Free Online Preparation for CAT with Minglebox eCAT Prep. Cover basic concepts of Data Sufficiency under Data Interpretation for MBA Entrance Exam Preparation with Study material, solved examples and tests prepared by CAT coaching experts.
The general structure of a data sufficiency problem is as follows:
A question is asked , followed by 2 statements. In order to answer the questions, we have to take support from either of the 2 statements one at a time and then we combine both the statements. Thus we get 4 possibilities.
1 statement 1 alone is sufficient,
2 Statement 2 alone is sufficient,
3 Question can be answered using both statements together,
4 Questions cannot be answered using both the statements together.
Question
What is the price of mangoes per kg?

Ten kg of mangoes and 2 dozen of orange cost Rs. 252.

Two kg of mangoes could be bought in exchange for one dozen oranges.
Solution
Statement I alone tells us the combined price of 10kg of mangoes and 2 dozen of oranges cost RS. 252. So from here we cannot change the price of mangoes. II alone gives us the relative comparison of the prices of mangoes and oranges. Hence if we combine both we can find the price of mangoes per kg. Note in data sufficiency problems emphasis is on determining whether question can be answered or not instead on finding what is the answer to the question.
Question
What are the ages of the three brother?

The product of their ages is 21.

The sum of their ages is not divisible by 3.
Solution
Let us assume the ages of the 3 brothers be x, y, z, then xyz = 21. If x, y, z were given as integers then we would have answered this using I alone, but some x, y, z are not given as integers hence we cannot answer this using I alone.
Using II alone we find that x+y+z can be any real number except 3,6,9  etc
Even if we combine I & II we find that x,y,z cannot be determined, hence answer is (4).
Question
What are the values of 3 integers a, b, c?

ab=8

bc = 9
Solution
Using statement I alone we find possible values of a, b as ( 1, 8) (2, 4) (8, 1) (4, 2) (1, 8) (8, 1) (2, 4) (4, 2) from these option we cannot find a and b.
Using statement II alone we get, possible values of (b, c) as (1,9) (9,1) (1, 9) (9, 1) (3, 3) (3,3) again as before we cannot find b, c.
Next if we combine I and II then also we cannot find a, b, c. Hence answer is (4).
Question
Given that x and y are nonnegative. What is the value of x?

II.
Solution
Using I and II we get
;
;
we find that
we find that putting y = 0, 1,2,3 etc we get different set of values of x. Hence x and y cannot be found out. Hence answer is (4).
Question
If x+yz+t even?

x+y+t is even II. t and z are odd.
Solution
Using I alone we find that x+y+tz is odd or even accordingly as z is odd or even (as x+y+t is even) hence I alone is not sufficient.
Using II also does not help as II alone does not give us any information about x and y.
Combining I and II we get x+y+z is odd and z is odd hence x+y+tz is odd, hence answer is (3).
Question
What is the profit Percentage?

The cost price is 80% of the selling price.

The profit is Rs. 50.
Solution
From I alone we find that CP= 80% of Selling Price.
Selling Price = of CP = of CP
Profit = SPCP =
Profit % = = 25%
Since we have to find the profit percent hence I alone is sufficient. Hence answer is (1). Suppose the problem had been to find the CP on SP, then we have to use both I and II and answer would have been (3).
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