total
Red ------w--------x------------ w+x
Green----y---------z------------ y+z
Total---w+y-----x+z---------w+x+y+z

(1) There are six cubes and 5 green objects in the box.
Given x+z=6 and y+z=5
We have no information about w. Insufficient
(2) There are two red spheres in the box.
Given w=2
Since we have no information about the other 3 variables,
we cannot give the final total of objects. Insufficient

On combining the information on both the statements,
We know w=2, x+z=6 and y+z=5
If z=2, x=4 and y=3 making total items in box(w+x+y+z = 11)
But, if z=1,x=5 and y=4 making total items in box(w+x+y+z =12)
Insufficient(Option E)
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Re: Every object in a box is either a sphere or a cube, and every object  [#permalink]

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Bunuel wrote:
Every object in a box is either a sphere or a cube, and every object in the box is either red or green. How many objects are in the box?

(1) There are six cubes and 5 green objects in the box.
(2) There are two red spheres in the box.

We are given that we have red or green spheres or cubes in a box. We need to determine the total number of objects.

Statement One Alone:

There are six cubes and 5 green objects in the box.

Although we know the number of cubes in the box, we do not know the number of spheres, and thus we cannot determine the total number of objects in the box. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

There are two red spheres in the box.

Since we do not know how many spheres or cubes are in the box, we cannot determine the total number of objects. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two together, although we know there are 6 cubes and 2 red spheres, we do not know the shapes of the green objects and thus cannot determine the total number of cubes and spheres. For example, if there is only one green sphere, then there are 5 - 1 = 4 green cubes, and thus 6 - 4 = 2 red cubes. In this case, there are 2 + 2 = 4 red objects and 5 green objects; thus, the total number of objects is 9. On the other hand, if there are two green spheres, then there are 5 - 2 = 3 green cubes, and thus 6 - 3 = 3 red cubes. In this case, there are 3 + 2 = 5 red objects and 5 green objects; thus, the total number of objects is 10. So, we cannot determine with certainty the total number of objects in the box.

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Every object in a box is either a sphere or a cube, and every object  [#permalink]

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1
Hi All,

We're told that every object in a box is either a sphere or a cube, and every object in the box is either red or green. We're asked for the TOTAL number of objects in the box. To answer this question, we need to know the exact number of Red spheres, Red cubes, Green spheres and Green cubes....

1) There are six cubes and 5 green objects in the box.

This Fact tells us NOTHING about the number of spheres nor the number of red objects. In addition, we don't know how many (if any) of the cubes are green (it could be any number from 0 - 5). Thus, there's no way to determine the number of objects in the box.
Fact 1 is INSUFFICIENT

2) There are two red spheres in the box.

Fact 2 tells us NOTHING about the number of Red cubes, Green spheres or Green cubes.
Fact 2 is INSUFFICIENT

Combined, we know:
There are six cubes and 5 green objects in the box.
There are two red spheres in the box.

Among the various unknowns, we still have know NOTHING about the number of Red cubes, so there's no way to determine the number of objects in the box.
Combined, INSUFFICIENT

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Every object in a box is either a sphere or a cube, and every object  [#permalink]

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Bunuel wrote:
Every object in a box is either a sphere or a cube, and every object in the box is either red or green. How many objects are in the box?

(1) There are six cubes and 5 green objects in the box.
(2) There are two red spheres in the box.

it clearly says : There are six cubes and 5 green objects in the box.

Doesnt it mean that 5 green objects are speres and 6 red objects are cubes ? why this statement isn't sufficient Math Expert V
Joined: 02 Sep 2009
Posts: 59587
Re: Every object in a box is either a sphere or a cube, and every object  [#permalink]

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1
1
dave13 wrote:
Bunuel wrote:
Every object in a box is either a sphere or a cube, and every object in the box is either red or green. How many objects are in the box?

(1) There are six cubes and 5 green objects in the box.
(2) There are two red spheres in the box.

it clearly says : There are six cubes and 5 green objects in the box.

Doesnt it mean that 5 green objects are speres and 6 red objects are cubes ? why this statement isn't sufficient Cannot any of the six cubes be green? Or Any of the green objects be cubes? Please re-read the solutions above carefully.
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Re: Every object in a box is either a sphere or a cube, and every object  [#permalink]

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Top Contributor
Bunuel wrote:
Every object in a box is either a sphere or a cube, and every object in the box is either red or green. How many objects are in the box?

(1) There are six cubes and 5 green objects in the box.
(2) There are two red spheres in the box.

Target question: How many objects are in the box?

Given: Every object in a box is either a sphere or a cube, and every object in the box is either red or green.
We can solve this using the Double Matrix Method.
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions)..
Here, we have a population of objects, and the two characteristics are:
- sphere or cube
- red or green

So, we can set up our matrix as follows: From here, I'll jump straight to . . .

Statements 1 and 2 COMBINED
When we combine the statements, we get the following matrix: There are several scenarios that satisfy BOTH statements. Here are two:
Case a: In this case, the total number of objects = 3 + 3 + 2 + 2 = 10
So, the answer to the target question is there are 10 objects in the box

Case b: In this case, the total number of objects = 5 + 1 + 2 + 4 = 12
So, the answer to the target question is there are 12 objects in the box

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

Here's a practice question too:

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Re: Every object in a box is either a sphere or a cube, and every object  [#permalink]

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Bunuel wrote:
dave13 wrote:
Bunuel wrote:
Every object in a box is either a sphere or a cube, and every object in the box is either red or green. How many objects are in the box?

(1) There are six cubes and 5 green objects in the box.
(2) There are two red spheres in the box.

it clearly says : There are six cubes and 5 green objects in the box.

Doesnt it mean that 5 green objects are speres and 6 red objects are cubes ? why this statement isn't sufficient Cannot any of the six cubes be green? Or Any of the green objects be cubes? Please re-read the solutions above carefully.

YOU ARE GREAT ............ GREAT AND EASY EXPLANATION Bunuel
_________________ Re: Every object in a box is either a sphere or a cube, and every object   [#permalink] 11 Sep 2019, 07:35
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