Data Sufficiency
Direction: In each of the following questions, a question is asked followed by three statements. You have to study the questions and all the three statements given and decide whether any information provided in the statement(s) is/are redundant and can be dispensed with while answering the questions.
 How much time will the train ‘X’ take to cross another train ‘Y’ running in opposite direction?
A. Train ‘X’ crosses a signal pole in 6 seconds.
B. Ratio of the speeds of trains ‘X’ and ‘Y’ is 3 : 2.
C. Length of the two trains together is 500 m.

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As per the given all details in above question ,
From statement A , Time taken by train‘X’ = 6 seconds
From statement B , Ratio of the speeds of trains ‘X’ and ‘Y’ = 3 : 2
Let speed of train X is 3k and speed of train Y is 2k.
Relative speed = 3k + 2k = 5k
From statement C , Length of the two trains = 500 m
Time taken = Length of the two trains / Relative speed = 500 / 5k = 100 / k seconds
Anyone of the three statements is not sufficient to answer the question. So, anyone is not suitable statements.Correct Option: E
As per the given all details in above question ,
From statement A , Time taken by train‘X’ = 6 seconds
From statement B , Ratio of the speeds of trains ‘X’ and ‘Y’ = 3 : 2
Let speed of train X is 3k and speed of train Y is 2k.
Relative speed = 3k + 2k = 5k
From statement C , Length of the two trains = 500 m
Time taken = Length of the two trains / Relative speed = 500 / 5k = 100 / k seconds
Anyone of the three statements is not sufficient to answer the question. So, anyone is not suitable statements.The question cannot be answered even with the information in all the three statements.
 Three friends X, Y and Z started a partnership business investing money in the ratio of 5 : 4 : 2, respectively for a period of 3 years. What is the amount received by X as the share in the total profit?
A. Total amount invested in the business is $ 22000.
B. Profit was distributed after a period of 2 years.
C. The average amount of profit earned per year is $ 2750.

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On the basis of above given details in question , we have
The ratio of investing money for 3 years = 5 : 4 : 2
Let the investment of X , Y and Z are 5k , 4k and 2k respectively .
From statement A , Total amount invested in the business = $ 22000.
From statement B , Profit was distributed after a period of 2 years.
From statement C , The average amount of profit earned = $ 2750.
According to question ,
Sum of investment money = Total profit
⇒ 5k + 4k + 2k = 2750 ⇒ 11k = 2750 ⇒ k = 2750 / 11 = $ 250
Amount received by X = 10k = 10 x 250 = $ 2500 ( for 2 years )Correct Option: D
On the basis of above given details in question , we have
The ratio of investing money for 3 years = 5 : 4 : 2
Let the investment of X , Y and Z are 5k , 4k and 2k respectively .
From statement A , Total amount invested in the business = $ 22000.
From statement B , Profit was distributed after a period of 2 years.
From statement C , The average amount of profit earned = $ 2750.
According to question ,
Sum of investment money = Total profit
⇒ 5k + 4k + 2k = 2750 ⇒ 11k = 2750 ⇒ k = 2750 / 11 = $ 250
Amount received by X = 10k = 10 x 250 = $ 2500 ( for 2 years )
When investment ratio is given, the amount of profit can be found out with the help of C only.
 Which is the area of the given rightangled triangle?
A. Length of the diagonal of rectangle is 5 cm.
B. Perimeter of the triangle is four times its base.
C. One of the angles of the triangle is of 60°.

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Let, the length and breadth of the rectangle be l and b, respectively.
From statement A → Diagonal of rectangle ( h ) = 5 ⇒ l^{2} + b^{2} = 25
From statement B → l + b + h = 4b ⇒ l = 3b − 5Correct Option: B
Let, the length and breadth of the rectangle be l and b, respectively.
From statement A → Diagonal of rectangle ( h ) = 5 ⇒ l^{2} + b^{2} = 25
From statement B → l + b + h = 4b ⇒ l = 3b − 5
From statement C → One of the angles of the triangle = 60°
From statement A and B , ( 3b  5 )^{2} + b^{2} = 25 ⇒ 9b^{2} + 25  30b + b^{2} = 25
⇒ 9b^{2}  30b + b^{2} = 0 ⇒ 10b^{2}  30b = 0 ⇒ 10b( b  3 ) = 0 ⇒ b = 3 cm
∴ l = 3 x 3  5 = 9  5 = 4 cm
∴ Area of right angle triangle = ( 1 / 2 ) x base x height
= ( 1 / 2 ) x 3 x 4 = 6 cm^{2}
After combining any of the above two statements, we get the values of l and b. Hence, any of them can be dispensed with.
 8 men and 14 women are working together in a field. After working for 3 days, 5 men and 8 women leave the work. How many more days will be required to complete the work?
A. 19 men and 12 women together can complete the work in 18 days.
B. 16 men can complete twothird of the work in 16 days.
C. In a day, the work done by three men is equal to the work done by four women.

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As per the given all details in above question , we can say that
Anyone of the three statements is alone sufficient to answer the question.Correct Option: E
As per the given all details in above question , we can say that
Anyone of the three statements is alone sufficient to answer the question. So, any two can be dispensed with.
Hence , A or B or C is required answer .
 P, Q and R together invested an amount of $ 20000 in the ratio of 5 : 3 : 2. What was the percent profit earned by them at the end of one year?
A. Q’s share in the profit is $ 2400.
B. The amount of profit received by P is equal to the amount of profit received by Q and R together.
C. The amount of profit received by Q and R together is $ 4000.

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As per the given above question ,
Statement (B) is useless because it is the same as the given statement. [Profit is distributed in the same ratio as their investment. Since their investments are in ratio 5 : 3 : 2, the profit of P (= 5) is equal to the profit of Q and R together (3 + 2 = 5)]
Statement (A) alone is sufficient to answer.Correct Option: A
As per the given above question ,
Statement (B) is useless because it is the same as the given statement. [Profit is distributed in the same ratio as their investment. Since their investments are in ratio 5 : 3 : 2, the profit of P (= 5) is equal to the profit of Q and R together (3 + 2 = 5)]
Statement (A) alone is sufficient to answer.
(Q's share = $ 2400Total profit of P + Q + R = 2400 × (5 + 3 + 2) 3
Total profit of P + Q + R = $ 8000∴ % Profit = 8000 x 100 = 40 % 20000
Similarly, statement (C) alone is sufficient to answer the question. Hence, (B) and (A) or (C) can be dispensed with.