NMMSE Mental Ability Test Questions 41–55
Detailed Step-by-Step Solutions
NMMSE MAT Questions 41–55:
This section covers logical ordering, family relationship problems
and a Venn-diagram-based reasoning set. The explanations below
follow the questions and figure given in the uploaded question paper.
Questions 41–45: Arrangement According to Height
Question 41
There are five friends—P, Q, R, S and T.
P is shorter than Q but taller than T.
R is the tallest. S is a little shorter than Q and
little taller than P. Who is the shortest?
Solution:
From the statement, P is shorter than Q but taller than T.
Therefore:
From the statement, P is shorter than Q but taller than T.
Therefore:
Q > P > T
We are also told that S is shorter than Q but taller than P:
Q > S > P
R is the tallest.
Therefore, the complete order from tallest to shortest is:
R > Q > S > P > T
Hence, T is the shortest.
Correct Answer: (A) T
Question 42
If they stand in the order of their height, who will be in the middle?
Solution:
From Question 41, the height order is:
The third person is S.
From Question 41, the height order is:
R > Q > S > P > T
There are five people. Therefore, the third person in the
order occupies the middle position.
The third person is S.
Correct Answer: (D) S
Question 43
Who is the second tallest?
Solution:
The height arrangement is:
That person is Q.
The height arrangement is:
R > Q > S > P > T
R is the tallest. The person immediately below R is
therefore the second tallest.
That person is Q.
Correct Answer: (B) Q
Question 44
Who is taller than S but shorter than R?
Solution:
We know:
taller than S
and
shorter than R.
Q satisfies both conditions:
We know:
R > Q > S > P > T
We need someone who is:
taller than S
and
shorter than R.
Q satisfies both conditions:
R > Q > S
Therefore, Q is the required person.
Correct Answer: (B) Q
Question 45
If they stand in the order of increasing heights, who will be the second?
Solution:
Increasing height means arranging from the shortest to the tallest.
1st = T
2nd = P
3rd = S
4th = Q
5th = R
Hence, the second person is P.
Increasing height means arranging from the shortest to the tallest.
T < P < S < Q < R
Therefore:
1st = T
2nd = P
3rd = S
4th = Q
5th = R
Hence, the second person is P.
Correct Answer: (B) P
Questions 46–50: Family Relationship Reasoning
Given information:
All the six members of a family—A, B, C, D, E and F— are travelling together.
• B is the son of C, but C is not the mother of B.
• A and C are a married couple.
• E is the brother of C.
• D is the daughter of A.
• F is the brother of B.
All the six members of a family—A, B, C, D, E and F— are travelling together.
• B is the son of C, but C is not the mother of B.
• A and C are a married couple.
• E is the brother of C.
• D is the daughter of A.
• F is the brother of B.
Question 46
How many male members are there in the family?
Step 1: B is the son of C, but C is not
the mother. Therefore, C is the father of B.
Step 2: E is the brother of C, so E is male.
Step 3: F is the brother of B, so F is male.
Therefore the male members are:
Step 2: E is the brother of C, so E is male.
Step 3: F is the brother of B, so F is male.
Therefore the male members are:
B, C, E and F
Thus, there are four male members.
Correct Answer: (D) 4
Question 47
Who is the mother of B?
B is the son of C.
Since C is not the mother, C is the father.
A and C are married. Therefore A is the mother of B.
Hence, the mother of B is A.
Since C is not the mother, C is the father.
A and C are married. Therefore A is the mother of B.
Hence, the mother of B is A.
Correct Answer: (D) A
Question 48
How many children does A have?
B is the son of C. Since A and C are married, B is also
A's child.
The question also states that D is the daughter of A.
Therefore A has:
The question also states that D is the daughter of A.
Therefore A has:
B and D
Hence A has two children.
Correct Answer: (B) 2
Question 49
Which of the following is a pair of female?
From the information:
B is a son, so B is male.
C is the father, so C is male.
E is the brother of C, so E is male.
F is the brother of B, so F is male.
D is the daughter of A, so D is female.
A is the wife of C and mother of B, so A is female.
Therefore the pair of females is:
B is a son, so B is male.
C is the father, so C is male.
E is the brother of C, so E is male.
F is the brother of B, so F is male.
D is the daughter of A, so D is female.
A is the wife of C and mother of B, so A is female.
Therefore the pair of females is:
A and D
Correct Answer: (D) A, D
Question 50
How E is related to D?
E is the brother of C.
C is the husband of A.
D is the daughter of A and C.
Therefore E is the brother of D's father. Hence E is D's uncle.
C is the husband of A.
D is the daughter of A and C.
Therefore E is the brother of D's father. Hence E is D's uncle.
Correct Answer: (C) Uncle
Questions 51–55: Venn Diagram / Set-Based Reasoning
Figure Key:
Circle = Teachers
Rectangle = Players
Triangle = Swimmers
The same figure is used for Questions 51–55.
