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

Question

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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RaghavKhanna · Answer

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

rajatchopra1994 · Answer

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

IanStewart · Answer

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.

Ahmed9955 · Answer

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'"?

IanStewart · Answer

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.

Gmat202023 · Answer

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

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