In this chapter , we will study the different types of problems such as - average, ratios and proportion, time and work, time and distance, percentage, profit and loss, etc. Analysis of given data to reach conclusion is called Data sufficiency.The data given in the form of statements is sufficient to answer the question asked. There is no need to solve the problem . The question can be answered without actually solving it.
As soon as you can tell that an answer will be obtained , you can stop working on further statements. First, all of you have to study the given questions and all the statements given and decide whether any information provided in the statement is sufficient or not. If we do not get a answer from a statement in any question, then try to get the answer from the information given in the second statement. The problems based on this topic consists of a mathematical or logical problem. Occasionally the data is not sufficient , in such case the proper answer would be "answer can not be obtained".

Directions ( Q. Nos. 1 - 5 ) Each of the questions below consists of two statements numbered Ⅰ and Ⅱ given below it .You are to decide whether the data provided in the statements are sufficient to answer the questions. Read both statements and give the answer .
Example 1: What is the perimeter of a semi - circle ?
Ⅰ. The radius of the semi circle is equal to half the side of a square .
Ⅱ. The area of the square is 196 sq. cm .
Solution: According to above given statements ,
From Ⅱ , The area of the square = 196 sq. cm
⇒ a² =196 ⇒ a = √196 = 14 cm
From Ⅰ , Let r be the radius of semi circle and a be the side of square .

r =	a	=	14	= 7 cm.
	2		2

{ From Ⅱ a = 14 }

=		22	× 7		= 22 cm.
		7

Hence both statements are required .

Example 2: What is the exact average of n , 35 , 39 , 42 , p and w ?
Ⅰ. n is six more than w.
Ⅱ. w is four less than p.
Solution: According to above given statements , we have
From Ⅰ , n = w + 6
From Ⅱ , w = p - 4 ⇒ p = w + 4

Average =		n + 35 + 39 + 42 + p + w		=		3w + 126
		6				6

Since exact average can not be determined because the value of w is not given .

Example 3: What will be the difference between two numbers ?
Ⅰ. The square of the first number is 9 times the second number.
Ⅱ. The ratio of first number to second number is 3 : 4 .
Solution: Let a and b are two numbers respectively .Then
First number = a and Second number = b
From Ⅱ , Ratio of a and b numbers = 3 : 4
⇒ a : b = 3 : 4 ⇒ a = 3k and b = 4k ( say )
From Ⅰ , ( First number )² = 9 x Second number
⇒ a² = 9 x b ⇒ a² = 9b
⇒ ( 3k )² = 9 x 4k ⇒ 9k² = 36k ⇒ k = 36 / 9 = 4
∴ Required Difference = b - a = 4k - 3k = k = 4
Hence the difference between two numbers will be 4 .

Example 4: What is Supriya ' s present age ?
Ⅰ. Supriya is 3 year older than Priya.
Ⅱ. The ratio of Priya 's and Reshma ' s age is 3 : 4 .
Solution: Let Supriya ' s present age is p and Priya 's present age is q . Then, according to given statements, we have
From Ⅰ , Supriya ' s present age = Priya ' s present age + 3 years
From Ⅱ , The ratio of Priya 's and Reshma ' s age = 3 : 4
Since data of both statements are not sufficient, so answer can not be determined .

Example 5: What is the ratio of two numbers p and q ?
Ⅰ. 40% of p is 20% of 50.
Ⅱ. 30% of q is 25% of 72.
Solution: According to above given statements , we have
From Ⅰ , 40% × p = 20% × 50

⇒		40		× p		20		× 50
		100				100

From Ⅱ , 30% × q = 25% × 72

⇒		30		× q		25		× 72
		100				100

⇒	3q	=	72	⇒	180	= 60
	10		4		3

Using Ⅰ and Ⅱ , we get
Required ratio p : q = 25 : 60 = 5 : 12.