Data Sufficiency
Direction: In each of the following questions, a question is asked followed by three statements. You have to study the questions and all the three statements given and decide whether any information provided in the statement(s) is/are redundant and can be dispensed with while answering the questions.
 What is the area of a rightangled triangle?
A. The perimeter of the triangle is 30 cm.
B. The ratio between the base and the height of the triangle is 5 : 12.
C. The area of the triangle is equal to the area of rectangle of length 10 cm.

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Let, the base, height and hypotenuse of a rightangled triangle be b, p and h, respectively.
From Statement A, b + P + h = 30 …(1)
From Statement B, b : p = 5 : 12 …(2)
Let the base of triangle is 5k and height of triangle is 12k .
We know that
h^{2} = p^{2} + b^{2} = 25k^{2} + 144k^{2} = 169k^{2}
∴ h = 13k …(3)
Combining equations (1), (2) and (3), we get
5k + 12k + 13k = 30 ⇒ k = 1Correct Option: B
Let, the base, height and hypotenuse of a rightangled triangle be b, p and h, respectively.
From Statement A, b + P + h = 30 …(1)
From Statement B, b : p = 5 : 12 …(2)
Let the base of triangle is 5k and height of triangle is 12k .
We know that
h^{2} = p^{2} + b^{2} = 25k^{2} + 144k^{2} = 169k^{2}
∴ h = 13k …(3)
Combining equations (1), (2) and (3), we get
5k + 12k + 13k = 30 ⇒ k = 1
∴ Area of triangle = 1 x 5 x 12 = 30 cm^{2} 2
Hence, only A and B together are sufficient.
 What is the sum of two numbers?
A. The bigger of these two numbers is 6 more than the smaller number.
B. 40% of the smaller number is equal to 30% of the bigger number.
C. The ratio between half of the bigger number and onethird of the smaller number is 2 : 1.

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Let, the bigger and smaller numbers be p and q, respectively.
From statement A, p − q = 6 ....... ( 1 )
From statement B, 40% of q = 30% of p ⇒ 4q = 3p …......(2)Correct Option: E
Let, the bigger and smaller numbers be p and q, respectively.
From A, p − q = 6 ....... ( 1 )
From B, 40% of q = 30% of p ⇒ 4q = 3p …(2)From C, p : q = 2 : 1 ⇒ 3p = 4q ....(3) 2 3
On solving equations ( 1 ) and ( 2 ) or ( 3 ) , we get
q = 18 and p = 24
Hence , the bigger and smaller numbers be 24 and 18.
We see that equations (2) and (3) are same. Hence, A and either B or C is required.
Direction: Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and Read both the statements and give answer
 What is the ratio of the number of boys and girls in a school?
I. Number of boys is 40 more than the girls.
II. Number of girls is 80 percent of the number of boys.

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On the basis of above given details in question , we can say
From statement I , B − G = 40From statement II , G = 80% of B = 4 B . 5 Correct Option: B
On the basis of above given details in question , we can say
From statement I , B − G = 40From statement II , G = 80% of B = 4 B . 5
∴ B : G = 5 : 4
Hence , the ratio of the number of boys and girls in a school is 5 : 4 .
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.
 What is the difference between two numbers?
I. First number is 60 percent of the other number.
II. 50 percent of the sum of first and second numbers is 24.

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On the basis of above given details in question ,
Let two numbers are a and b respectively .
From statement I , a = 60% of b,
From statement I , a = 60% of b,a = 60 x b . 100 a = 6 b, . 10
⇒ 10a  6b = 0
Correct Option: E
On the basis of above given details in question ,
Let two numbers are a and b respectively .
From statement I , a = 60% of b,a = 60 x b . 100 a = 6 b, . 10
⇒ 10a  6b = 0 ⇒ 5a  3b = 0
From statement II , (a + b) x 50% = 24
∴ a + b = 2 x 24 = 48
On solving both equations of a and b , we get a = 18 and b = 30
The difference between two numbers = 30  18 = 12
 What was the speed of the running train?
I. Length of the train was 120 m.
II. The train crossed the other train whose length was 180 m in 4 sec.

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From statement I , Length of the train = 120 m
From statement II , Length of the other train = 180 m and time taken = 4 sec
Combining both the statements, we getThe speed of train = Length of the first train + Length of the second train Km/h. Time taken
Correct Option: E
From statement I , Length of the train = 120 m
From statement II , Length of the other train = 180 m and time taken = 4 sec
Combining both the statements, we getThe speed of train = Length of the first train + Length of the second train Km/h. Time taken The speed of train = 180 + 120 x 18 = 270 Km/h. 4 5