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📌 Section 1 is Logical reasoning specially designed for CAT
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SET 1 — 🔍 CAT Level
The following table gives the distribution of students selected for the MBA programme from a coaching institute in the year 2022. Table I gives the percentage distribution of the total number of students selected according to their respective backgrounds, for each zone. Table II gives the percentage distribution of the total number of students selected according to their respective zones, for each background.
Table I
Zone | Engineering | Arts | Science | Commerce | Others |
|---|---|---|---|---|---|
North | 60 | 16 | 36 | 64 | 28 |
South | 4 | 14 | 8 | 4 | 6 |
East | 20 | 8 | 16 | 4 | 12 |
West | 6 | 26 | 22 | 8 | 18 |
Central | 10 | 36 | 18 | 20 | 36 |
Total | 100 | 100 | 100 | 100 | 100 |
Table II
Background | North | South | East | West | Central |
|---|---|---|---|---|---|
Engineering | 50 | 24 | 64 | 16 | 20 |
Arts | 8 | 42 | 10 | 42 | 36 |
Science | 10 | 16 | 14 | 20 | 12 |
Commerce | 28 | 12 | 8 | 10 | 20 |
Others | 4 | 6 | 4 | 12 | 12 |
Total | 100 | 100 | 100 | 100 | 100 |
All the values in Table I were entered correctly. However, while entering the values in Table II, some mistakes occurred, as a result of which the values in only two of the five columns of the table are completely correct, while each of the other columns has one or more mistakes.
Question 1
Of the total students selected, what is the ratio of the number of students with an engineering background to that of those with a science background?
a) 4 : 1
b) 5 : 2
c) 3 : 1
d) 3 : 2
Question 2
The values in which two columns of Table II are correct?
a) North and South
b) South and East
c) East and West
d) None of these
Question 3
The total number of students selected from which two zones is the same?
a) East and South
b) South and West
c) East and Central
d) East and West
Question 4
Among the students selected from the West zone, the difference between the number of students with an arts background and the number of those with a commerce background is 27. What is the total number of students selected?
✅ Answers & Explanations
Let the total number of students from the five backgrounds be:
Engineering = E
Arts = A
Science = S
Commerce = C
Others = O
Table I is fully correct. Since each column of Table I totals 100, it tells us how each background is distributed across zones.
Table II gives the background-wise percentage within each zone. Only two columns of Table II are completely correct.
Now check Table II columns.
For a correct zone column:
Table II value = Number from that background in that zone / Total students from that zone × 100
Using South column of Table II:
Engineering in South = 4% of E
Arts in South = 14% of A
Science in South = 8% of S
Commerce in South = 4% of C
Others in South = 6% of O
Table II says South distribution is:
Engineering = 24
Arts = 42
Science = 16
Commerce = 12
Others = 6
So,
4E : 14A : 8S : 4C : 6O = 24 : 42 : 16 : 12 : 6
Divide background-wise:
E : A : S : C : O
= 24/4 : 42/14 : 16/8 : 12/4 : 6/6
= 6 : 3 : 2 : 3 : 1
Now check Central column.
From Table I, Central values are:
Engineering = 10
Arts = 36
Science = 18
Commerce = 20
Others = 36
Table II Central column:
Engineering = 20
Arts = 36
Science = 12
Commerce = 20
Others = 12
So,
10E : 36A : 18S : 20C : 36O = 20 : 36 : 12 : 20 : 12
E : A : S : C : O
= 20/10 : 36/36 : 12/18 : 20/20 : 12/36
= 2 : 1 : 2/3 : 1 : 1/3
Multiplying by 3:
= 6 : 3 : 2 : 3 : 1
So, South and Central are the two correct columns.
Answer for Question 2: d) None of these
Because the correct pair is South and Central, which is not given.
Now,
Engineering : Arts : Science : Commerce : Others
= 6 : 3 : 2 : 3 : 1
Question 1:
Engineering : Science = 6 : 2 = 3 : 1
Answer: c) 3 : 1
Now find zone totals using Table I.
Assume:
Engineering = 6x
Arts = 3x
Science = 2x
Commerce = 3x
Others = x
Total students = 15x
North total:
60% of 6x + 16% of 3x + 36% of 2x + 64% of 3x + 28% of x
= 3.6x + 0.48x + 0.72x + 1.92x + 0.28x
= 7x
South total:
4% of 6x + 14% of 3x + 8% of 2x + 4% of 3x + 6% of x
= 0.24x + 0.42x + 0.16x + 0.12x + 0.06x
= x
East total:
20% of 6x + 8% of 3x + 16% of 2x + 4% of 3x + 12% of x
= 1.2x + 0.24x + 0.32x + 0.12x + 0.12x
= 2x
West total:
6% of 6x + 26% of 3x + 22% of 2x + 8% of 3x + 18% of x
= 0.36x + 0.78x + 0.44x + 0.24x + 0.18x
= 2x
Central total:
10% of 6x + 36% of 3x + 18% of 2x + 20% of 3x + 36% of x
= 0.6x + 1.08x + 0.36x + 0.6x + 0.36x
= 3x
So zone totals are:
North : South : East : West : Central
= 7 : 1 : 2 : 2 : 3
Question 2:
From the detailed work, the background ratio is:
Engineering : Arts : Science : Commerce : Others
= 6 : 3 : 2 : 3 : 1
Now check each Table II column.
