## Data Sufficiency

#### Data Interpretation

Direction: Each question below is followed by two statements I and II. You are to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the possible answer.

1. What are the number of teachers in the school ?
I. The total number of teacher is less than the total number of student. There are different type of teachers in schools for Math, Science and English Subject.
II. The number of students for science are 20 and for math are 50. There are 300 students in school.

1. The total number of student is given in the question.
Number of teachers are less than students.

##### Correct Option: E

The total number of student is given in the question.
Number of teachers are less than students, But we cannot tell exact how many teachers are there in school.

Data is insufficient, so we cannot get answer from all two statements.

1. In how many year can a simple interest of ₹6570 be obtained on an amount of ₹ 36500 ?
I. The rate of simple interest is 6% per annum.
II. The difference between the simple interest and compound interest is ₹ 402.084.

1. Apply the law of Simple Interest.
Simple Interest ( S.I ) = (P x R x T)/100
where Principal amount = P,
Rate of Interest = R% per year and
Time = T years.

##### Correct Option: A

Apply the law of Simple Interest.
Simple Interest ( S.I ) = (P x R x T)/100
where Principal amount = P,
Rate of Interest = R% per year and
Time = T years.
Then
T = (S.I x 100)/P x R
From Statement I,
⇒ T = 6570 x 100/36500 x 6
⇒ T = 6570 x 1/365 x 6
⇒ T = 1095 x 1/365
⇒ T= 1095/365
⇒ T= 3 yr

I statement is enough to answer the question. II statement is not enough alone to answer the question.

1. What is Raveena's age ?
I. Raveena is half as old as Karishma.
ii. Raveena's age is three-fifth of her mother's age who is 45 yr old.

1. From Statement I,
Raveena is half as old as Karishma. But we don't know the age of Karishma.

From Statement II,
Age of Raveena = three-fifth of her mother's age
Age of Raveena = Age of her Mother x 3/5

##### Correct Option: B

From Statement I,
Raveena is half as old as Karishma. But we don't know the age of Karishma.

From Statement II,
Age of Raveena = three-fifth of her mother's age
Age of Raveena = Age of her Mother x 3/5
Age of Raveena = 45 x 3/5 = 27 yr

Direction: Each of the question 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 statement are sufficient to answer the question.

1. What is the value of p2 + q + r ?
I. 4p + 3q + 5r = 60, 2p = q, 2q = r
II. 3p + 3q + 2r = 34, 2p + 5q + 6r = 72

1. From Statement I , given that
4p + 3q + 5r = 60...............(i)
2p = q
⇒ p = q/2 ................(ii)
and 2q = r ....................(iii)
put the value of p and r in terms of q in Eq. (i), and solve the equation.

From Statement II,
3p + 3q + 2r = 34 ..............(a)
2p + 5q + 6r = 72 ..............(b)

##### Correct Option: A

From Statement I , given that
4p + 3q + 5r = 60...............(i)
2p = q
p = q/2 ................(ii)
and 2q = r ....................(iii)
putting the value of p and r in terms of q in Eq. (i),
4 x q/2 + 3q + 5 x 2q = 60
15q = 60
q = 4
put the value of q in Eq. (ii)
⇒ p = q/2 = 4/2
p = 2;
put the value of q in Eq. (iii)
r = 2q = 2 x 4
r = 8
∴ value of p2 + q + r = (2)2 + 4 + 8 = 16
From Statement II,
3x + 3y + 2z = 34 ..............(a)
and 2x + 5y + 6z = 72 ....(b)
We cannot find the value of p, q and r from Eqs. (a) and (b)

1. What is the respective ratio between the length of a rectangle and side of square ?
I. Area of the square is 576 sq cm and the area of the rectangle is 600 sq cm
II. Breadth of the rectangle is half the side of the square.

1. From Statement I,
Area of square = 576 sq cm
∴ Side of square = Square root of Square's area

and area of rectangle = 600 sq cm
area of rectangle = ( length x breadth ) of rectangle

From Statement II,
Breadth of rectangle = side of square x 1/2

Solve the equation and find the ratio.

##### Correct Option: E

From Statement I,
Area of square = 576 sq cm
∴ Side of square = Square root of Square's area
∴ Side of square = Square root of 576 = 24 cm
and area of rectangle = 600 sq cm
area of rectangle = ( length x breadth ) of rectangle
We cannot find the length of rectangle
From Statement II,
Breadth of rectangle = side of square x 1/2
Breadth of rectangle = 24 x 1/2 = 12 cm
∴ Length of rectangle = 600/12 = 50 cm
∴ Ratio = Length of rectangle/ Side of square = 50/24
= 25/12