22-07-2021

 1. What is/are the statement(s) necessary/sufficient to answer the below question. What is the age of Dinesh ?
Statements : (1) Ratio between the ages of Arul and Dinesh is 4 : 3
                    (2) After 6 years Arul's age will be 26 years.
                    (3) Dinesh's father was 28 years when he was born.

Answer: Statements 1 and 2

Solution: By statement 1, Let the ages be x. So Arul's age : Dinesh's age = 4x : 3x

By statement 2, 4x + 6 = 26

                          => 4x = 26 - 6  => 4x = 20      => x = 5

So Dinesh's age = 3x = 15

So statements 1 and 2 are sufficient to answer

2. What is/are the statement(s) necessary/sufficient to answer the below question.
Find the value of x and y?
Statements: (1) x is three times y.
                       (2) y is15 percent of 300.

Answer: BOTH statements together are sufficient.

Solution: Solving the equations by using both the statements yield the result.

Hence, both statements are necessary to answer the question.

3. In the following questions, mark
1) if statement I alone can help determine the conclusion
2) if statement II alone can help determine the conclusion
3) if statement I and II taken together can help determine the conclusion
4) if none of the statements, taken together or separately can help determine the conclusion
Conclusion: Praveena knows how to drive a car.
Statement I: Praveena travelled from Salem to Chennai in 3 hours by car.
Statement II: Praveena goes to office using her own vehicle.

Answer: 4

Solution: I is not enough as it could be the chauffeur who drove the car.

II is not enough as Praveena may go to office using a bike.

4. Which of the given sentences is / are sufficient to answer the given question
Find the perimeter of the rectangle.
(i) Diagonal of rectangle is √41 cm
(ii) Area of rectangle is 20 sq.cm

Answer: Both (i) and (ii) are sufficient

Solution: By statement 1, diagonal = √(l2 + b2) = √41

By statement 2, Area = l * b = 20

So, √(l2 + b2) = √[(l+b)2 - 2(l*b)]

               √41 = √[(l+b)2 - 2(20)]

Removing square root from both sides, we have

                  41 = (l+b)2- 40

So (l+b)2 = 81

l + b = 9; Hence perimeter = 2(l+b) = 18.

So both the statements are necessary to answer the question.

5. The question below consists of a few statements. After analysing the statements, decide which statement(s) can give the answer.
What is the age of Giri's father ?
Statements : (1) Giri's father was thrice Giri's age 3 years ago.
                     (2) Giri's present age is twice his brothers age
                     (3) Giri's is 17 years old presently.

Answer: Statement 1 and 3

Solution: Statements 1 and 3 are enough to answer the given question

6. Choose the option based on the following conditions
A: Statement 1 alone is sufficient to answer the question.
B: Statement 2 alone is sufficient to answer the question.
C: Both statements when taken together, are sufficient to answer the question.
D: Both statements when taken together, are not sufficient to answer the question.
Each person on a committee with 40 members voted for exactly one of 3 candidates, F, G, or H. Did Candidate F receive the most votes from the 40 votes cast?
(1) Candidate F received 11 of the votes.
(2) Candidate H received 14 of the votes.

Answer: A

Solution: As F received only 11, even if other two people had slit equally the answer will be that F did not get the maximum number of votes.

7. In the following questions, mark
1) if statement I alone can help determine the conclusion
2) if statement II alone can help determine the conclusion
3) if statement I and II taken together can help determine the conclusion
4) if none of the statements, taken together or separately can help determine the conclusion
Conclusion: Sunil goes to gym everyday.
Statement I: Sunil has a well built physique.
Statement II: Sunil takes part in body building competitions.

Answer: 4

Solution: I is not sufficient as by nature one can have a well built physique. II is not sufficient as it only confirms he goes to gym which could be even 5 or 6 days in a week.

To know if he goes to gym everyday both statements are not enough.

8. Choose the option based on the following conditions
Choose 1: if the question can be answered by using one of the statements  alone but not by using the other statement alone
Choose 2: if the question can be answered by using either of the statements alone
Choose 3: if the question can be answered by using both the statements together but not by either statement alone
Choose 4: if the question cannot be answered even by using both statements together.
lf x is a positive integer, is it a perfect cube ?
A. x has two factors other than one and itself.
B. x has only two Prime factors.

