## Data Sufficiency

Q:

In a container there is a mixture of milk and water. What percent of the mixture in the container is milk?
(1) The ratio of milk to water in the container is 5:4
(2) The ratio of milk in mixture is 4:9

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
3. Both statements 1 and 2 together are sufficient to answer the question.
4. Each statement alone is sufficient to answer the question
5. Statements 1 and 2 together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Level: Medium

statement 4
according to statement 1 the required percentage is = (5/11) *100
According to statement 2 the required percentage is = (4/13) * 100
So both statements alone are sufficient to answer the given problem.

Q:

By what percent will the population of the town increase in 1 year?
(1) The current population of the town is 246000.
(2) The population of the town doubles every 3 months.

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
3. Both statements 1 and 2 together are sufficient to answer the question.
4. Each statement alone is sufficient to answer the question.
5. None of these.
Level: Medium

statement 2
according to statement 2 population doubles in every 3 months so after one year it will be 4 times or 400 % increase
So, statement 2 is alone sufficient.

Q:

Machine A, B and C work in a ratio of 2:4:3 hours respectively. For how many hours is the machine B used?
(1) Together machine A, B and C are operated for 81 hours.
(2) Machine C is operated for 9 hours more than machine A.

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
2. Statement 2 alone is sufficient but statement 1 alones not sufficient to answer the question asked
3. Both statements 1 and 2 together are sufficient to answer the question.
4. Each statement alone is sufficient to answer the question.
5. Statements 1 and 2 together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Level: Medium

statement 4
let the working hours of machines are: A = 2x, B=4x , C= 3x
According to statement 1
2x + 4x + 3x = 81
9x = 81
X =9
Machine B is used for 36 hours
According to statement 2
3x – 2x = 9
X = 9
So again, machine B is used for 36 hours

Q:

What percent is x of y?
(1) Three Fifth of x is half of y.
(2) 20% of x is 17.

1. Statement I alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
2. Statement 2 alone is sufficient but statement I alone is not sufficient to answer the question asked.
3. Both statements 1 and 2 together are sufficient to answer the question.
4. Each statement alone is sufficient to answer the question
5. Statements 1 and 2 together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Level: Medium

statement 1
According to statement 1
(3/5)x = (½)y
(6/5)x = y
So, 120% of x is y
Statement to doesn’t provide any data to compare.
So, statement 1 is alone sufficient.

Q:

Did the seller earn a profit?
(1) The selling price of 20 items equals the cost of 15 items
(2) The cost of 10 items is Rs. 55 greater than the selling price of 8 items.

1. (1) Statement I alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
2. Statement 2 alone is sufficient but statement I alone is not sufficient to answer the question asked.
3. Both statements 1 and 2 together are sufficient to answer the question but neither statement 1 nor statement 2 is sufficient alone.
4. Each statement alone is sufficient to answer the question.
5. Statements 1 and 2 together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Level: Medium

statement 1
According to statement 1 it can be clearly said that the seller is in loss as the selling price of 20 items is equal to cost of 15 items.
In statement 2 we cannot find the cp or sp of one item so we cannot compare them so it is not sufficient to answer the given problem.

Q:

Mr. Gupta usually starts at 9:00AM and reaches his office just in time, driving at his regular speed. Last Wednesday he started at 9:30AM and drove 25% faster than his regular
speed. Did he reach the office in time?
(1) Last Monday, he started to his office 20 minutes early drove 20% slower than his regular speed, and reached his office just in time.
(2) Last Tuesday, he started to his office 10 minutes early and reached the office 10 minutes early driving at his regular speed.

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
3. Both statements 1 and 2 together are sufficient to answer the question but neither statement 1 nor statement 2 is sufficient alone.
4. Each statement alone is sufficient to answer the question.
5. Statements 1 and 2 together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Level: Medium

statement 1
– In statement 1
Let the time to reach office be t
Now according to provided data
(t) = d/s
Where d is the total distance and s is speed at which he reaches on time
(t – 20) = d/

Q:

How much time does Mr. Ramesh take to reach his office from home?
(1) One day, he started 30 minutes late from home and reached his office 50 minutes late, while driving 25% slower than his regular speed.
(2) He needs to drive at a constant speed of 25 km per hour to reach his office just in time if he is 30 minutes late from home.

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked
2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked
3. Both statements 1 and 2 together are sufficient to answer the question but neither statement 1 nor statement 2 is sufficient alone.
4. Each statement alone is sufficient to answer the question.
5. Statements 1 and 2 together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Level: Medium

statement 1
According to statement 1 –
The 25% lower speed accounts for 20 minutes delay and remaining 30 minutes for his late start from home so it takes 30 minutes for him to do his journey.
According to statement 2 –
If he is 30 min late than he would have to drive at 25 km/hr to reach on time
Let the initial time be x minutes to complete his journey now, x + 30 = d/25
2 variables can’t be solved by 1 equation so statement 2 is not sufficient to answer the given problem.

Q:

In a country, 65% of male citizens and 65% of the female citizens are eligible to vote. What fraction of the citizens voted during the election?
(1) 68% of the male citizens eligible to vote voted.
(2) 65% of the female citizens eligible to vote voted.

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked
2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked
3. Both statements 1 and 2 together are sufficient to answer the question but neither statement 1 nor statement 2 is sufficient alone.
4. Each statement alone is sufficient to answer the question.
5. Statements 1 and 2 together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Level: Medium

statement 3

Q:

The total Income of Mr. Sharma in the years 2003, 2004, and 2005 was Rs. 36,400. What was his income in 2005?
(1) His income increased by 20% each year.
(2) His income in 2004 was Rs. 2000 more than in 2003.

