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Important Data Sufficiency Questions with PDF for Bank Exams like SBI, IBPS, RBI, LIC, CET Etc

Directions: 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 give answer:
» Explain it
D
Statement I :

Let, total work be LCM of (16, 20) = 80 units

One day’s work of A and B together =  80  = 5 units
16

One day’s work of C and B together =  80  = 4 units
20

One day’s work of (A + 2B + C) = 5 + 4 = 9 units

Statement II :

As, efficiency of A and B is same, so time taken by each of A and B to complete the work = 16 × 2 = 32 days

One day’s work of B or A =  80  = 2.5 units
32

Using both statements:

One day’s work of C = 9 – 3 × 2.5 = 1.5 units

Time taken by C to complete the work

80  =  160  days
1.5 3

So option (D) is the correct answer.
2
A shopkeeper sold two items of same marked price of Rs. 1500 at a profit of 20% and 25% respectively. Find the selling price of item B.
 
Statement I : The discount offered by the shopkeeper for item A is 20% and the ratio of the cost price of item A to the cost price of item B is 10: 11 respectively
 
Statement II : The selling price of item A and selling price of item B are in the ratio of 48: 55, respectively
» Explain it
A
Statement I :

Marked price of item A = marked price of item B

Discount offered in item A = 20%

Selling price of item A = 0.8 × 1500 = Rs. 1200

Cost price of item A =  1200  = Rs. 1000
1.2

Cost price of item B =  11  × 1000 = 1100
10

Selling price of item B = 1100 × 1.25 = 1375

So, statement I alone is sufficient to answer the question

Statement II :

We cannot find the cost price or selling price of any article

So, statement II alone is not sufficient to answer the question

Hence, option A is correct.
3
Ram invested a sum of Rs. 80, 000 in scheme A offering simple interest. What is the interest earned by him after 2 years?
 
Statement I : If Rajan had invested the same money for same time at the same rate of interest but compounded annually, he would have gained Rs. 1800 more
 
Statement II : Scheme B offers an interest rate of 10%, compounded annually. If Rajan had invested the money partially in Scheme A and rest in scheme B, then the interest earned by him after 2 years will be Rs. 15600
» Explain it
A
Statement I :

Let the rate of interest = r%

So, simple interest after 2 years

80000 × 2 × r  = 1600r
100

Compound interest earned after 2 years

= 80000  { ( 1 +  r ) 2  – 1 }  = 8(r2 + 200r)
100  

(8r2 + 1600r)

According to the question,

(8r2 + 1600r – 1600r) = 1800

8r2 = 1800

r =15%

So, interest earned in scheme A after 2 years

80000 × 2 × 15  = Rs. 24000
100

So, statement I alone is sufficient

Statement II :

Let the money invested in scheme A = x

Let the money invested in scheme B = 80000 – x

Let the rate of interest in scheme A = r%

According to the question,

x × r ×  2  + (80000 – x) ×  { ( 1 +  10 ) 2  – 1 }  = 15600
100 100  

2xr  + (80000 – x) ×  ( 21 )  = 15600
100 100

2xr + 1680000 – 21x =1560000

21x – 2xr = 120000

Here we have two unknown variables so it is not possible to solve this equation

So, statement II alone is not sufficient to answer the question

Hence, option A is correct.
4
A man mixes 20 litres of water in a mixture P of milk and water such that the ratio of milk and water becomes equal in the mixture P. Another mixture Q, contains milk and water in the ratio 2 : 1 respectively. Now, if 25% of mixture P is added into mixture Q, then find the quantity of milk in the resultant mixture Q
 
Statement I : Initially the ratio of water to milk in the mixture P was 3 : 8, respectively and the quantity of milk in mixture Q initially was 15 litres more than the quantity of water in mixture Q initially
 
Statement II : Initially the ratio of water to milk in the mixture P is 3 : 8, respectively and the ratio of milk to water in the mixture Q is 38 : 23, respectively, after adding 25% mixture of P.
» Explain it
C
Statement I :

Let the quantity of milk and water in mixture P initially be 8x and 3x respectively

So, 8x = 3x + 20; x = 4

So the quantity of milk in the mixture P initially = 32 litres

So the quantity of water in the mixture P initially = 12 litres

So the quantity of water in the mixture P after adding 20 litres of water = 32 litres

Let the quantity of milk and water in mixture Q initially be 2y and y respectively

2y – y = 15; y = 15

Quantity of milk in the resultant mixture Q = 25% of 32 + 2 × 5 = 38 litres

So, statement I alone is sufficient to answer the question

Statement II :

Initially ratio of milk and water in mixture P = 8 : 3

Let the quantity of milk and water in mixture P initially be 8x and 3x respectively

So, 8x = 3x + 20; x = 4

So the quantity of milk in the mixture P initially = 32 litres

So the quantity of water in the mixture P initially = 12 litres

So the quantity of water in the mixture P after adding 20 litres of water = 32 litres

Let the quantity of milk and water in mixture Q initially be 2y and y respectively

25% of 32 + 2y  =  38  ; y = 15
25% of 32 + y 23

Quantity of milk in the resultant mixture Q = 25% of 32 + 2y = 38 litres

So, statement II alone is sufficient to answer the question

Hence, option C is correct.
5
Find the value of x
 
Statement I : Ram and Shyam started a company where their investment is in the ratio of 5 : x respectively. After 2 months, Ganshayam joined them such that the ratio of the initial investment of Shyam and Ganshayam is 7 : 8 respectively. After a year, they received a total profit of Rs. 16800
 
Statement II : The profit share of Ganshayam after a year is Rs. 6000 out of total profit of Rs. 16800
» Explain it
E
Statement I :

Ratio of investment: Ram: Shyam: Ganshayam = 5 × 7 : x × 7 : 8 × x = 35 : 7x : 8x

Ratio of profit share = Ram: Shyam: Ganshayam = 35 × 12 : 7x × 12 : 8x × 10 = 210 : 42x : 40x

Total profit = Rs. 16800

Let, constant be k,

(210 + 42x + 40x) k = 16800

Statement II :

Ganshayam’s share = Rs. 6000

Using I and II together, we get

40x  =  6000
210 + 42x + 40x 16800

40x  =  15
210 + 82x 42

1680x = 3150 + 1230x

450x = 3150

x =  3150  = 7
450

Hence, option E is correct.

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