1. Direction: Each question below is followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer.
The average of three numbers is 120. Is the highest number less than or equal to 140?
Statement I: The lowest number is 90
Statement II: One of the numbers is 125
A. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
B. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
C. If the data either in statement I alone or in statement II alone is sufficient to answer the question.
D. If the data in both statements I and II together are necessary to answer the question.
E. If the data given in both statements I and II together are not sufficient to answer the question.
Answer: Option (D)
Explanation:
Total of 3 numbers = 120 x 3 = 360
From Statement I:
Since, the lowest number is 90
It means the value of both the numbers is 270
Now, the biggest number can be, if the second highest number is 91, then the highest number = 270 – 91 = 171
But, the two numbers can be 134 and 136 also.
So, the data in statement I alone is not sufficient to answer the question
From Statement II:
Here also we get multiple values. So, the data in statement II alone is not sufficient to answer the question
Now, if we combined both the statements, then the value of the largest number would be 145.
So, the data in both statements I and II together are necessary to answer the question.
So option (D) is the correct answer.
2. Direction: Each question below is followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible
answer.
What will be the time taken to fill a leaking tank of volume 100 litres?
I. The time taken to fill the tank when the leak is closed is half of the time taken to empty the tank if all the water is allowed to leak with no water being poured in the tank.
II. The leak rate is halved if half of the hole is covered.
A. The question can be answered by using statement I alone but cannot be answered using the other statement alone.
B. The question can be answered by using statement II alone but cannot be answered using the other statement alone.
C. The question can be answered by using either of the statement alone.
D. The question can be answered using both of the statements together, but cannot be answered using either of the statement alone.
E. The question cannot be answered even by using both the statements together.
Answer: Option (E)
Explanation:
Statement 1: if the time taken to fill the tank (without the leak) be x and that of leaking (without filling) be y, then this statement says
x= 1/2y
But we need another equation between x and y.
Statement 2: this statement neither answers the question nor does it provide a relation between x and y.
Hence, option is E.
3. Direction: Each question below is followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer.
A and B finish 3/4th of a specific piece of work in 6 hours. How much time does A take to finish the work?
I. B finishes the work in 10 hours.
II. A and B together finish the work in 8 hours.
A. The question can be answered by using statement I alone but cannot be answered using the other statement alone.
B. The question can be answered by using statement II alone but cannot be answered using the other statement alone.
C. The question can be answered by using either of the statement alone.
D. The question can be answered using both of the statements together, but cannot be answered using either of the statement alone.
E. The question cannot be answered even by using both the statements together.
Answer: Option (A)
Explanation:
3/4th work in 6 hours. Total work can be completed in 8 hours.
From statement 1:
1/a + 1/b = 1/8
⇒ 1/b = 1/10
Therefore, A finishes the work in 40 hours.
Statement 2 alone is not sufficient.
Hence, option is A.
4. Direction: Each question below is followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer.
The ages of Anand and Sumit are in the ratio of 6 : 5 respectively. What is the age of Anand?
I. The ages of Anand and Sudeep are in the ratio of 10 : 7.
II. After 5 years the ratio of Anand’s and Sumit’s ages will be 7 : 6.
A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question
B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
C. If the data either in Statement I or in Statement II alone are sufficient to answer the question
Answer: Option (B)
Explanation:
statement I only gives ratio values, its not sufficient to answer.
By using statement II, we can compare two ratio of Anand’s & Sumit’s age in difference of 5 years. So we can find values.
So statement II is sufficient to answer.
5. Manish and Meena are two of Mr. Varma’s children. Manish has half as many brothers as sisters. Meena has as many brothers as sisters. Number of children Mr.Varma has is?
Answer: Option (E)
Explanation:
Let the number of sons and daughters be s and d. Manish has s - 1 brothers and d sisters.
s - 1 = (1/2 )d
Meena has d-1 sisters and s brothers
s = d - 1 (substituting this in the above equation)
d - 2 = (1/2)d
2d - 4 = d
d = 4
s = 3
s + d = 7