Quantitative Aptitude

Data Sufficiency 1

Quantitative Aptitude Exercise Mode

Data Sufficiency 1

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Directions to Solve

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and

Give answer (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.

Give answer (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.

Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.

Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.

Give answer (E) if the data in both Statements I and II together are necessary to answer the question.

Question 1

What is the speed of the boat in still water ?

I. The boat covers a distance of 48 kms in 6 hours while running upstream.

II. The boat covers the same distance in 4 hours while running downstream.

A
I alone sufficient while II alone not sufficient to answer
B
II alone sufficient while I alone not sufficient to answer
C
Either I or II alone sufficient to answer
D
Both I and II are not sufficient to answer
E
Both I and II are necessary to answer
Correct Answer: Option E

 I. Speed upstream = 48 km/hr = 8 km/hr.
6

II. Speed downstream = 48 km/hr = 12 km/hr.
4

Speed of the boat = 1 (8 + 12) km/hr = 10 km/hr.
2

Thus, I and II together give the answer.

Correct answer is (E).

Question 2

What is the speed of the boat in still water ?

I. It take 2 hours to cover the distance between A and B downstream.

II. It take 4 hours to cover the distance between A and B upstream.

A
I alone sufficient while II alone not sufficient to answer
B
II alone sufficient while I alone not sufficient to answer
C
Either I or II alone sufficient to answer
D
Both I and II are not sufficient to answer
E
Both I and II are necessary to answer
Correct Answer: Option D

Let AB = x km.

 I. Speed downstream = x km/hr
2

II. Speed upstream = x km/hr.
4

Speed of boat in still water = 1 x + x km/hr.
2 2 4

Thus, I and II both even do not give the answer.

Correct answer is (D).

Question 3

A boat takes a total time of three hours to travel downstream from P to Q and upstream back from Q to P. What is the speed of the boat in still water ?

I. The speed of the river current is 1 km per hour.

II. The distance between P and Q is 4 km.

A
I alone sufficient while II alone not sufficient to answer
B
II alone sufficient while I alone not sufficient to answer
C
Either I or II alone sufficient to answer
D
Both I and II are not sufficient to answer
E
Both I and II are necessary to answer
Correct Answer: Option E

 I. Speed of the current = 1 km/hr.

II. PQ = 4 km.

Let the speed of the boat in still water be x km/hr. Then,

4 + 4 = 3. This gives x.
(x + 1) (x - 1)

Correct answer is (E).

Question 4

What is the speed of the stream ?

I. The ratio of the speed upstream to the speed downstream of a boat is 2 : 3.

II. The distance travelled upstream in 2 hours by the boat is more than the distance travelled by it downstream in 1 hour by 4 km.

A
I alone sufficient while II alone not sufficient to answer
B
II alone sufficient while I alone not sufficient to answer
C
Either I or II alone sufficient to answer
D
Both I and II are not sufficient to answer
E
Both I and II are necessary to answer
Correct Answer: Option E

I. Let speed upstream = 2X km/hr and speed downstream = 3X km/hr.

II. (2X x 3X) - (1 x 2X) = 4

<=> 4X = 4

<=> X = 1.

∴ Speed upstream = 2 km/hr

Speed downstream = 3 km/hr.

Speed of the stream = 1/2 (3 - 2) km/hr = 1/2 km/hr.

Thus, I and II together give the answer.

∴ Correct answer is (E).

Question 5

What is the speed of the boat in still water ?

I. The speed downstream of the boat is thrice the speed upstream.

II. The sum of the speeds of the boat, upstream and downstream is 12 kmph.

A
I alone sufficient while II alone not sufficient to answer
B
II alone sufficient while I alone not sufficient to answer
C
Either I or II alone sufficient to answer
D
Both I and II are not sufficient to answer
E
Both I and II are necessary to answer
Correct Answer: Option B

Let the speed upstream be X km/hr. Then,

I. Speed downstream = 3X km/hr.

II. gives, speed of the boat in still water :

= (1/2 x 12 ) km/hr = 6 km/hr.

So, II only give the answer.

∴ Correct answer is (B).