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23 Jan 2019, 19:07
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
46% (01:48) correct
54%
(01:58)
wrong
based on 35
sessions
History
Date
Time
Result
Not Attempted Yet
100 students appeared for two tests-Maths and English. For every student who passed in both the tests, 8 students passed only in Maths and 9 students passed only in English. How many students passed in neither Maths nor English?
(1) More than 4 students passed in both the tests.
(2) Less than 6 students passed in both the tests.
(1) More than 4 students passed in both the tests.
(2) Less than 6 students passed in both the tests.
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KanishkM
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Gekkdude
After having a discussion with fellow gc members, i understood the question, Inline is the approach.
Total students = 100
students who passed in both the tests = x
Passed only in Maths = 8x
Passed only in English = 9x
Total students = x + 9x + 8x
We have to find students passed in neither Maths nor English
8x + 9x + x = 100 - N
N = 100 - 18x
Statement 1
More than 4 students passed in both the tests.
x can be 5, it cant be further than this
N = 100 - 18*5 = 100 - 90 = 10
Statement 2
Less than 6 students passed in both the tests.
here x can be 1,2,3,4,5.
When we substitute these values in
N = 100 - 18x
We get different values.
OA=A
23 Jan 2019, 22:10
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Official Solution - OA "A"
Understand Question and Draw Inferences
Total number of students = 100
Let the number of students who passed in both tests = X
Let the number of students who passed in neither Math nor English = N
Therefore,
Number of students who passed only in Maths = 8X
Number of students who passed only in English = 9X
Representing this information in Venn Diagram we get, (sorry couldnt draw a Venn diagram)
|Math--Common---Eng-----total students=100|
|(8X (X) 9X)----------------------------------------|
|-------------------neither Math nor English = N|
8X + X + 9X + N = 100
18X + Neither = 100
N = 100 – 18X
Therefore,
We need a unique value of X
Also, notice here that 18X < 100,
So, the possible values of X are 1, 2, 3, 4 ,5
Statement 1: More than 4 students passed in both the tests.
X > 4
From the question stem inference, we deduced that the possible values of X are 1,2,3,4 or 5.
Since X > 4 the only possible value of X = 5
Hence, Statement 1 is sufficient.
Statement 2: Less than 6 students passed in both the tests.
X < 6
From the question stem inference, we deduced that the possible values of X are 1,2,3,4 or 5.
Therefore, with Statement 2 alone we cannot find a unique value of X .
Hence, Statement 2 is not sufficient.
Correct Answer: Option A
Understand Question and Draw Inferences
Total number of students = 100
Let the number of students who passed in both tests = X
Let the number of students who passed in neither Math nor English = N
Therefore,
Number of students who passed only in Maths = 8X
Number of students who passed only in English = 9X
Representing this information in Venn Diagram we get, (sorry couldnt draw a Venn diagram)
|Math--Common---Eng-----total students=100|
|(8X (X) 9X)----------------------------------------|
|-------------------neither Math nor English = N|
8X + X + 9X + N = 100
18X + Neither = 100
N = 100 – 18X
Therefore,
We need a unique value of X
Also, notice here that 18X < 100,
So, the possible values of X are 1, 2, 3, 4 ,5
Statement 1: More than 4 students passed in both the tests.
X > 4
From the question stem inference, we deduced that the possible values of X are 1,2,3,4 or 5.
Since X > 4 the only possible value of X = 5
Hence, Statement 1 is sufficient.
Statement 2: Less than 6 students passed in both the tests.
X < 6
From the question stem inference, we deduced that the possible values of X are 1,2,3,4 or 5.
Therefore, with Statement 2 alone we cannot find a unique value of X .
Hence, Statement 2 is not sufficient.
Correct Answer: Option A
------- doesn't match OA ! 
