Data Sufficiency

Q:

What is the average Speed of the car during its entire trip?
(1) The car traveled at 75 mph for the first half (by time) of the trip and at 40 mph for the second half of the trip.
(2) The car would have taken 5 hrs. to complete the trip if it traveled at 75 mph for the entire trip.

  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

statements 5
let the first half distance be x and the second half distance be y and time be t
According to statement 1 :-
75 = x/(t/2)
And 40 = y/(t/2)
So, we have 3 variables and 2 equations so it is not sufficient to solve the given problem.
In statement 2 we are only provided with total journey speed but in terms of average speed we need to calculate the total distance in different path and then divide it by total time taken. So statement 2 is also not sufficient to answer the given problem.

Q:

What is the height of the rectangular tank?
(1) The area of the base of the tank is 100 sq. ft.
(2) It takes 20 Seconds to fill up the tank with water poured at the rate of 25 cubic feet per second

  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 population of the town continuously increased in the two decades 1960 through 1969 and 1970 through 1979. Was the percentage increase greater in the first decade than in the second Decade?
(1) The population increase in the first decade was 10,082.
(2) The population increase by the same amount in both decades.

  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
In statement 1 the data of population increase in first year is provided but no data is given for the second decade so nothing could be deduced from this.
In statement 2 it’s given that the population is increased in same amount
Let’s say population in 1970 was 2000 and it is increased by 1000 after 1st decade so % increase is 50% now in second decade the population goes from 3000 to 4000 so the % increase is 33.33 % so it can be said that it is sufficient to compare the % increase.
So, statement 2 is alone sufficient.

Q:

How many families in the town of the Windsor have exactly one car?
(1) 250 Families have at least one car.
(2) 60 Families have at least two cars.

  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:

In a factory, there are workers, executives, and clerks. How many Employees are there in the factory?
(1) 41 % are the employees are workers, 460 are executives, and the remaining 720 employees are clerks.
(2) 460 of the employees are executives and the account for 23% of the employees in the factory.

  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
Let the total numbers employees be x
According to statement 1 :-
59% of x = 460 + 720
So, from here we can easily find a unique value of x.
So, statement 1 is alone sufficient.
According to statement 2 :-
23% of x = 460
So, from here also we would get a unique value of x
So, both statements are alone sufficient.

Q:

What fraction of the students in a class have blue eyes?
(1) 10% of the girls have blue eyes.
(2) 20% of the boys have blue eyes.

  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 5
since the total number of students is not given so we can’t find what fraction of students have blue eyes.

Q:

What is the average temperature from Monday through Saturday of a week?
(1) The average temperature from Monday through Wednesday of the week is 36o C.
(2) The minimum and maximum temperature between Thursday and Saturday of the week are 25o C and 38o C, respectively.

  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 5
the statement 1 is not alone sufficient as it deals with only Monday through Wednesday.
The statement 2 talks about only minimum and maximum temperature of Thursday and Saturday and doesn’t give any relevant information to find average temperature from Thursday to Saturday so, even after combining both statement it is impossible to get the average temperature from Monday through Saturday.

Q:

The savings from a person’s income is the difference between his or her income and expenditure. What is the ratio of Mr. Kunal’s savings in the year 1998 to the year 1999?
(1)The ratio of his income in the years 1998 to 1999 is 3:4.
(2) The ratio of his expenditure in the years 1998 to 1999 is 5:6.

  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 5
since the exact income and expenditure is not give we cannot find the requisite ratio.
For example, may be his income is Rs 75 in 1998 and Rs 100 in 199 or Rs 150 in 1998 and Rs 200 in 1999.

Q:

What is the average score of the test takers on a test?

(1) Exactly half the test takers scored above 500.
(2) The lowest and the highest scores are 200 and 800. Respectively.

  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 5
since the total number of test takers are not given in any statement so we can’t find the average score from both the above statements and additional data is required to answer the given problem.

Q:

Is the product of two numbers x and y a prime number?
(1) x and y are two prime numbers .
(2) x and y are two odd numbers not equal to 1.

  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
The definition of prime number says that it’s a number greater than 1 which is divisible by 1 and the number itself.
So, if any one number from x and y is 1 and the other is prime than only the condition will satisfy else not.
So, from both the above statements we can say that the product cannot be a prime number so, both are alone sufficient to answer the given condition.

Q:

A rectangular field is 3.2 yards long. What is the area of the fields in square yards?
(1) A fence marking the boundary is 11.2 yards in length.
(2) The distance between the diagonally opposite corners of the rectangular field is 4 yards.

  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
In statement 1 the perimeter is given to us so by using perimeter we can find the breadth of the rectangle and if we have both length and breadth we have the area so, statement 1 is alone sufficient.
In statement 2 we have length of diagonal = 4 so by using Pythagoras theorem we can find out the breadth of the rectangle and hence area.
So, each statement is alone sufficient.

Q:

Rajesh Jogged to a restaurant at x km per hour and jogged back home along the same route at y km per hour. He took 30 Minutes for whole trip. What is the average speed at which he jogged for the whole trip?
(1) The restaurant is 2 km from home.
(2) x = 12, and y = 6.

  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
the average speed is = (total distance covered)/(total time taken)
In statement 1 the distance from restaurant to home is given so total distance covered is 4 km and total time is 30 min. or ½ hr so average speed is 8km/hr .
In statement 2 the speeds x,y are given and we have total time taken so total distance covered is = (12+6)/2 = 10km. Now we can easily find the average speed.
So, each statement is alone sufficient.

Q:

Sanjay deposited Rs. 100 to open a savings account. If there are no other transactions in the account, what amount of money would the account accrue in 6 months after opening the account?
(1) The interest rate is 4%
(2) Interest is compounded quarterly

  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
In statement 1 the interest rate is given but the time for the interest is not given, it could be monthly, quarterly or yearly or something else so it couldn’t tell the amount after 6 months.
In statement 2 we have been provided the data that interest is added as compound interest and the time frame for the interest is a quarter or 3 months
So, by using both the statements we can find the amount after 6 months.

Q:

How much is 20 percent of a certain number a?
(1) 20 is 20 percent of the number a
(2) 80 percent of the number a is 80

  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

In statement 1 the 20 percent of a is given = 20 so it’s alone sufficient

In statement 2 80 percent of a is 80 so the number a is 100

20 % of a = 20

So, it’s also alone sufficient.

Q:

If p is the circumference of the circle Q, what is the value of p?
(1) The radius of circle Q is 5
(2) The area of circle Q is 25

  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 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

circumference of circle is 2πr so if we get the radius than we can find the circumference.

In statement 1 radius is give

In statement 2 we have area so we can easily find the radius.

So, both are alone sufficient.

 

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