## HCL Practice Data Sufficiency Problems

Below are three problems to practice for data sufficiency checking problems. Essentially two statements will be given followed by a question which need to be checked for data sufficiency.

Directions for Question 1 to 3 : 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

1. Give answer (A) if the data in Statement I alone is/are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
2. Give answer (B) if the data in Statement II alone is/are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
3. Give answer (C) if the data either in Statement I or in Statement II alone is/are sufficient to answer the question.
4. Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
5. Give answer (E) if the data in both Statements I and II together are necessary to answer the question.

Question 1

Murari can complete a task in 14 days. Murari and Karthikeyan together can do it in 40 days. In Project titled 'ABC' What part of the work was carried out by Murari?

I. During project 'ABC' Murari completed the job alone after Murari and Karthikeyan worked together for 5 days.
II. Part of the work done by Murari during project 'ABC' will be lesser than that of Alamelu's work when Karthikeyan and Alamelu work together for 6 days.

Answer : a) data in Statement I alone is/are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.

Solution :

To prove this, let us try to solve the question with the data from statement I in hand :
Murari can do the job in 14 days. One day of Murari's work = 1/14. -> eq 1
Murari and Karthikeyan can do the job in 40 days. So in one day Karthikeyan can do
1/14 - 1/40 = 13/280 of the work

Statement I says both of them work together for 5 days during project 'ABC'. Therefore work completed by both during the first 5 days of the project
= (one day's work of Murari + one day's work of Karthikeyan)x 5
= (1/14 + 13/280)x5 = 33/280 x 5 = 33/56
Work that remains in project ABC = whole unit of work - part of work completed during first 5 days = 1 - 33/56 = 23/56 -> eq 2
After 5 days, the remaining work i.e 23/56 of work will be taken care by Murari alone.

Therefore work done by Murari alone in the project 'ABC' = five days of Murari's work + remaining work of Murari after 5 days
= (one day work of Murari) x 5 + remaining work of Murari after 5 days
Substituting values from eq 1 and eq 2 in the above equation we get
work done by Murari alone in the project 'ABC' = (1/14)5 + 23/56
(23 + 20) divided by 56 = 43/56
Statement II doesn’t help us in any way because it just says Murari's contribution would be lesser than that of Alamelu if Karthikeyan and Murari work together. With this we can't calculate the work done by Murari alone.

Question 2

How long will Ramsons company take to make ten benches?

I. Krishnasons company take 10 days to make twenty benches
II. Ramsons company and Krishnasons company take 6 days to make forty benches

Answer : d) data in both Statements I and II together are necessary to answer the question

Solution :

Statement I tells about how many benches Krishnasons will take to make 20 benches and hence we can find out in one day how many benches (Krishnasons) can make. This data is not suficient to find the working duration of Ramsons company.
Statement II tells about number of days taken by both the companies together to make 40 benches. From this we can find how many benches the two companies together can make in one day . Hence statement II alone is not sufficient to answer the question on the efficiency of Ramsons company.
But when statement I and statement II are considered together one can find the solution as follows.
Let R and K represent the one day's work of Ramson's and Krishnasons companies respectively.

Considering Statement I : Krishnasons company take 10 days to make twenty benches. This can be represented as,
10K = 20
Or K = 2 -> eq 1

Considering Statement II : Ramsons company and Krishnasons company take 6 days to make forty benches. This can be represented as
6R + 6K = 40
R + K = 40/6 -> eq 2
Substituting K = 2 from eq 1 in eq 2, we get,
R + 2 = 40/6
R = 40/6 - 2 = 28/6 = 4.67
Therefore by considering statements I and II together we have arrived at the solution that Ramson's company in one day can complete 4.67 benches.
Since both statements were considered to arrive at the solution, answer is d) data in both Statements I and II together are necessary to answer the question

Question 3

How many days will Arihant Constructions take to complete the construction of 10 quarters for government employees?

I. Sumanth Constructions took 6 months for a similar work about five years ago
II. Arihant Constructions was started by Mr. Hariram about three years ago

Answer : d) data even in both Statements I and II together are not sufficient to answer the question.

Solution :

Statement I tells about Sumanth Constructions and is not helpful to arrive at any information regarding Arihant Constructions.
Statement II is completely irrelevant to the question and doesn’t help us in identifying the working ability of Arihant Constructions.

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