[email protected] wrote:Of the companies surveyed about the skills they
required in prospective employees, 20 percent
required both computer skills and writing skills. What
percent of the companies surveyed required neither
computer skills nor writing skills?
(1) Of those companies surveyed that required
computer skills, half required writing skills.
(2) 45 percent of the companies surveyed required
writing skills but not computer skills.
Please solve the question.Unable to figure out the solution through the 4 box matrix.
Hey
[email protected]!
Setting up the matrix can be a challenge so let's start with that. I always start by looking for whatever the "both" category would be in the problem. From the stem, we see that some companies require "BOTH computer skills and writing skills" so this is how I begin setting up the table. Build a 3x3 box (I put my labels outside the box, or you can build a 4x4 if you want to make boxes for your label). Then, I put the cross labels for the 2 BOTH categories at the top left (so the BOTH box is the top left):
(NOTE: Remember that we read this table as a cross of the labels, not unlike an old map with the Alpha/Number grids!)
Now, the rest of the labels are the exact OPPOSITES of what you just wrote. So the exact opposite of "Computer Skills" would be "NOT Computer Skills" and you would put it right next to "Computer Skills" and the same for "Writing Skills". And then finish off the labels with "Totals":
Now, a quick scan of the problem + statements will show us that there are no real numbers given, so we might want to set up our initial table using a smart number. The Stem tells us that 20% of all those interviewed required BOTH, so if we make the total of all interviewed = 100, then 20 would fit in our BOTH box. And the only other thing we get from the Stem is that we want to find NEITHER, so let's circle that box.
Ready for the statements? I like to create 2 tables quickly with the basic information so that I don't confuse the information from the statements in one table!
Statement 1: "Of those companies surveyed that required computer skills, half required writing skills."
This tells us that of those that required computer skills, 1/2 required writing - BUT we don't know how many required computer skills, so let's assign a variable = X! And HALF of that X would require writing skills as well as computer skills - so we can put .5X in the BOTH box.
So what does it mean when 2 items are in the same box, what do we know? They MUST be equal!
20 = 0.5(X) ...multiply both sides by 10
200 = 5X
40 = X
Now, another cool thing about this table is that the rows and columns are additive, so we can actually use that new value of X=40 to calculate other boxes (a 100-40= 60 in the NOT Computer Skills Total, and a 40-20= 20 in the Computer but NOT writing box).
But can we get to that middle square?? [spoiler]NO - Not Sufficient![/spoiler]
Statement 2: "45 percent of the companies surveyed required writing skills but not computer skills."
This tells us that of the total surveyed (100), 45 percent (45) required writing but NOT computer. So get a clean table and plug in 45 in the box that crosses Writing & NOT Computer. Then we can use the additive rows/columns to get 20+45= 65 for the total for Writing and then 100-60= 35 for the total NOT Writing.
But can we get to that middle square?? [spoiler]NO - Not Sufficient![/spoiler]
Statement 1&2:
Now we just put the 2 tables together:
And now we can see that the middle square is either 60-45=15 or 35-20=15, so we know that the answer is 15 out of 100 (or 15%) so [spoiler]SUFFICIENT![/spoiler]
Hope this helps!
Whit
