The ratio of the number of women to the number of men to the number of children in a room is 5:2:7, respectively. What is the total number of people in the room?
(1) the total number of women and children in the room is 12.
(2) there are fewer than 4 men in the room.
Target question: What is the total number of people in the room?
Given: women : men : children = 5:2:7
So, there are many possible scenarios where the ratio is 5:2:7. Let's LIST a few:
Scenario #1: 5 women, 2 men, 7 children
Scenario #2: 10 women, 4 men, 14 children
Scenario #3: 15 women, 6 men, 21 children
Scenario #4: 20 women, 8 men, 28 children
.
.
.
and so on
Okay, now let's examine the statements:
Statement 1: the total number of women and children in the room is 12.
Let's check some of the scenarios that we LISTED.
Scenario #1: total number of women and children = 12 (NICE!)
Scenario #2: total number of women and children = 24 (no)
Scenario #3: total number of women and children = 36 (no)
...and so on.
We can see that ONLY scenario #1 fits the information in statement 1.
So, there MUST be 5 women, 2 men, and 7 children
In other words,
the total number of people in the room MUST equal 14
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: There are FEWER THAN 4 men in the room.
When we check some of the scenarios that we LISTED, we see that ONLY scenario #1 fits the information in statement 2.
So, there MUST be 5 women, 2 men, and 7 children
In other words,
the total number of people in the room MUST equal 14
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
D
Cheers,
Brent
