There are 10 people studying A, 11 people studying B and 14

Question

There are 10 people studying A, 11 people studying B and 14 people studying C. The number of people learning just one is 20. The number of people learning all three is 3. How many people only learn two of three?

GMATT73 · Answer

10+11+14=35 total

35-20-3= 12

What am I missing here?

GMATT73 · Answer

Why do we need to make the second deduction?

Professor · Answer

when u add a, b and c, you counted abc (=3) three times but you should count only once. so you need to deduct 2 (3).

ipc302 · Answer

There was a similar question posted few days back ... 

The answer is 3 .


say
x study both A &B
y study both A &C
z study both B&C

so the people ONLY studyA is 10 -( 3 +x+y) 
the people ONLY study B is 11 -(3 +x +z) 
the people ONLYstudy C is 14 -(3 +y +z) 

But according to question only 20 people study only one subject so 
if we add all the 3 above we get 26 -2 *(x+y+z) = 20 

it means x + y+ z = 3 

so 3 people study 2 kinds .

ps_dahiya · Answer

x - Only A
y - Only B
z- Only C

a - A and B
b - B and C
c - C and A

We have to find (a + b + c) = W

We get (x+y+z) + (a + b + c) + 3 = Total
20 + (a + b + c) + 3 = T

T = 23 + (a + b + c) i.e T = 23+W........EQ1

Also
10+11+14 -2 * 3 - (a+b+c) = T i.e T = 29 - W.... EQ2

Solve these two equations and we get W = 3

ywilfred · Answer

Represent intersect using '^'

A + (A^B^C) + (A^B) + (A^C) = 10
A + (A^B) + (A^C) = 7 ----(1)

B + (A^B^C) + (A^B) + (B^C) = 11
B + (A^B) + (B^C) = 8 ----(2)

C + (A^B^C) + (B^C) + (C^A) = 14
C + (B^C) + (C^A) = 11 ----(3)

(1) + (2) + (3)

(A + B + C) + 2(A^B) + 2(A^C) + 2(B^C) = 26
(A^B) + (A^C) + (B^C) = 3

Number of people learning two of the three = 3

lhotseface · Answer

3.

Venn diagram where a,b and c represent people learning two things.

10-(3+a+c) + 11 -(3+c+b) + 14-(3+a+b) = 20.
26-20 = 2(a+b+c)

a+b+c = 3 = Total number of people learning two of three things.

Professor · Answer

hmmmmm.......... all for 3 but i still stick with 9. laxi, did you forget to explain this with OA?

SimaQ · Answer

I think the answer shoud be 9....

You guys who calculated a+b+c=3 got what the statement was telling, i.e. that 3 people learn all three disciplines...

laxieqv · Answer

this OE is the clearest one. Thus OA is 3

I just want to complement a little to the bold part:
x= study both A and B without C
y= study both A and C without B
z= study both B and C without A

HIMALAYA · Answer

laxi, good to see you after a long time. and i am still waiting for your words. :wink:

There are 10 people studying A, 11 people studying B and 14

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