Joy Shaha wrote:Q. 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
Hi Joy Shaha,
Let's take a look at your question.
Total scientists that attended the workshop = 50
There are two groups of the attendants. One is the group who were Wolf Prize laureates and the other group who were not Wolf Prize laureates.
Let's discuss the
group 1 who were Wolf Prize laureates.
This group has 31 Wolf Prize laureates out of those
13 were Nobel Prize laureates. ------ (i)
Now,
group 2 who were not Wolf Prize laureates.
Number of attendants group 2 = Total scientists that attended the workshop - Number of scientists in group 1
Number of attendants group 2 = 50 - 31 = 19
The question states that "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".
Let
Number of scientists that are not Nobel Prize laureates in group 2 = x
Number of scientists that are Nobel Prize laureates in group 2 = x + 3
Then we can say that
x + (x+3) = 19
x + x + 3 = 19
2x + 3 = 19
2x = 16
=> x = 16/2 = 8
It means 8 scientists of group 2 are not Nobel Prize laureates.
Therefore,
Number of scientists that are Nobel Prize laureates in group 2 = x + 3 = 8 + 3 = 11 ------ (i)
From (i) and (ii), we can find the total number of Nobel Prize laureates out of total 50 scientists, i.e.
Nobel Prize laureates in group 1 + Nobel Prize laureates in group 2
= 13 + 11 = 24
Therefore, Option
C is correct.
I am available if you'd like any followup.
