If 65 percent of a class answered...

[A4Fever]

the first question on a certain test corectly, 45 percent answered the second question on the test correctly, and 10 percent answered neither of the questions correctly, what percent answered both correctly?

This is from OG 10th edition however I did change the numbers in order to post on the forum. Hope this is ok.

My question- I set up the double set matrix but can't seem to be able to answer this one. Can someone set one up & explain how they got to their answer?

Thanks
A4Fever

[RonPurewal]

the key to the double-set matrix is to recognize that the total of all the students is, of course, 100 percent. once you insert this number into the grid, the rest of the arithmetic is seamless.

i know the grid will be nearly impossible to format in the forum, and i really don't feel like making a word document right now, so here's the way these grids will work:
rows:
Q1 correct / Q1 incorrect / Total

columns:
Q2 correct
Q2 incorrect
Total

here's the way the grid should look with the initial information:

__ __ 45
__ 10 __
65 __ 100

once you have this, just do the appropriate arithmetic (addition/subtraction) on each row/column that already contains 2 numbers:
__ __ 35
__ 10 55
65 35 100

next:
__ 25 45
45 10 55
65 35 100

finally:
20 25 45
45 10 55
65 35 100

ans = 20

did you forget about the 100 percent?

--

another common issue on this problem is incorrect setup of the matrix. many students try to set it up as
rows: Q1 / Q2 / Total
columns:
correct
incorrect
Total

you can't do this. the things on the rows, and the things on the columns, must be mutually exclusive alternatives, as in the correct setup above. if you've ever constructed something called a "two-way table" in a statistics class, this is essentially the same thing.

[Guest]

You hit the nail on its head. I set up the matrix as you stated at the bottom of your answer. using the 100% isn't the issue as I regularly use it but setting it up like you did is why I wasn't getting it right.

Thanks
A4Fever

[JonathanSchneider]

Yes, be very careful with the double set matrix. One tip: you should be able to draw it out by labeling your first row "x" (or whatever else you want to call it, in this case: "q1") and have your second column be that same "q1" but with a slash through it, representing the opposite.

For your rows, do the same: "q2", and "q2" with a slash through it.

This should help to keep it clear.