MathRevolution wrote:

There are 40 people, 28 invested in A, 16 invested in B, and 18 invested in C. Among 10 of the people who invested in both A and C, 3 also invested in B. All people who invested in B also invested in A. How many people did not invest in any of the three investments?

A. 2 B. 3 C. 4 D. 5 E. 6

Attachment:

ABCvenn.png [ 7.7 KiB | Viewed 1124 times ]
I used a Venn diagram, too, but I got

A only = 5.

kunalsinghNS - how did you arrive at A only = 2?

GIVEN40 people total

A = 28. B = 16. C = 18

A + C = 10

-------> and A + C + B = 3

All people who invested in B also invested in A

---If B, then A

---B only = 0

CALCULATIONSPer diagram, I entered numbers into color spaces in this order: blue, pink, green, yellow, gray, purple, white

1. Take most restrictive condition first. Blue. Three circles overlap.

"Among 10 of the people who invested in both A and C, 3 also invested in B." That means

A + C + B = 3. Put 3 in blue*

2. Next pink, which is A + C, which follows from #1.

A + C = 10.

Careful - don't put 10 in pink. Blue already has 3 of those who are also in A + C.

A + B

+ C = 3, where "B also" = 3

10 - 3 = 7. Put 7 in pink

3. Green. Another restrictive condition: All B are A

B = 16

So B + A

total must = 16

But blue has 3 of those 16. 16 - 3 = 13 for the rest of A + B (green). Put 13 in green

4. Yellow and gray. Finish B. B = 16. Yellow is B only. Gray is B + C.

All 16 B are accounted for.

Put ZERO in yellow.

Put ZERO in gray

5. Purple, C only. Finish C. C = 18

Areas surrounding C are pink, blue, gray. All have numbers now. Add their numbers: 7 + 3 + 0 = 10

Total 18 - 10 = 8. C only = 8. Put 8 in purple

6. White, A only. Finish A. A = 28

Areas surrounding A are pink, blue, green. All have numbers now. Add their numbers: 7 + 3 + 13 = 23

A only: 28 - 23 = 5. A only = 5. Put 5 in white7. Now add

all numbers, from every color, to get total that have "fallen" into the Venn diagram. Working outside to inside, clockwise from A only

5 + 0 + 8 + 13 + 0 + 7 + 3 = 36 invested the three investments A, B, C

8. There are 40 people total. (40 - 36) = 4 who did not invest in any of the three investments

Answer C*Blue will affect everything. Check its numbers and contents (A + B + C) for overlap with surrounding intersecting spaces (green, pink, gray: A + B, B + C, and C + A, respectively)

_________________

SC Butler has resumed!Get

two SC questions to practice, whose links you can find by date,

here.Tell me, what is it you plan to do with your one wild and precious life? --

Mary Oliver