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# A surprise inspection of 200 companies revealed that 80 of

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GMAT Instructor
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A surprise inspection of 200 companies revealed that 80 of [#permalink]  19 Jul 2006, 13:54
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A surprise inspection of 200 companies revealed that 80 of them had evaded paying taxes, 60 had bribed public officials and 90 had filed fraudulent Social Security claims. How many of the 200 companies inspected were not guilty of any of these offenses?

(1) 90 companies were guilty of at least two of these offenses.
(2) 5 companies were guilty of all three offenses.
Manager
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I am tempted to go with C ...I will explain if that is correct
SVP
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First look tells me to go with C.
But Kevin's pride would be hurt if he gave such an easy question.

Ok let me try

I think A is sufficient.

A says there are 90 people with at least 2 of the offenses.
Hence it means that these 90 also include the number of people who have commited all three offenses.

Therefore total number who have not commited any of the offense
200 = 90+80+60 - 90

That is 60.
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Drawing a venn diagram, we get:

#(all three offences) = n
#(tax + social security) = a
#(social security + bribe) = c
#(bribe + tax) = b
#(tax only) = 80-n-a-b
#(social security only) = 90-n-a-c
#(bribe only) = 60-n-b-c
#(neither) = x

St1:
Total number = 200 = 230-2n-a-b-c + x
200 = 140-n+x
x-n = 60

Insufficient as we have no information about the # of companies that committed all 3 offences.

St2:
Total number = 200 = 230-2(5)-a-b-c+x
200 = 220-a-b-c+x
a+b+c-20 = x

Insufficient as we do not have information about # of comapnies that committed 2 offences.

Using St1 and St2:
x-n = 60
x-5 = 60
x = 65

Sufficient.

Ans C
Manager
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"at least 2" ...so A is sufficient.
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CEO
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C

A+B+C-AB-BC-CA+ABC + NONE = Total

St1: 80+60+90-(AB+BC+CA+ABC)+2ABC + x = 200
230- 90 + 2ABC + x = 200
we don't know ABC so can't find x.: INSUFF

St2: 80+60+90-(AB+BC+CA)+ 5 + x = 200 Clearly INSUFF

Combined:
230- 90 + 2ABC + x = 200 becomes
140+10+x = 200
x = 50: SUFF
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

GMAT Instructor
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St1: 80+60+90-(AB+BC+CA+ABC)+2ABC + x = 200

Does AB mean A intersect B or A intersect B intersect not C

I think from what you wrote earlier, it means the former.
If this is true, we are NOT given AB+BC+CA+ABC.
CEO
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kevincan wrote:
St1: 80+60+90-(AB+BC+CA+ABC)+2ABC + x = 200

Does AB mean A intersect B or A intersect B intersect not C

I think from what you wrote earlier, it means the former.
If this is true, we are NOT given AB+BC+CA+ABC.

I meant former. Ok my bad.
Lets do it again

A+B+C-AB-BC-CA+ABC + NONE = Total
i.e A+B+C-AB-BC-CA+2ABC-2ABC+ ABC + NONE = Total
i.e A+B+C-(AB+BC+CA-2ABC)-2ABC+ ABC + NONE = Total
i.e A+B+C-(AB+BC+CA-2ABC)-ABC+ NONE = Total

St1: We are given (AB+BC+CA-2ABC) = 90
so 80+60+90 - 90 + ABC + x = 200
ABC + x = 60: INSUFF

St2: we are given ABC = 5: Clearly INSUFF

Together:
5 + x = 60
x = 55

Is this correct????
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

GMAT Instructor
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Kudos [?]: 152 [0], given: 0

Correct! It's too bad we can't draw circles to illustrate, huh?
CEO
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kevincan wrote:
Correct! It's too bad we can't draw circles to illustrate, huh?

I did with circles but made a small mistake.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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