Circle = Teachers
Rectangle = Players
Triangle = Swimmers
The same figure is used for Questions 51–55.
Question 51
Corresponding Figure for Questions 51–55
How many players are teachers?
The circle represents teachers and the rectangle represents
players.
Therefore, we need the region common to the circle and rectangle.
That region contains the number 15.
Therefore, 15 players are teachers.
Therefore, we need the region common to the circle and rectangle.
That region contains the number 15.
Therefore, 15 players are teachers.
Correct Answer: (A) 15
Question 52
Corresponding Figure for Question 52
How many swimmers are neither players nor teachers?
We need swimmers who are:
• swimmers
• not players
• not teachers
So we look at the portion inside the triangle but outside both the circle and rectangle.
That region contains 12.
• swimmers
• not players
• not teachers
So we look at the portion inside the triangle but outside both the circle and rectangle.
That region contains 12.
Correct Answer: (B) 12
Question 53
Corresponding Figure for Question 53
How many players are neither teachers nor swimmers?
We need players who are:
• inside the rectangle
• outside the circle
• outside the triangle
The rectangle-only region is marked 10.
Therefore, the required number is 10.
• inside the rectangle
• outside the circle
• outside the triangle
The rectangle-only region is marked 10.
Therefore, the required number is 10.
Correct Answer: (C) 10
Question 54
Corresponding Figure for Question 54
How many players are both teachers and swimmers?
Important observation:
This question asks for people who are simultaneously:
Players + Teachers + Swimmers
In other words, we need the region common to the circle, rectangle and triangle.
However, in the printed figure, there is no region carrying a numerical value that belongs to all three sets.
The region marked 5 is inside the rectangle and triangle, but it is outside the circle.
Therefore, the figure as printed gives:
The option (D) 5 would be correct only if the region marked 5 were intended to represent the intersection of all three sets, which the printed geometry does not show.
This question asks for people who are simultaneously:
Players + Teachers + Swimmers
In other words, we need the region common to the circle, rectangle and triangle.
However, in the printed figure, there is no region carrying a numerical value that belongs to all three sets.
The region marked 5 is inside the rectangle and triangle, but it is outside the circle.
Therefore, the figure as printed gives:
Teachers ∩ Players ∩ Swimmers = 0
But 0 is not included among the four printed options.
Therefore this question appears to contain an inconsistency
between the figure and the answer choices.
The option (D) 5 would be correct only if the region marked 5 were intended to represent the intersection of all three sets, which the printed geometry does not show.
Answer according to the printed figure: 0
Note: No valid option is provided in the question paper.
Note: No valid option is provided in the question paper.
Question 55
Corresponding Figure for Question 55
How many teachers neither players nor swimmers?
We need people who are:
• teachers
• not players
• not swimmers
Therefore, we look at the part of the circle that lies outside both the rectangle and triangle.
That region is marked 40.
Hence the required number is 40.
• teachers
• not players
• not swimmers
Therefore, we look at the part of the circle that lies outside both the rectangle and triangle.
That region is marked 40.
Hence the required number is 40.
Correct Answer: (B) 40
Answer Summary: Questions 41–55
| Question | Answer | Topic |
|---|---|---|
| 41 | A – T | Height Order |
| 42 | D – S | Height Order |
| 43 | B – Q | Height Order |
| 44 | B – Q | Height Order |
| 45 | B – P | Height Order |
| 46 | D – 4 | Family Relation |
| 47 | D – A | Family Relation |
| 48 | B – 2 | Family Relation |
| 49 | D – A, D | Family Relation |
| 50 | C – Uncle | Family Relation |
| 51 | A – 15 | Venn Diagram |
| 52 | B – 12 | Venn Diagram |
| 53 | C – 10 | Venn Diagram |
| 54 | 0* | Venn Diagram |
| 55 | B – 40 | Venn Diagram |
Quick Revision:
For Questions 41–45, first convert every statement into a height relationship and then arrange the people from tallest to shortest or shortest to tallest.
For Questions 46–50, identify the gender and relationship clues carefully. Words such as son, daughter, brother, married couple are the key to solving these questions.
For Questions 51–55, remember:
Circle = Teachers
Rectangle = Players
Triangle = Swimmers
Always identify the exact common region before selecting an answer.
*Question 54: The supplied figure and printed options appear inconsistent. The mathematical interpretation of the supplied figure gives 0, although 0 is not among the printed choices.
For Questions 41–45, first convert every statement into a height relationship and then arrange the people from tallest to shortest or shortest to tallest.
For Questions 46–50, identify the gender and relationship clues carefully. Words such as son, daughter, brother, married couple are the key to solving these questions.
For Questions 51–55, remember:
Circle = Teachers
Rectangle = Players
Triangle = Swimmers
Always identify the exact common region before selecting an answer.
*Question 54: The supplied figure and printed options appear inconsistent. The mathematical interpretation of the supplied figure gives 0, although 0 is not among the printed choices.