For South:
From Table I, South percentages are:
Engineering = 4% of 6 = 0.24
Arts = 14% of 3 = 0.42
Science = 8% of 2 = 0.16
Commerce = 4% of 3 = 0.12
Others = 6% of 1 = 0.06
So South total = 1
Hence South distribution:
Engineering = 0.24/1 = 24%
Arts = 0.42/1 = 42%
Science = 0.16/1 = 16%
Commerce = 0.12/1 = 12%
Others = 0.06/1 = 6%
This exactly matches Table II South column.
So South is correct.
For Central:
From Table I, Central percentages are:
Engineering = 10% of 6 = 0.60
Arts = 36% of 3 = 1.08
Science = 18% of 2 = 0.36
Commerce = 20% of 3 = 0.60
Others = 36% of 1 = 0.36
Central total = 3
Hence Central distribution:
Engineering = 0.60/3 = 20%
Arts = 1.08/3 = 36%
Science = 0.36/3 = 12%
Commerce = 0.60/3 = 20%
Others = 0.36/3 = 12%
This exactly matches Table II Central column.
So Central is also correct.
Therefore, the two correct columns are:
South and Central
But the options are:
a) North and South
b) South and East
c) East and West
d) None of these
Since South and Central is not given, the answer is:
d) None of these
Question 3:
East and West are the same.
Answer: d) East and West
Question 4:
In West zone,
Arts students = 26% of Arts = 26% of 3x = 0.78x
Commerce students = 8% of Commerce = 8% of 3x = 0.24x
Difference = 0.78x - 0.24x = 0.54x
Given difference = 27
0.54x = 27
x = 50
Total students = 15x = 15 × 50 = 750
Answer for Question 4: 750
Final Answers:
c) 3 : 1
d) None of these
d) East and West
750
Let the total number of students from the five backgrounds be:
Engineering = E
Arts = A
Science = S
Commerce = C
Others = O
Table I is fully correct. Since each column of Table I totals 100, it tells us how each background is distributed across zones.
Table II gives the background-wise percentage within each zone. Only two columns of Table II are completely correct.
Now check Table II columns.
For a correct zone column:
Table II value = Number from that background in that zone / Total students from that zone × 100
Using South column of Table II:
Engineering in South = 4% of E
Arts in South = 14% of A
Science in South = 8% of S
Commerce in South = 4% of C
Others in South = 6% of O
Table II says South distribution is:
Engineering = 24
Arts = 42
Science = 16
Commerce = 12
Others = 6
So,
4E : 14A : 8S : 4C : 6O = 24 : 42 : 16 : 12 : 6
Divide background-wise:
E : A : S : C : O
= 24/4 : 42/14 : 16/8 : 12/4 : 6/6
= 6 : 3 : 2 : 3 : 1
Now check Central column.
From Table I, Central values are:
Engineering = 10
Arts = 36
Science = 18
Commerce = 20
Others = 36
Table II Central column:
Engineering = 20
Arts = 36
Science = 12
Commerce = 20
Others = 12
So,
10E : 36A : 18S : 20C : 36O = 20 : 36 : 12 : 20 : 12
E : A : S : C : O
= 20/10 : 36/36 : 12/18 : 20/20 : 12/36
= 2 : 1 : 2/3 : 1 : 1/3
Multiplying by 3:
= 6 : 3 : 2 : 3 : 1
So, South and Central are the two correct columns.
Answer for Question 2: d) None of these
Because the correct pair is South and Central, which is not given.
Now,
Engineering : Arts : Science : Commerce : Others
= 6 : 3 : 2 : 3 : 1
Question 1:
Engineering : Science = 6 : 2 = 3 : 1
Answer: c) 3 : 1
Now find zone totals using Table I.
Assume:
Engineering = 6x
Arts = 3x
Science = 2x
Commerce = 3x
Others = x
Total students = 15x
North total:
60% of 6x + 16% of 3x + 36% of 2x + 64% of 3x + 28% of x
= 3.6x + 0.48x + 0.72x + 1.92x + 0.28x
= 7x
South total:
4% of 6x + 14% of 3x + 8% of 2x + 4% of 3x + 6% of x
= 0.24x + 0.42x + 0.16x + 0.12x + 0.06x
= x
East total:
20% of 6x + 8% of 3x + 16% of 2x + 4% of 3x + 12% of x
= 1.2x + 0.24x + 0.32x + 0.12x + 0.12x
= 2x
West total:
6% of 6x + 26% of 3x + 22% of 2x + 8% of 3x + 18% of x
= 0.36x + 0.78x + 0.44x + 0.24x + 0.18x
= 2x
Central total:
10% of 6x + 36% of 3x + 18% of 2x + 20% of 3x + 36% of x
= 0.6x + 1.08x + 0.36x + 0.6x + 0.36x
= 3x
So zone totals are:
North : South : East : West : Central
= 7 : 1 : 2 : 2 : 3
Question 3:
East and West are the same.
Answer: d) East and West
Question 4:
In West zone,
Arts students = 26% of Arts = 26% of 3x = 0.78x
Commerce students = 8% of Commerce = 8% of 3x = 0.24x
Difference = 0.78x - 0.24x = 0.54x
Given difference = 27
0.54x = 27
x = 50
Total students = 15x = 15 × 50 = 750
Answer for Question 4: 750
Final Answers:
c) 3 : 1
d) None of these
d) East and West
750
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Stay consistent with your daily practice, challenge your assumptions, and keep sharpening your reasoning skills.
See you in tomorrow’s challenge!