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

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SVP
Joined: 24 Sep 2005
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There are 10 people studying A, 11 people studying B and 14 [#permalink]  25 Feb 2006, 21:06
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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?
Current Student
Joined: 29 Jan 2005
Posts: 5244
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Kudos [?]: 179 [0], given: 0

10+11+14=35 total

35-20-3= 12

What am I missing here?
Current Student
Joined: 29 Jan 2005
Posts: 5244
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Kudos [?]: 179 [0], given: 0

Professor wrote:
GMATT73 wrote:
10+11+14=35 total

35-20-3= 12

What am I missing here?
deduct 3 twice.

Why do we need to make the second deduction?
VP
Joined: 29 Dec 2005
Posts: 1349
Followers: 7

Kudos [?]: 30 [0], given: 0

GMATT73 wrote:
Professor wrote:
GMATT73 wrote:
10+11+14=35 total

35-20-3= 12

What am I missing here?
deduct 3 twice.

Why do we need to make the second deduction?

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).
Manager
Joined: 13 Dec 2005
Posts: 224
Location: Milwaukee,WI
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Kudos [?]: 7 [0], given: 0

There was a similar question posted few days back ...

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 .
CEO
Joined: 20 Nov 2005
Posts: 2913
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 18

Kudos [?]: 121 [0], given: 0

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
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
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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
VP
Joined: 20 Sep 2005
Posts: 1023
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Kudos [?]: 27 [0], given: 0

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.
VP
Joined: 29 Dec 2005
Posts: 1349
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Kudos [?]: 30 [0], given: 0

hmmmmm.......... all for 3 but i still stick with 9. laxi, did you forget to explain this with OA?
Director
Joined: 05 Feb 2006
Posts: 902
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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...
SVP
Joined: 24 Sep 2005
Posts: 1893
Followers: 11

Kudos [?]: 139 [0], given: 0

ipc302 wrote:
There was a similar question posted few days back ...

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 .

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
SVP
Joined: 05 Apr 2005
Posts: 1733
Followers: 5

Kudos [?]: 38 [0], given: 0

laxieqv wrote:
ipc302 wrote:
There was a similar question posted few days back ...

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 .

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

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