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In an interview for a certain job, 120 candidates appeared and two que

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Bunuel
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In an interview for a certain job, 120 candidates appeared and two que [#permalink] New post   02 Jul 2020, 00:15
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65% (02:24) correct 35% (02:24) wrong based on 159 sessions
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In an interview for a certain job, 120 candidates appeared and two questions were asked to each candidate. How many candidates did not answer any question correctly?

(1) Of all the candidates who appeared for the interview, 20% of the candidates who answered at least one question correctly, answered both questions correctly.
(2) Of all the candidates who appeared for the interview, 25% of the candidates who answered none or both questions correctly, answered both questions correctly.


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C
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RaghavKhanna
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Re: In an interview for a certain job, 120 candidates appeared and two que [#permalink] New post   02 Jul 2020, 00:29
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Question 1 correct : a + b
Question 2 correct : b + c
No correct : d

a + b + c + d = 120

To find: d

St. 1:
b = 0.2(a+b+c)

Cannot find d from this.

=> St. 1 is insufficient.

St. 2:
0.25(d + b) = b

Cannot find the value of d from this
=> St. 2 is insufficient.

St. 1 & St. 2:
a + c = 0.8b
d = 3b

=> a + b + c + d = 120
=> 0.8b + b + 3b = 120
=> 4.8b = 120
=> b = 25

=> d = 3 * 25 = 75

=> St. 1 and St. 2 together are sufficient.

Answer: C
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Re: In an interview for a certain job, 120 candidates appeared and two que [#permalink] New post   02 Jul 2020, 02:48
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Explanation:
Given: A= number of candidates who gave 0 correct answers,
B= 1 correct answer
C= 2 correct answers
A + B + C = 120
find the value of A?

Statement 1:
Number of students who answered at least one question correctly = B + C
20% of (B+C) = C
1/5 x (B+C) = C
B=4C
Not Sufficient.

Statement 2:
Number of students who answered none or all questions correctly = A + C
25% of (A+C) = C
A=3C
Not Sufficient.

From 1 & 2,
A + B + C = 120
3C + 4C + C = 120
C = 15
then A = 45

Sufficient

IMO-C
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Re: In an interview for a certain job, 120 candidates appeared and two que [#permalink] New post   02 Jul 2020, 08:08
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Statement 1 tells us almost nothing about those answering neither question correctly (it does tell us that at least 5 people answered a question correctly, so at most 115 did not, which isn't too helpful here), and Statement 2 tells us almost nothing about those answering exactly one question correctly, so neither can be sufficient.

Statement 1 tells us the ratio of "both right" to "only one right" is 1 to 4
Statement 2 tells us the ratio of "both right" to "none right" is 1 to 3
So the ratio of "both" to "only one" to "none" is 1 to 4 to 3, and 3/8 of the 120 people, or 45 people, answered neither question correctly. So the answer is C.
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Re: In an interview for a certain job, 120 candidates appeared and two que [#permalink] New post   10 Dec 2020, 00:53
IanStewart wrote:
Statement 1 tells us almost nothing about those answering neither question correctly (it does tell us that at least 5 people answered a question correctly, so at most 115 did not, which isn't too helpful here), and Statement 2 tells us almost nothing about those answering exactly one question correctly, so neither can be sufficient.

Statement 1 tells us the ratio of "both right" to "only one right" is 1 to 4
Statement 2 tells us the ratio of "both right" to "none right" is 1 to 3
So the ratio of "both" to "only one" to "none" is 1 to 4 to 3, and 3/8 of the 120 people, or 45 people, answered neither question correctly. So the answer is C.


Hi Ian,
How did you arrive at the ratio?

I think I'm not understanding what exactly the statements are saying.
If 20% answered at least one correct it includes all three cases-
1st correct 2nd incorrect
1st wrong 2nd correct
1st correct 2nd correct

then what does the last line tell us -" answered both correctly'"?
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Re: In an interview for a certain job, 120 candidates appeared and two que [#permalink] New post   10 Dec 2020, 08:39
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Ahmed9955 wrote:
Hi Ian,
How did you arrive at the ratio?

I think I'm not understanding what exactly the statements are saying.
If 20% answered at least one correct it includes all three cases-


I think you're misinterpreting Statement 1. It does not tell us that "20% answered at least one correct". It says "20% of the candidates who answered at least one question correctly, answered both questions correctly." So Statement 1 is not talking about all candidates, nor about candidates who answered neither question correctly. It's only telling us that, if you look only at the people who did get at least one question right, 20% of those people got both questions right. And if that's true, the rest of those people, so 80% of those people, got exactly one question right, and the ratio of people with exactly one right answer to people with two right answers must be 80 to 20, or 4 to 1.
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Re: In an interview for a certain job, 120 candidates appeared and two que [#permalink] New post   14 Dec 2020, 14:03
a( 0 correct), b(1 correct), c( 2 correct)

Given a+b+c=120
To find: a=?

S1 : 0.20(b+c)=c Hence b=4c Not sufficient
S2 : 0.25( a+c)=c Hence a=3c Not sufficient

S1 + S2 : c= 15 a= 3c = 45 Sufficient

Thefore C is the answer
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Re: In an interview for a certain job, 120 candidates appeared and two que [#permalink] New post   11 Sep 2023, 01:15
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Re: In an interview for a certain job, 120 candidates appeared and two que [#permalink]
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