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

[BTGmoderatorDC]

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.

OA E

Source: Official Guide

[Jay@ManhattanReview]

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.

OA E

Source: Official Guide

This one is already answered. Pl. see here https://www.beatthegmat.com/every-objec ... 95878.html

-Jay
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[fskilnik@GMATH]

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.
Source: Official Guide

\[? = \left( {\# {\text{cubes}}} \right) + \left( {\# {\text{spheres}}} \right)\]
Let´s go straight to (1+2):

\[\left( {1 + 2} \right)\,\,\,\left\{ \begin{gathered}
\,\left( {{\text{6}}\,\,{\text{cubes}}{\text{,}}\,\,{\text{only}}\,\,5\,\,{\text{green}}} \right)\,\,\,{\text{and}}\,\,\,\left( {{\text{2}}\,\,{\text{spheres}}{\text{,}}\,\,{\text{both}}\,\,{\text{red}}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 8 \hfill \\
\,\left( {{\text{6}}\,\,{\text{cubes}}{\text{,}}\,\,{\text{only}}\,\,{\text{4}}\,\,{\text{green}}} \right)\,\,\,{\text{and}}\,\,\,\left( {{\text{3}}\,\,{\text{spheres}}{\text{,}}\,\,{\text{only}}\,\,{\text{two}}\,\,{\text{red}}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 9 \hfill \\
\end{gathered} \right.\]

The correct answer is therefore (E).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

[Brent@GMATPrepNow]

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.

OA E

Source: Official Guide

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: https://www.youtube.com/watch?v=jK-tiBrrf04
Here's a practice question too: https://www.youtube.com/watch?v=DsbPUSH_Wu4