# Level 3- Data Sufficiency Practice Quiz 3- Hard

1. Two friends A and B together can complete a piece of work in 10 days. In how many days A alone complete the piece of work?

Statement I : B alone can complete half of the work in 12.5 days.

Statement II : The efficiency of A is 50% more than that of B.
A The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
B The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
C Either Statement I or Statement II alone is sufficient to answer the question.
D Neither statement I nor statement II is sufficient to answer the questions.
E The data in both the statements I and II together is necessary to answer the question.

Correct Option: C
From the statement I, we can conclude the number of days A alone will take to complete the work.

From the statement II, efficiency is given so it is easy to find the number of days, A alone or B alone will take to complete the work.

Therefore, either Statement I or Statement II alone is sufficient to answer the question.

Hence, option C is correct.

2. When length of a rectangle was increased by 20% and breadth remains constant then area was increased by 100 sq. cm. What is the perimeter of the rectangle.

Statement I : After increasing the length, the rectangle becomes a square.

Statement II : After increasing the length, all the angles of the rectangle becomes 90 degree.
A The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
B The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
C Either Statement I or Statement II alone is sufficient to answer the question.
D Neither statement I nor statement II is sufficient to answer the questions.
E The data in both the statements I and II together is necessary to answer the question.

Correct Option: A
Let the length = x and breadth = y

When length was increased by 20% then the new length = 1.2x

From the statement I, we can conclude that 1.2x = y (because it changes to square)

x /y= 1/1.2 = 5/6
Let us assume that x = 5a then y = 6a

Original area = 5 × 6 × a2

New area = 5 × 5 × 1.2a2

From here we can conclude the value of a = 3 cm

Once we get the value of a, we can conclude the length and breadth and can get perimeter

From the Statement II, we could not conclude either new figure becomes rectangle or square because even in rectangle all angles are 90 degree.

Therefore, the data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

Hence, option A is correct.

3. One day I left my home at 7 : 00 AM and assumed that if I run at uniform speed then I will reach my school at 12 : 00 AM. If my brother left the school for home at 8 : 00 AM with his uniform speed then at what time will he meet me?

Statement I : The uniform speed of my brother is 14 km per hour.

Statement II : He can reach home at 11:30 AM.

A The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
B The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
C Either Statement I or Statement II alone is sufficient to answer the question.
D Neither statement I nor statement II is sufficient to answer the questions.
E The data in both the statements I and II together is necessary to answer the question.

Correct Option: B
The time taken by me = 12 – 7 = 5 hours

From the statement I, speed of my brother = 14 km per hour

From the statement II, the time taken by my brother = 11: 30 – 8 : 00 = 3 : 30 hours

From the question and statement II, we can conclude the ratio of time = 5 : 3:30 = 10 : 7

Now we know that, speed = inversely proportional to time

So, the ratio of speed = 7 : 10

Let the distance between by house and the school is 70 km

Then my speed = 70/7 = 10 km per hour
And my brother speed = 70 /10= 7 km per hour
Now, we can conclude the time at which I will meet my brother but from the statement II, we could not conclude distance or any ratio.

Therefore, the data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

Hence, option B is correct.