Answer: 3

Solution: Analysing both statements we can answer the question.

9. What is/are the statement(s) necessary/sufficient to answer the below question.
Rahul, Gokul and Naren are running a business firm in partnership. What is Gokul's share in the profit earned by them?
Statements : (1) Rahul, Gokul and Naren invested the amounts in the ratio of 2 : 4 : 7.
                    (2) Naren's share in the profit is Rs. 8750.

Answer: Both Statements 1 and 2

Solution: Let us name Rahul, Gokul and Naren by R, G and N respectively.

By statement 1,  R : G : N = 2 : 4 : 7; By statement 2,  N = 8750.

Let total profit be X

(7/13)*X = 8750 => X = 16250 Rs

Gokul's share in profit = (4 / 13)  * 16250 = Rs 5000 approximately

So both statements 1 and 2 are needed.

10. What is/are the statement(s) necessary/sufficient to answer the below question.
What is the value of x?
Statements: (1). x = 80% of y.
                 (2). y is three fourth of 2400.

Answer: Statements 1 and 2 

Solution: From statement2, y=2400(3/4) = 1800; From statement1,  x = 1800*(80%) = 1440.

Hence both statements are required (necessary) to answer the question.

11. Which of the given sentence(s) is / are sufficient to answer the given question
What is the age of Arun’s father?
Statements: (i) Arun's age was 10 when his younger brother was born before 3 years
                  (ii) Arun’s father age is three times greater than Arun

Answer: Both (i) and (ii) are needed

Solution: Let Arun be  A, Arun's brother be B, Arun's father be F

By statement 1, A = 10 when B was born; So at present  A = 10 + 3 = 13

By statement 2, F = 3A; So, F = 3(13) = 39

So statements (i) and (ii) are needed to answer the question

12. Choose the options with reference to sufficiency of statements I and II provided below to answer the given question.
Question: Find the value of x^15
Statement I: x is a prime number
Statement II: x is an even number

Answer: Both Statement I and II are required

Solution: Statement I says x is a prime number which means it can be any prime number like 5, 13, 17 , 19. Hence we cannot find the value.

Statement II says x is an even number which means it can be any even number like 4,66,88. Hence we cannot find the value.

But combining both the statements, 2 is the only number which is prime and even.

Hence both statement I and II are required.

13. In the following questions, mark
1) if statement I alone can help determine the conclusion
2) if statement II alone can help determine the conclusion
3) if statement I and II taken together can help determine the conclusion
4) if none of the statements, taken together or separately can help determine the conclusion
Conclusion: Dhruv drove the car after consuming alcohol.
Statement I: Dhruv's car was moving in a zig zag fashion.
Statement II: Dhruv paid fine to the traffic police.

Answer: 4

Solution:  II is not sufficient as he could even have paid fine for reckless driving or some other violation like over speeding etc. 

I is not sufficient as the road itself could be zig zag or for fun Dhruv would have driven in a zig zag fashion.

14. Which of the given sentences is / are sufficient to answer the given question?
What is the height of the ladder leaning on a wall ?
(i) Height of the wall is 24 m
(ii) Ladder is inclined at an angle 30º to the ground at a certain distance.

Answer: Both (i) and (ii) are needed

Solution: By rules of trigonometry, Height of the wall / Height of the ladder = sin 30

24 / Height of the ladder = 1 / 2

So height of the ladder = 48 m; So only with the data given by both the statements, we can findthe height of the wall

15. What is/are the statement(s) necessary/sufficient to answer the below question.

What is the speed of the boat in still water ?

Statements : (1) The boat goes 11 km along the stream.

                    (2) The boat travelled one hour downstream and one hour upstream.

                    (3) The boat goes 5 km against the stream.

Answer: Statements 1, 2 and 3

Solution: By statement 2, time given is 1 hour

By statement 1, Speed downstream = 11 km/hr

By statement 3, Speed upstream = 5 km/hr

So Speed of the boat in still water = (1/2) (11+5) = 8 km/hr

So statements 1,2,3 are needed to answer the question