DI - Overview - TenADay.co.in

DATA SUFFICIENCY

For more information and FREE online practice tests, visit: www.tenaday.in

What is Data Sufficiency?

In DS questions you are required to find out whether a given set of information or parts of it are sufficient to lead you to an answer to a given question.

Cognitive skills tested through DS:
Data sufficiency questions test your ability to reason quantitatively, unlike problem solving section, where the focus lies in testing your abilities with numbers.

Format

Every Data Sufficiency problem consists of a question followed by two statements. You have to decide not what the answer is, but whether the question can be answered based on the information given in the two statements.
Given below is a simple example to give a feel of the format type:
E.g. 0
What is x?
A. x + y = 17
B. 4x + 4 = 18
Options:
1. If the question can be answered by one of the statements alone, but cannot be answered by using the other statement alone.
2. If the question can be answered by using either statement alone.
3. If the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
4. If the question cannot be answered even by using both statements together.
Answer: 1
Solution: 4x+4=18
4x=14
x=3.5
Thus, B gives the value of x. However, A alone can not lead us to the value of x as it is one equation in two unknowns.

Solving a DS question
Treat each of the two statements and the question posed as an independent question. This simplifies things a lot, and takes care that you do not use inferences from a previous statement in analyzing the next statement.

Sample Question

E.g. 1
What is the value of modulus X?
Statement 1: x = - (modulus x)
Statement 2: x ^2 = 4.
Options:
1. If the question can be answered by one of the statements alone, but cannot be answered by using the other statement alone.
2. If the question can be answered by using either statement alone.
3. If the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
4. If the question cannot be answered even by using both statements together.

Solution:
We would be tempted here, to use both the statements to arrive at a value of x=-2. But then that is not what we need.
The question is asking for modulus X. Statement 1 is not sufficient because it only tells you that x <=0. However, statement 2, implies x = 2 or -2. Regardless, modulus x = 2. Hence, the answer is 1.

CAT Galaxy - Questions asked in past CATs

Options:
1. If the question can be answered with the help of one statement alone
2. If the question can be answered with the help of any one statement independently
3. If the question can be answered with the help of both the statements together
4. If the question can not be answered even with the help of both the statements together

E.g.2. After what time will the two persons Tez and Gati meet while
moving around a circular track? Both of then start from the same point
and at the same time.
1. Tez moves at a constant speed of 5m/s while Gati starts at a speed of 2m/s and increases his speed by 0.5m/s at the end of every second there after.
2. Gati can complete one entire lap in exactly 10 seconds.
Solution: D.
The statement 1 alone is sufficient to calculate the time when two persons will meet around the circular track. But time calculated will be different in case both are moving in the same direction from the time calculated when they are moving in opposite direction. Since no unique solution is achieved, the answer is 1.

E.g.3. Is the number completely divisible by 99?
1. The number is divisible by 9 and 11 simultaneously.
2. If the digits of the number are reversed, the number is divisible by 9 and 11.
Solution: 2
If the number is divisible by 9 and 11 simultaneously, it will be divisible by the LCM of (9,11) or 99. Hence statement 1 alone is sufficient to answer the question. Now, take a number which is divisible by 99, e.g. 198. The number obtained after reversing the digits is 891, which is divisible by 9 and 11 as well. Hence statement 2 alone is sufficient to answer the question.

E.g. 4. What is the value of a^3 + b^3?
1. a^2 + b^2 = 22
2. ab = 3
Solution: 2.
From statements 1 and 2, we bet (a+b)=sqrt28 and –sqrt28. Though we can solve a^3+b^3, we will not have a unique solution for the same as there are two values of a+b. Hence we can not have a unique solution for a^3+b^3.

E.g. 5 Three friends P, Q and R are wearing hats, either black or white. Each
person can see the hats of the other two persons. What is the color of P’s?
hat?
1. P says that he can see one black hat and one white hat.
2. Q says that he can see one white hat and one black hat.
Solution: 4. Even if we combine the information given in statements 1 and 2, we can not find the color of P’s hat.

E.g. 6 What is the distance x between two cities A and B in integral number of Kms?
1. x satisfies the equation logx 2 = sqrt x
2. x < = 10 kms
Solution: 3.
Using statement 1 alone, we get values of x to be 4 and 16. satisfying the given equation. Using statement 2 simultaneously, we can rule out 16 to get the answer as 4. Hence both statements are required.

E. g 7 Mr. Mendel grew 100 flowering plants from black seeds and white seeds. Each seed giving rise to one plant. A plant gives flowers of only one color. From a black seed comes a plant giving red or blue flowers. From a white seed comes a plant giving red or white flowers. How many black seeds were used by Mr. Mendel?
1. The number of plants with white flowers was 10.
2. The number of plants with red flowers was 70.
Solution: 4.
It is given that white seed grows white or red flowers and black seed grows red or blue flowers. Now from statement 1 we know that out of 100 flowering plants, 10 are white flowering plants. Hence, there are at least 10 white seeds, but number of black seeds used can not be known. Using statement 2 together with it, we still can not find out number o black seeds as information about the color of remaining 20 flowers is still not known.

E. g 8 The average weight of students in a class is 50kgs. What is the number of students in the class?
1.The heaviest and the lightest members of the class weigh 60kg and 40kg respectively
2.Exclusion of the heaviest and the lightest members from the class does not change the average weight of the student.
Solution: 4.
Even with 1 and 2 taken together, the number of students can not be found out.

Tips and Tricks

1. After some practice, you will automatically memorize the order of the four options in a DS question. But questions with a different order of options have been asked in the past, so beware! Overlooking the order can be a big mistake if the test-makers jumble up the options order.
2. Once again, remember, you don't have to find all conclusions from the given set of information; you have to find answer only to the question asked. E.g.1 illustrates the point well.
3. Be careful not to carry over any information from one numbered statement to another.
4. If a question asks for a numerical value (as opposed to a quantitative expression that includes variables), the question is answerable only if a numbered statement (1 and/ or 2) yields one and only one possible numerical answer--not a range of values.
5. Data Sufficiency questions are designed to test you primarily on quantitative concepts, not on your ability to manipulate numbers (that's what Problem Solving questions are for). So if you find yourself doing a lot of calculations, you're probably on the wrong track.
6. Just as in Problem Solving questions, in Data Sufficiency questions cast in a real-world setting you should make reasonable real-world assumptions. Don't split hairs by looking for subtle meanings or ambiguous language. The test-makers are not out to trick you in this way.
7. Do not assume things which are not given in the question. Remember, there is an option which says 'if the question cannot be answered even by using both statements together'.
Trained as we are to 'crack questions and get answers', it is relatively simpler to assume things so as to lead us to some answer. E.g. 2 illustrates this point well.

For more information and FREE online practice tests, visit: www.tenaday.in