Instructions

Each question consists of a set of numbered statements. Assume that each one of these statements is individually true. Each of the four choices consists of a subset of these statements. Choose the subset as your answer where the statements therein are logically consistent among themselves:

Question 41

A. Only if the water level in the coastal areas rises, then the people change their lifestyle.
B. People change their lifestyle only if they are rewarded.
C. If people are rewarded, then they will not change their lifestyle.
D. If the temperature rises, then the water level in the coastal areas rises.
E. Whenever the water level in the coastal area rises, then the temperature rises.
F. Unless the people change their lifestyle, temperature rises.
G. People are rewarded.
H. Water level in the coastal areas does not rise.

Video Solution

Solution

Let us solve the problem by eliminating the options.
G: People are rewarded
C: if people are rewarded then they will not change their lifestyle.
F: Unless people change their lifestyle, temperature rises This can also be put In the following manner.
If people do not change their lifestyle then temperature rises.
This is an example of binary logic - If not A then B which can also be expressed as if not B then 'A'.
Thus if the temperature doesn't rise then people change their lifestyle.
Here, accordingtoG and C, people do not change their lifestyle and so temperature rises.
D: If temperature rises, then water level in the coastal area rises.
H: Water level In the coastal area doesn't rise.
Here, D is in accordance with G, C and F but H is not So option (A) is incorrect.
B: People change their lifestyle only if they are rewarded.
This means that if people have changed their lifestyle then they have been rewarded.
Note that if people are rewarded, they may or may not have changed their lifestyle.
G: People are rewarded.
From B and G. we don't know whether people have changed their lifestyle or not.
F: Unless the people change their lifestyle, temperature rises.
This can also be put as - If the people don't change their lifestyle then temperature rises
But

as we don't know whether people have changed their lifestyle or not,

v/e cannot conclude whether temperature has risen or not.
D: if temperature rises, then water level in the coastal area rises.
H: Water level in the coastal area doesn't rise.
As we don’t know whether temperature has risen or not, H cannot be concluded using D.
Hence, option (B) is also incorrect.

Question 42

A. If Kumar sings, then the audiences sleep.
B. If Kumar sings, then the audiences dance.
C. Unless audience do not dance, the concert will be successful.
D. Only if the audience dance, the concert will be successful.
E. If Vina dances, then Kumar sings.
F. Kumar sings only if Vina dances.
G. Vina dances
H. The concert is successful.

Video Solution

Solution

In option 2, statement A says- If Kumar sings then the audiences sleep.
Out

of the other 4 statements C, F,G and H, none of the statements mention

anything about sleep and hence option (B) is incorrect.
If option (B) is incorrect, option (D) is also incorrect as it mentions both (B) and (C).
C: Unless audience does not dance, the concert will be successful.
This can also be put as - If the audience dance, the concert will be successful.
F: Kumar sings, only if Vina dances.
This means that - If Kumar has sung, then Vina has danced.
But if Vina has danced, Kumar may or may not have sung.
B: if Kumar sings, then the audience dances.
We

don't know whether Kumar has sung or not and so we don't know whether

the audience have danced or not. Hence we cannot conclude that the

concert is successful as given in statement H.
So option (A) is also logically incorrect.
E: if Vina dances, then Kumar sings.
G: Vina dances.
Thus from these two statements v/e know that Kumar sings.
B: If Kumar sings, then audiences dance.
Thus audiences have danced.
C: Unless audience does not dance, the concert will be successful.
This can also be put as - If the audience dance, the concert will be successful.
Thus the concert is successful as mentioned in statement H.

Instructions

These questions are based on the data given below.
There are only four members of a family viz., A, B, C and D and there is only one couple among them. When asked about their relationships, following were their replies:
a: A: B is my son. D is my mother.
b: B: C is my wife. Dis my father.
c: C: D is my mother - in - law. A is my daughter.
d: D: A is my grand - daughter. B is my daughter - in - law

Question 43

Who always speaks the truth?

Video Solution

Solution

From the statement of A, we cannot state any information about C. Similarly B and C are also providing partial details. We can find out that Dis the grandfather and A is the grandson, and CB are the couple, thus statement B is a complete truth.

We are able to set the relationship.

Option D

Question 44

How is B related to C?

Video Solution

Solution

From the statement of A, we cannot state any information about C. Similarly B and C are also providing partial details. We can find out that Dis the grandfather and A is the grandson, and CB are the couple, thus statement B is a complete truth.

We are able to set the relationship.

Option C

Question 45

Which of the following statements must be true?

Video Solution

Solution

From the statement of A, we cannot state any information about C. Similarly B and C are also providing partial details. We can find out that Dis the grandfather and A is the grandson, and CB are the couple, thus statement B is a complete truth.

We are able to set the relationship.

Both the statements of B are false.

Option D

Instructions

These questions are based on the following information.
A cube of 7cm × 7cm × 7cm is kept in the corner of a room and painted in three different colours, each face in one colour. The cube is cut into 343 smaller but identical cubes.

Question 46

How many smaller cubes do not have any face painted?

Video Solution

Solution

Three faces are painted as given in the figure.

Total number of cubes= 343

Total number of painted cubes=7x7+7x6+6x6=49+42+36=127

Number of cubes which are colourless = 343-127=216

Option D

Question 47

How many smaller cubes have exactly one colour on them?

Video Solution

Solution

Three faces are painted as given in the figure.

Total number of cubes= 343

The number of cubes with only one color on them: Blue= 6x6

Green= 6x6

Red=6x6

=3x36

=108

Option A

Question 48

How many smaller cubes have at the most two faces painted?

Video Solution

Solution

Three faces are painted as given in the figure.

Total number of cubes= 343

Faces with three sides painted =1
Answer= 343-1=342

Option B

Instructions

Amit was driving in New Town, where all roads either north - south or east - west forming a grid. Roads were at a distance of 1 km from each other in parallel.

Question 49

Amit started at the intersection of streets no. 7 and 8. He drove 3 km north, 3 km west and 4 km south. Which further route could bring him back to his starting point?
I. 3 km east, then 2 km south
II. 1 km north, then 3 km east
III. 1 km north, then 2 km west

Video Solution

Solution

We can draw the following diagram for its initial movement:

To return to its original position it can move along the path II, mentioned above.

Option B is correct.

Question 50

After driving as stated in question no. 49 above, Amit did not return to his starting point but instead drove 4 km east and 1 km north. How far is he from his starting point?

Video Solution

Solution

We can draw the following diagram for its initial movement:

Further, it moves 4 km east and 1 km north.

He is 1km from the starting point.
Option C

CAT Content

SNAP 2011 Question Paper

Who always speaks the truth?

How is B related to C?

Which of the following statements must be true?

How many smaller cubes do not have any face painted?

How many smaller cubes have exactly one colour on them?

How many smaller cubes have at the most two faces painted?

Amit started at the intersection of streets no. 7 and 8. He drove 3 km north, 3 km west and 4 km south. Which further route could bring him back to his starting point?
I. 3 km east, then 2 km south
II. 1 km north, then 3 km east
III. 1 km north, then 2 km west

After driving as stated in question no. 49 above, Amit did not return to his starting point but instead drove 4 km east and 1 km north. How far is he from his starting point?

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