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How many of the 100 people in the room are males that

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Source: — Data Sufficiency |
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by Vincen » Thu Mar 22, 2018 3:36 am
How many of the 100 people in the room are males that watch movies?

(1) Thirty people are females that watch movies.
(2) Forty-five people are males that do not watch movies.

The OA is E.

Why cannot I get an answer using both statements? May you clarify this for me, experts? Thanks.
Hello Vjesus12.

We know that there are 100 people in the room.

(1) Thirty people are females that watch movies.

This doesn't tell us anything about the other 70 people. We don't know how many of them are males, females, how many watch movies.... INSUFFICIENT.

(2) Forty-five people are males that do not watch movies.

Again, this doesn't tell us anything about the other 55 people. INSUFFICIENT.

Using both statements together we will obtain that: "Thirty people are females that watch movies and Forty-five people are males that do not watch movies."

Again, we don't know about the other 25 people. We don't know if all of them are males or females. Hence, we cannot say anything. INSUFFICIENT.

Therefore, the correct option is E.

I hope it helps.
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by ErikaPrepScholar » Mon Mar 26, 2018 11:14 am
A great idea here is to make a double matrix and fill it in for each statement. With double matrices, we know that if we have two values in either a row or a column, we can solve for the third value in that row or column. (Note: the bbcode for inserting images directly into posts isn't working for this type of link, so you can click through the links to view what your double matrix should look like at each step.)

Stem: https://cl.ly/3V3K1Y3l2w1H
Statement 1: https://cl.ly/0z3q1p0K3i18
Statement 2: https://cl.ly/3u0n1R3a1u45
Both: https://cl.ly/0N311R1Q0y3K

Because we never end up with a row or column that has two values in it (allowing us to solve for the third value), we can't fill in any other cells in the matrix. Since we are never able to determine the total number of males in the room or the total number of people who watch movies, we aren't able to solve for males who watch movies.
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