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked
2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked
3. Both statements 1 and 2 together are sufficient to answer the question but neither statement 1 nor statement 2 is sufficient alone.
4. Each statement alone is sufficient to answer the question.
5. Statements 1 and 2 together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Level: Medium

statement 1
according to statement 1
Let Mr. Sharma’s income in 2003 be x . Now, in 2004 his income will be 1.2x and in 2005 his income will be 1.44 x
X + 1.2x + 1.44x = 36400
X= 10000
So, income in 2005 = 14400
So statement 1 is alone sufficient.
According to statement 2
His income in 2004 is 2000 more than in his income in 2003 but there is no relevant data given for his income in 2005 so the requisite data can’t be determined from statement 2.

Q:

Charu traveled from point A to the point B and then from Point B to point C. If she took 1 hour to complete the trip, what is the total distance she traveled?
(1) From A to B, her average speed was 40 mph, and from B to C her average speed was 60 mph.
(2) Her average speed for the complete trip was 50 mph.

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked
2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked
3. Both statements 1 and 2 together are sufficient to answer the question but neither statement 1 nor statement 2 is sufficient alone.
4. Each statement alone is sufficient to answer the question.
5. Statements 1 and 2 together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Level: Medium

statement 2
average speed = (total distance covered)/(total time taken)
In statement 1 the average speed is given for two different paths and time is for the complete trip so the information is not sufficient to answer the requisite problem.
In statement 2 the average speed is given for the complete journey and we also have the time taken for the complete trip so the given data is sufficient to answer the requisite problem.

Q:

A father distributed his total wealth to his two sons. How much wealth did the father have?
(1) The elder son received 3/5 of the wealth .
(2) The younger son received Rs. 30,000.

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked
2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked
3. Both statements 1 and 2 together are sufficient to answer the question but neither statement 1 nor statement 2 is sufficient alone.
4. Each statement alone is sufficient to answer the question.
5. Statements 1 and 2 together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Level: Medium

statement 3
let the total wealth be Rs x
3/5x + 30000 = x
2/5x = 30000
x = 75000
His remaining wealth = 75000 – 30000 – 45000 = 0
So, by both statements together we can answer his remaining wealth.

Q:

A bank Compounds interest for its Customers annually. How much Interest is earned in one year on Rs. 300?
(1) Interest rate per annum is 20%.
(2) Interest earned in two years on Rs. 300 is Rs. 132.

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked
2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked
3. Both statements 1 and 2 together are sufficient to answer the question but neither statement 1 nor statement 2 is sufficient alone
4. Each statement alone is sufficient to answer the question.
5. Statements 1 and 2 together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Level: Medium

statement 4
according to statement 1 interest rate per annum is given and for 1 year we can calculate the interest just by simple interest formula = p.1.r/100
So, statement 1 is alone sufficient.
According to statement 2 interest earned inn two years is Rs. 132
Applying the compound interest formula:
432 = 300 (1 + r)2
144/100 = (1+r)2
(1+r) = 1.2
From here we will get r = .2
So the rate is again 20%
Now, again we could calculate the interest for 1 year.
So, statement 2 is also alone sufficient.

Q:

An old man distributed his estate worth Rs. x to his three sons Rajesh, Mahesh, and Tarkesh. Who received the smallest part of the estate?
(1) Rajesh got 4/5 of what Mahesh got and 3/5 of what Tarkesh got.
(2) Tarkesh got 5/4 of what Mahesh got and Mahesh got Rs. 100 More than what Rajesh got?

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked
2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked
3. Both statements 1 and 2 together are sufficient to answer the question but neither statement 1 nor statement 2 is sufficient alone.
4. Each statement alone is sufficient to answer the question.
5. Statements 1 and 2 together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Level: Medium

statement 4
According to statement 1
Money with Rajesh = 4/5 of Mahesh
Money with Rajesh = 3/5 of Tarkesh
So, from here we can decide that Tarkesh > Mahesh > Rajesh
So, it’s alone sufficient to answer the given problem
According to statement 2
Tarkesh > Mahesh > Rajesh
So, statement 2 is also sufficient to answer the given problem.

Q:

Which one is greater on the farm: the total number of pigs and horses or the number of chickens?
(1) The ratio of the number of Chickens to the number of pigs to the number of horses on his farm is 33: 17: 21.
(2) The total number of the chickens, pigs, and horses on his farm is 142.

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked
2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked
3. Both statements 1 and 2 together are sufficient to answer the question but neither statement 1 nor statement 2 is sufficient alone.
4. Each statement alone is sufficient to answer the question.
5. Statements 1 and 2 together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Level: Medium

statement 1
let the total number of animals on farm be 71x which consists of pigs, horses and chickens.
Now, according to statement 1 number of pigs and horses = 21x + 17x = 38x
Number of chickens = 33x
And x can never be negative as it comprises the number of animals
So, 38x > 33x

Q:

The Cost of production of a certain instrument increases with the number of units produced. What is the cost of production for 270 units?
(1) The cost of production for 300 Units is Rs. 300
(2) The cost of production is directly proportional to the number of units produced.

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked
2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked
3. Both statements 1 and 2 together are sufficient to answer the question but neither statement 1 nor statement 2 is sufficient alone.
4. Each statement alone is sufficient to answer the question.
5. Statements 1 and 2 together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Level: Medium

statement 3
From statement 1 we cannot say that how much it will cost to produce 270 units as we only know the cost of production of 300 units but we don’t know in what relation it haas been increased
From statement 2 we can say that cost of production = k * (number of units produced)
Where k is proportionality constant
Now using statement 1 we can say that k=1
So, cost of producing 270 units is Rs. 270
So, both statements together can answer the given problem.