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# 31 of the scientists that attended a certain workshop were Wolf Prize

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31 of the scientists that attended a certain workshop were Wolf Prize [#permalink]

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30 Apr 2016, 19:18
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31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 13 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates?

A)11
B)18
C)24
D)29
D)36
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Re: 31 of the scientists that attended a certain workshop were Wolf Prize [#permalink]

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30 Apr 2016, 20:23
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ruben2navega wrote:
31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 13 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates?

A)11
B)18
C)24
D)29
D)36

Can you help me?

You can solve by Venn diagrams too..

lets solve by creating equation..

W = 31..
Total = 50..
Not W = 50 -31= 19..

Now let people who were neither be x, so out of 19 who won Nobel = x+3..
so x+x+3=19 or x=8..

so who won Nobel but not Wolf = x+3 = 11..

But people who won BOTH W and N = 13..
so total who won N = 11+13 = 24..
C
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31 of the scientists that attended a certain workshop were Wolf Prize [#permalink]

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30 May 2016, 15:26
Total atendees = 50
Only Waltz = 31 - 13 = 18
Only Nobel = X+3
Both Waltz and Nobel = 13
Not Waltz or Nobel = X

Not Waltz or Nobel = 50 - 18 - 13 - X - 3 = X
Not Waltz or Nobel =16 = 2X
Not Waltz or Nobel = X = 8

If X = 8, then
Nobel = Only Nobel + Both Waltz and Nobel = 8 + 3 + 13 = 24

Note: I personally believe that phrasing the question as "3 greater than the number of scientists" is confusing. I first though Only Nobel is 3X. But perhaps it's just the way GMAT catches unattentive readers like i.
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Re: 31 of the scientists that attended a certain workshop were Wolf Prize [#permalink]

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31 May 2016, 05:38
1
KUDOS
I always solve this with a table:
W nW t
N 13 x+3
nN x
t 31 50

the bold parts are the given things
so we know that nW = 19 (because 50-31 is 19) and we know that x+3 + x = 19; therefore x is 8 and x+3 is eleven. Then just fill in the blank space and read out the answer

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Re: 31 of the scientists that attended a certain workshop were Wolf Prize [#permalink]

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05 Aug 2017, 12:15
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Re: 31 of the scientists that attended a certain workshop were Wolf Prize [#permalink]

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19 Aug 2017, 23:15
ruben2navega wrote:
31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 13 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates?

A)11
B)18
C)24
D)29
D)36

Total number of Scientists $$= 50$$

Number of Scientist with Wolf Prize $$= 31$$

$$13$$ of these $$31$$ Scientist with Wolf Prize were also Nobel Prize.

Therefore Scientist with Noble prize (Out of Wolf Prize) $$= 13$$

Number of Scientist Without Wolf Prize $$= 50 - 31 = 19$$

Out of $$19$$, Let the Scientist with Non noble Prize be $$= x$$

Therefore Scientist with Noble Prize (Out of $$19$$) $$= x + 3$$

Total Scientist Without Wolf Prize $$=> x+x+3 = 19$$

$$2x = 19 - 3 = 16$$

$$x = \frac{16}{2} = 8$$

Therefore Total Scientist with Nobel Prize $$= 13 + x + 3 = 13 + 8 + 3 = 24$$

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Re: 31 of the scientists that attended a certain workshop were Wolf Prize [#permalink]

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20 Aug 2017, 11:34
ruben2navega wrote:
31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 13 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates?

A)11
B)18
C)24
D)29
D)36

Attachment:

matrixnobel.png [ 12.72 KiB | Viewed 204 times ]

Double matrix worked very well here.

Total attendees: 50
Total Wolf Prize winners = 31
Total who did not win a Wolf Prize: 50 - 31 = 19

Total who won both Wolf and Nobel prizes: 13

Total Nobel prize winners?

"Of those who attended and had not received Wolf prize . . ." (not W column)

"the number of those who had received Nobel prize was 3 greater than the number of those who had not

x = those who won neither Wolf nor Nobel
x + 3 = those who did not win Wolf but did win Nobel

Solve for x as in diagram
2x + 3 = 19
x = 8

No W, no N = 8
No W, yes N = 11

Total the N row (Wolfram and Nobel) + (Nobel only): 13 + 11 = 24

Hope that's coherent. And helpful to some. :-)

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Re: 31 of the scientists that attended a certain workshop were Wolf Prize   [#permalink] 20 Aug 2017, 11:34
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