Data Sufficiency :

Data Sufficiency by definition means deducing the sufficiency of information in answering the given problem.

Data sufficiency questions consist of a question followed by two or more statements. The task is to decide whether the information in the statements (taken singly or together) is sufficient to answer the question. These questions do not require calculation but evaluation of statements. Data sufficiency questions can be based on mathematical concepts as well as reasoning concepts. For example, a data sufficiency problem can be based on determining the speed of a train while another could be on determining the direction of a moving person.

The questions asked usually consist or two or three statements. Let’s have a look at them.

Data sufficiency involving two statements :

Here the problem consists of a question and two statements labelled (1)and (2), in which certain data are given The options in this case are:

– Statement (1) ALONE is sufficient,but statement (2) alone is not sufficient to answer the question.

– Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question.

– BOTH statements (1) and (2) TOGETHER are sufficient to answer the question, but NEITHER statement  ALONE is  sufficient to answer the question.

– EITHER statement ALONE Is sufficient to answer the question.

– Statements (1)and (2) TOGETHER are NOT sufficient to answer the question.

Illustration of the five possible answers

Statement I alone is sufficient but statement II alone is not sufficient.

Is Shankar older than Ganesh?

I. Kartik is four years younger than Shankar and two years younger than Ganesh.

II .The  average of Shankar’s age in years and Ganesh’s age years is 17

In this example Statement I by it self is sufficient to answer the question asked. If Kartik is four years younger than Shankar and two years younger than Ganesh, then Shankar must be two years older than Ganesh. From the second statement about the average of their ages no conclusion can be drawn about their respective ages. Thus only Statement by itself is sufficient to answer the question but statement II is not.

Statement II alone is sufficient but statement I alone is not sufficient .

If p, q and r are consecutive integers, is q even?
I.  p < q < r

II. The product pr is an odd integer.

Statement I alone is not sufficient to answer the questions asked.Statement II is, however, by itself sufficient to find out whether q is even or not. If pr is odd then p u0026amp; r must be odd integers. Given that p,q and r are three consecutive integers. Therefore if p u0026amp; r are odd, then q must be even. Statement II alone is sufficient to answer the question but statement I is not.

Statement I and statement II together are sufficient to answer.

How many students are there in the class?

I. If three more students are there and none drop out, there will be more than 35 students in the class.

II. If four students drop out of the class and no more are admitted then there will be fewer than 30 students in the class.

Statement I alone is not sufficient to answer the question, but one can infer form the first statement that at least 33 students are there in the class. Statement II alone is also not sufficient to answer the question, but one can infer form this statement that there are no more than 33 students in the class. Thus neither of the statement alone is sufficient to answer the question, but we can infer from both of them that the number of students in class must be 33. Therefore both statements are needed to answer the question.

Either statement by itself is sufficient to answer

What is the area of a square ABCD?

I. The perimeter of the square is 20.

II. The length of the diagonal is 5√2

From I: the perimeter of the square is 20. Therefore the length of each side is 5. Therefore the area is 25 sq. units.Thus statement I alone is sufficient the question. From Statement II we can find out the area based on the information given in Statement II alone.Thus, either statement alone is sufficient.

Both statements together cannot answer

Is a < b?

I. -0.30 < a < 0.30
II. 0.25 < b < 0.50
Statements II  and I define ranges for a and b respectively but do not give any relation between a and b. Thus statement I alone is not sufficient to answer the question asked. Statement II alone is also not sufficient to answer the question asked. Even if the statements are taken together one cannot answer the question because a can be larger than b over the range of 0.25 to 0.3, and smaller than b at other values. Thus, the two statements even when taken together do not provide information to answer the question asked.

Tips to solve two statement Data Sufficiency problems:

– Please let us not try to calculate the final answer as it is not asked. We need to find whether the information provided is enough to solve the given problem or not.
– Let us solve question step by step in the below manner:

Data sufficiency involving three statements:

Here the problem consists of a question and three statements, labelled (1), (2) and (3) in which certain data are given. One has to determine which of the statements or the combination of statements are necessary to answer the given question.

Solved Examples:
Question: What is the principal?
(I) The compound interest on the sum in 2 years at 10% per annul is Rs 5250
(II) The sum doubles itself in 8 years at 12.5% per annum at simple interest
(Ill) The simple interest received at 8% per annul in 2 year is Rs 160 less than the compound interest on same sum at 8% per annul in 2 year.

(1) Either I or Ill is sufficient to answer the question.
(2) Both I and II together are sufficient to answer the question.
(3) Both 11 and 111 together are sufficient to answer tne question.
(4) Both I and Ill together are sufficient to answer the question.
(5) Either I or II is sufficient to answer the question.

Ans with Explanation

From I,

CI= P t  – P  

We are given the values of CI, R and T. Hence P can be calculated. From 11,
SI = = P
We are given R = 12.5% and T = 8 years.
The above equation will be true for all values of P.Hence the principal cannot be determined From Ill,
We know that for two years,

Difference between CI and SI = P()2.
We are given the difference and rate of interest, so principal can be calculated. Hence we see that either statement I or Ill is sufficient to answer the question.

Question

If a real estate agent received a commission of 6 percent of the selling price of a certain house, what was the selling price of the house?

(1) The selling price minus the real estate agent’s commission was $84,600.
(2) The selling price was 250 percent of the original purchase price of $36,000.

• (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• (D) EACH statement ALONE is sufficient.
• (E) Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: (D)