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
Every object in a box is either a sphere or a cube, and ever
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Target question: How many objects are in the box?BTGmoderatorDC 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.
OA E
Source: Official Guide
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