# Level 3- Data Sufficiency Practice Quiz 2- Hard

1. Pranav and Pankaj started working together. After a few days, Prashant joined them and they were able to finish the work in 10 days. All of them together were paid a total of Rs. 800. Find the share of Prashant.

Statement I : Pranav can do the work in 20 days, while Pankaj can do the same work in 25 days.

Statement II : Pranav can do the work in 60 days, while Pankaj can do the same work in 15 days.

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.

Correct Option: C
From statement I:

In 1 day, Pranav finishes 1/20th of the work.

In 1 day, Pankaj finishes 1/25th of the work.

The work was completed in 10 days.

Part of work completed by Pranav and Pankaj in 10 days

= 10 ( 1/20 + 1/25 ) = 9/10

Part of work completed by Prashant = 1 – 9/10 = 1/10
Amount received as payment will be proportional to the amount of work done.

Amount paid to Prashant = 800 × 1/10 = Rs. 80
Similarly, from statement II we also can find the share of Prashant.

∴ Either of the statements alone is sufficient to answer this question.

Hence, option C is correct.

2. Two partners, P and Q entered in a business, what profit will Q get at the end of 2 years?

Statement I : P and Q started the business by investing in the ratio 4: 7 and After 2 years, P’s share is Rs. 95000.

Statement II : P joined the business with an amount of Rs. 500000

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.

Correct Option: A
From statement I:

Share of profit of P and Q will be in the ratio of 4 : 7

After two years,

Let the share of profit of Q be Rs. y

∴ 4/7 = 95000/y

⇒ y = 95000 × 7/4
⇒ y = Rs. 166250

∴ Statement I alone is sufficient to answer.

From statement II: Only P’s investment is given so we can’t find the profit of Q.

Hence, option A is correct.

3. Find the total population of Kanpur.

Statement I : The ratio of the population of males and females in Kanpur is 33 : 29 and the difference between their population is 24000.

Statement II : The population of Kanpur is 60% of that of Patna, and the difference between the population of Kanpur and Patna is 35000.

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.

Correct Option: C
From statement I:
Let the total population of Kanpur be X.
⇒ 32X – 29X = 24000
⇒ 4X = 24000
⇒ X = 6000
∴ The total population 33X + 29X = 62X
62X = 62 × 6000 = 372000
From statement II:
Let the total population of Kanpur be X.
So, population of Patna = 100X/60 = 5X/3
∴ 5X/3 – X = 35000
⇒ 2X = 105000
⇒ X = 52500
∴ Statement I or II alone is sufficient to answer the question.
Hence, option C is correct.