Data sufficiency:

• It is defined as a typical question containing a problem followed by two or more statements numbered I, II, and even III containing certain data/information that are required to solve the question.


• It is the test of skill.


• Determine minimum information required for solving the questions so that most appropriate answer is to be choosen.


• Apart from the given questions and statements, nothing should be taken granted.


• Should depend only on the information given in the question and the statements.

Topics under data sufficiency may be like general intelligence or critical reasoning such as a ranking, arrangement, coding -decoding, blood relationships, age problems, distance and direction test, mathematical problems etc.

• Questions are asked on different format and in different approach.

Example:
"Indian cricket team won the match against Pakistan."
Statement (A) A match was played between India and Pakistan.
Statement (B) Indian team scored more goals than Pakistan team. Reporter derived "Indian cricket team won the match against Pakistan.", by combining the two statements.
Suppose, if the two statements are like:
Statement (A) A match was played.
Statement (B) Indian cricket team scored more.
By these statements, conclusion cannot be determined as the information is in-sufficient.
Sometimes, only one statement is given and from that conclusion has to be determined. and while sometime two or three statements taken together may give the conclusion.

1. How many people are there in the bus?
Statement I : 25% passengers are women.
Statement II : There are 150 men in the bus.

(A) Statement I is alone sufficient.
(B) Statement II is alone sufficient.
(C) Both statements are required.
(D) Question cannot be solved with the given statements.

Solution:

Given that
From statement I, 25% passengers are women. So, 75% are of men. Here as percentage doesn't answer the question properly, number has to be found. Thus, answer is not (A).
From the statement II, it is clear that (B) is also not the answer.
By combining both the statements, answer is 200 people in the bus. So, answer is (C).

2. Is [latex]x[/latex] divisible by 28?
Statement I: [latex]x[/latex] is divisible by 20.
Statement II: [latex]x[/latex] is divisible by 21.

(A) Statement I is alone sufficient.
(B) Statement II is alone sufficient.
(C) Both statements are required.
(D) Question cannot be solved with the given statements.

Solution:

Given that,
Is [latex]x[/latex] divisible by 28. That means is [latex]x[/latex] divisible by 7 x 2 x 2
As, L.C.M of 28 = 7 x 2 x 2
Is [latex]x[/latex] divisible by 20. That means is [latex]x[/latex] divisible by 5 x 2 x 2
As, L.C.M of 20 = 5 x 2 x 2
Is [latex]x[/latex] divisible by 21. That means is [latex]x[/latex] divisible by 7 x 3
As, L.C.M of 21 = 7 x 3
From statement I, As 20, is not divisible by 7 so, answer is not (A).
From statement II, as there are no common elements or numbers from L.C.M answer is not (B).
By combining both the statements, solution is solved as 7 and 4 are common numbers. So, the answer is (C).

3. Reading the statements carefully, answer the given questions?
1. What is the speed of the boat in still water?
Statement I: The speed downstream is 12km/hr.
Statement II: The speed upstream is 4km/hr.
Statement III: In a to and fro journey between two points, the average speed of the boat was 6km/hr.

(A) I and II only
(B) All I, II, and III
(C) III and either I or II
(D) Any two of the three.
(E) None of these.

2. What is the speed of stream?
Statement I: The boat covers 24 km in 6 hours moving upstream.
Statement II: The boat covers 24 km in 3 hours moving downstream.
Statement III: The ratio between the speed of boat and stream is 3 : 1 respectively.

(A) Any of the three
(B) I and II only
(C) II and III only
(D) I and III only
(E) All I, II, and III

Solution:

1. From statements I and II, speed of the boat in still water = [latex]\frac{1}{2}(12 + 4)[/latex] km/hr = 8 km/hr
From statements II and III, using average speed = [latex]\frac{2xy}{x + y}[/latex]
[latex]\frac{2 * 4 * y}{4 + y}[/latex] = 6
⇒ 8[latex]y[/latex] = 24 + 6[latex]y[/latex]
⇒ [latex]y[/latex] = 12
Therefore, required speed = [latex]\frac{1}{2}(12 + 4)[/latex] km/hr = 8km/hr.
Similarly, By statements I and III, same solution will be obtained.
Therefore, option (D), is the answer.
2. From Statement I, Speed upstream = [latex]\frac{24}{6}[/latex] km/hr = 4 km/hr
From statement II, Speed downstream = [latex]\frac{24}{6}[/latex] km/hr = 8 km/hr
From statement III, let the speed of the boat in still water be 3[latex]x[/latex] km/hr. Then, speed of the stream be [latex]x[/latex] km/hr.
Therefore, Speed downstream = 2[latex]x[/latex] km/hr and
Speed upstream = [latex]x[/latex] km/hr.
From statements I and II, speed of stream = [latex]\frac{1}{2}(8 - 4)[/latex] km/hr = 2 km/hr.
From statements II and III, 2[latex]x[/latex] = 4 or [latex]x[/latex] = 2
Therefore, Speed of downstream = 8km/hr.
Speed of stream = [latex]\frac{1}{2}(8 - 4)[/latex] km/hr = 2 km/hr.
From statements I and III, [latex]x[/latex] = 2 and 2[latex]x[/latex] = 4
Therefore, Speed of stream = [latex]\frac{1}{2}(8 - 4)[/latex] km/hr = 2 km/hr.
Thus, any two of the three will give the answer. So, option (A) is correct.

4. The last Sunday of month March fall on which date?
Statements I: First Sunday falls on fifth.
Statements II: The last day of month was Friday.

(A) Statement I is alone sufficient.
(B) Statement II is alone sufficient.
(C) Both statements are required.
(D) Question cannot be solved with the given statements.
(E) Can be answered either of the statements.

Solution:

From the Statement I,
If 5th is Sunday, then 12th, 19th and 26th are next Sundays after 5th of that month.
So, the last Sunday falls on 26th.
Statement I alone can give the answer.
From statement II,
last day i.e. 31st March is Friday and
30th was Thursday
29th was Wednesday
28th was Tuesday
27th was Monday
26th was Sunday
So, by statement II also, the answer can be solved.
Therefore, option (E) is the correct answer.

5. Joseph, George and Jack are running a business firm in partnership. What is George's share in the profit earned by them?
Statement I: Joseph, George and Jack invested the amounts in the ratio 2 : 4 : 7.
Statement II: Jack's share in the profit is Rs. 8750.

(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.
(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.
(C) If the data either in statement I or in statement II alone are sufficient to answer the question.
(D) If the data in both statements I and II together are not sufficient to answer the question.
(E) If the data in both statements I and II together are necessary to answer the question.

Solution:

Given that,
Joseph : George : Jack = 2 : 4 : 7
Profit of Jack = Rs. 8750
From statements I and II, when Jack = 7, then George = 4
when Profit = Rs. 8750, then G = [latex]\frac{4}{7} * 8750[/latex] = 5000
Thus both I and II are needed to get the solution.
Therefore, the correct option is (E).