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OG 11 PS #197

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Intern
Joined: 11 Apr 2008
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22 Apr 2008, 08:50
1
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Question Stats:

0% (00:00) correct 100% (00:16) wrong based on 2 sessions

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If 75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?

A. 10%
B. 20%
C. 30%
D. 50%
E. 65%

OA:E

I tried using the (group 1) + (group 2) - (neither) + (both) formula, but I seem that I cannot answer the question. What numbers do I need to plug in the above formula to receive E?

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SVP
Joined: 24 Aug 2006
Posts: 2130

Kudos [?]: 154 [1], given: 0

Re: OG 11 PS #197 [#permalink]

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22 Apr 2008, 09:00
1
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wwallace1 wrote:
If 75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?

A. 10%
B. 20%
C. 30%
D. 50%
E. 65%

OA:E

I tried using the (group 1) + (group 2) - (neither) + (both) formula, but I seem that I cannot answer the question. What numbers do I need to plug in the above formula to receive E?

Something doesn't seem right. If 65% answered both correctly, then how did only 55% answer the second question correctly.

Otherwise, it's D. 50% = both right, 25% = only A right, and 5% = only B right; finally 20% with none right.

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Intern
Joined: 11 Apr 2008
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Re: OG 11 PS #197 [#permalink]

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22 Apr 2008, 09:17
Ah yes, sorry the answer is D.

How did you get 5% right for only B? when 55% answered the second question correctly?

I'm very confused how you solved this answer

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Director
Joined: 01 Jan 2008
Posts: 504

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Re: OG 11 PS #197 [#permalink]

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22 Apr 2008, 09:31
1
KUDOS
wwallace1 wrote:
Ah yes, sorry the answer is D.

How did you get 5% right for only B? when 55% answered the second question correctly?

I'm very confused how you solved this answer

The answer is D. 75+55-80 :- 50 D

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Intern
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Re: OG 11 PS #197 [#permalink]

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22 Apr 2008, 09:49
why are you subtracting by 80, i know .20 did not get either question right but what logic did you use to say that you needed to subtract by 80? (besides 100-20 = 80)

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Intern
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Re: OG 11 PS #197 [#permalink]

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22 Apr 2008, 10:46
2
KUDOS
I got this question in PowerPrep and the explanation had a graph... let me see if I can recall what it said.

...something like this.
Attachments

Untitled.jpg [ 19.73 KiB | Viewed 1788 times ]

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SVP
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Re: OG 11 PS #197 [#permalink]

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22 Apr 2008, 10:52
wwallace1 wrote:
amazing, Kudos! :D

Right. The formula is A + B - AB = 100

20% got neither correct, therefore --> A + B - AB = 80, plug and solve.

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Director
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Re: OG 11 PS #197 [#permalink]

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22 Apr 2008, 11:34
Got D , Good question and Good explanation
_________________

Persistence+Patience+Persistence+Patience=G...O...A...L

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Current Student
Joined: 28 Dec 2004
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Schools: Wharton'11 HBS'12
Re: OG 11 PS #197 [#permalink]

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22 Apr 2008, 14:29
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assume 100 people in class..

100-20= got some question correct

80=75+55-Both
Both=50

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Manager
Joined: 27 Mar 2008
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Re: OG 11 PS #197 [#permalink]

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22 Apr 2008, 15:52
1
KUDOS
o.o wrote:
I got this question in PowerPrep and the explanation had a graph... let me see if I can recall what it said.

...something like this.

How does C get calculated? I'm not understanding the Venn Diagram

Kudos [?]: 122 [1], given: 0

SVP
Joined: 24 Aug 2006
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Kudos [?]: 154 [0], given: 0

Re: OG 11 PS #197 [#permalink]

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22 Apr 2008, 16:49
droopy57 wrote:
o.o wrote:
I got this question in PowerPrep and the explanation had a graph... let me see if I can recall what it said.

...something like this.

How does C get calculated? I'm not understanding the Venn Diagram

You just have to remember that A + B - C = The entire set. C = AB

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Intern
Joined: 07 Nov 2007
Posts: 27

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Location: Dominican Republic
Re: OG 11 PS #197 [#permalink]

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22 Apr 2008, 17:28
droopy57 wrote:
o.o wrote:
I got this question in PowerPrep and the explanation had a graph... let me see if I can recall what it said.

...something like this.

How does C get calculated? I'm not understanding the Venn Diagram

C is what we're being asked to look for, the number of people that got both questions right.

75% 1st question right
55% 2nd question right

Remember that the people that got both questions right are contained within those two percentages.

As said before, 75+55 = 130-80= 50.

50% represents the number of people that got both questions correct, so in fact only 5% of the grand total got only the 2nd question right and 25% got only the 1st one right.

Thus,
50+25+5+20=100

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Manager
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Re: OG 11 PS #197 [#permalink]

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22 Apr 2008, 21:23
I found the Kaplan method... wwallace1 improperly set up the equation:

Total = Group 1 + Group 2 - Both + Neither

100 = 75 + 55 - x + 20

x = 50

I think this is a much easier approach, though I see how a Venn can visually aid.

Question for everyone:

How would you set up a chart diagram to solve this question? Column and Row set up

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Manager
Joined: 05 Oct 2011
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Re: OG 11 PS #197 [#permalink]

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03 Nov 2011, 12:29
Group1+Group2+Neither-Both=Total

75+55+20-B=100
150-100=B
b=50

Kudos [?]: 55 [0], given: 62

Re: OG 11 PS #197   [#permalink] 03 Nov 2011, 12:29
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