## Data Sufficiency

#### Data Interpretation

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

1. What is a two-digit number?
I. The number obtained by interchanging the digits is smaller than the original number by 63.
II. Sum of the digits is 11.

1. Suppose units place of number is occupied by q and tens place by p.
From statement I : (10p + q) − (10q + p) = 63
⇒ 9p − 9q = 63
⇒ p − q = 7 …(1)
From statement II : p + q = 11 …(2)
On solving equations (1) and (2) , we get
p = 9, q = 2
Hence, required number = 10 x 9 + 2 = 92

##### Correct Option: E

Suppose units place of number is occupied by q and tens place by p.
From statement I : (10p + q) − (10q + p) = 63
⇒ 9p − 9q = 63
⇒ p − q = 7 …(1)
From statement II : p + q = 11 …(2)
On solving equations (1) and (2) , we get
p = 9, q = 2
Hence, required number = 10 x 9 + 2 = 92
Basically, to answer these type of questions we need the following information :
A. Difference of units and tens digits of the two-digit number.
B. Sum of units and tens digits.
C. Comparison of the value of units and tens digits. With the help of the information in statements I and II together we get the required information.

1. What is the rate of interest p.c.p.a.?
I. Difference between compound interest and simple interest on an amount or \$ 10,000 for two years is \$ 225.
II. The amount doubles itself on simple interest in 62/3 years.

1. We know, if we have been given difference of CI and SI during two years, then this difference (D) is equal to

 P x r 2 100 2

where, P = Principal, r = rate of interest
From I : We get the value of P and D. Hence, statement I alone is sufficient.
 Again, we known SI = P x R x T 100

##### Correct Option: C

We know, if we have been given difference of CI and SI during two years, then this difference (D) is equal to

 P x r 2 100 2

where, P = Principal, r = rate of interest
From I : We get the value of P and D. Hence, statement I alone is sufficient.
 Again, we known SI = P x R x T 100
where, P = principal
r = rate of interest
T = time period
From II : We get value of P = K(say).
 Then, SI = K and T = 6 2 years 3

Hence, using the above formula we can get rate of interest from II alone also.

1. What is the cost of laying carpet in a rectangular hall?
I. Cost of the carpet is \$ 450 per m2,
II. Perimeter of the hall is 50 metre.

1. According to question ,
From statement I ,
Cost of carpet = \$ 450 per m2
From statement II ,
Perimeter of the hall = 2( L + B ) = 50 metre
To find out the cost of laying carpet we need
(i) cost of carpet per m2 and,
(ii) Area of the floor to be carpeted.

##### Correct Option: D

According to question ,
From statement I ,
Cost of carpet = \$ 450 per m2
From statement II ,
Perimeter of the hall = 2( L + B ) = 50 metre
To find out the cost of laying carpet we need
(i) cost of carpet per m2 and,
(ii) Area of the floor to be carpeted. Both the information even together are not sufficient to fulfil our need.

1. What was the population of State ‘A’ in 1999?
I. Population of the State increases every year by 20% and its population in 1997 was 120000.
II. Population of State A in 1997 was twice that of State B in the same year.

1. According to above given statements , we have
From statement I ,
Population in 1997 = 120000.
Population increases in 1997 = 120000 of 20% = 120000 x ( 20 / 100 ) = 24000
Population in 1998 = Population in 1997 + Population increase = 120000 + 24000 = 144000
Population increases in 1998 = 144000 of 20% = 144000 x ( 20/ 100 ) = 28800
Now , Population in 1999 = Population in 1998 + Population increase = 144000 + 28800 = 172800
From statement II ,
Population of State A in 1997 = 2 x Population of State B in 1997

##### Correct Option: A

According to above given statements , we have
From statement I ,
Population in 1997 = 120000.
Population increases in 1997 = 120000 of 20% = 120000 x ( 20 / 100 ) = 24000
Population in 1998 = Population in 1997 + Population increase = 120000 + 24000 = 144000
Population increases in 1998 = 144000 of 20% = 144000 x ( 20/ 100 ) = 28800
Now , Population in 1999 = Population in 1998 + Population increase = 144000 + 28800 = 172800
From statement II ,
Population of State A in 1997 = 2 x Population of State B in 1997
From above both statements , it is clear that Only statement I alone is sufficient.

1. How many children are there in the class?
I. Numbers of boys and girls are in the respective ratio of 3 : 4.
II. Number of girls is more than the number of boys by 18.

1. On the given all information in above question , we can say that
From I : Ratio of boys and girls = 3k : 4k
From II : Number of girls − Number of boys = 18
From I and II : 4k − 3k = 18

##### Correct Option: E

On the given all information in above question , we can say that
From I : Ratio of boys and girls = 3k : 4k
From II : Number of girls − Number of boys = 18
From I and II : 4k − 3k = 18
k = 18
Now , total number of children in the class = Number of boys + Number of girls
∴ 4k + 3k = 7 × 18 = 126.
Hence , Combining statement I and statement II .