why cant we use the formula as follows

G1 + G2 + N - B = Total

40+G2+40-40=200
G2= 160

why is this wrong.

Hey TJ,

There are a few ways that they can give you the information in one of these multiple-groups problems:

Group 1 TOTAL
Group 1 ONLY

This one gives us group X "ONLY", so we have to adjust for that in the formula. The people who used ONLY X represent the "X total" group minus the "both" group.

Group X then represents the group who ONLY used X (25%) and the group that used both X and Y (25%), so of the 160 people who used any product, 50% used X.

So group x is 80 people:

Group X + Group Y - Both + Neither = 200
80 + Group Y - 40 + 40 = 200
80 + Y = 200
Y = 120 (answer choice D)


Just as in the Venn Diagram problem in your previous post, they're not testing your ability to plug numbers into the formula as much as they're testing your ability to determine what the numbers represent. This is much more a test of how you think than of what you know, so knowing the formulas is only about 10% of the battle...the rest comes down to slowing down, determining what each value represents, and thinking critically about how to arrange the information to determine the answer.

thanks brian.
i understand now.

Just as a follow-up on
this overlapping set problem,
if you had to find out the people who are
AT LEAST in one of the two groups,
then could you get the answer
by subtracting the neither from the total?

X and Y - both = total - neither X nor Y

Thank you, and doesn't this mean
either X or Y, but not both?

to find the "X or Y", we'd have to add the "X only" and the "Y only"

that would be 40 + 80 = 120


"X, Y, or both" would be 40 + 80 + 40 = 160

or

200 - 40 = 160 (all - neither)

-- Veritas Help