Every object in a box is either a sphere or a cube, and every object

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.

Answer: E

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

Final Answer:

GMAT assassins aren't born, they're made,
Rich

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.

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

Answer: E

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

To learn more about the Double Matrix Method, watch this video:



Here's a practice question too:

YOU ARE GREAT ............ GREAT AND EASY EXPLANATION Bunuel

Hi Bunuel and VeritasKarishma

I'm having an issue with the language of statement 2. It says "There are six cubes and 5 green objects in the box." Does this not imply that there are 6 cubes AND SEPARATELY there are 5 green objects. Since the box has only cubes and spheres; there must be 5 green spheres. We don't know the number of red spheres, and hence this statement is insufficient. Statement 2 gives us this said info and therefore C is correct.

I know this is the OG and i cant questions it; i am just confused with the language of st A and would appreciate your input to not make this mistake during the exam

Every object is sphere or cube.
Every object is red or green.

Break the stmnt 1 into two:
- There are 6 cubes in the box.
- There are 5 green objects in the box.

The two give you information on how many total cubes and how many total green objects there are. There is no need to assume that they don't have an overlap. What says that the 6 cubes must be red?
Stmnt 1 just combines the two above.

Video solution from Quant Reasoning:
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Answer: Option E

Video solution by GMATinsight


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To determine the number of objects in the box, we need information about the total number of cubes, spheres, red objects, and green objects. Let's analyze the given statements:

Statement (1) tells us that there are six cubes and 5 green objects in the box. However, it doesn't provide any information about the spheres or the red objects. Therefore, statement (1) alone is insufficient to determine the total number of objects.

Statement (2) tells us that there are two red spheres in the box. While it provides information about the red spheres, it doesn't give any details about cubes or green objects. Hence, statement (2) alone is also insufficient to determine the total number of objects.

By considering both statements together, we can conclude that the total number of objects in the box is unknown. Therefore, the answer is (E) The information provided is insufficient to determine the number of objects in the box.

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