Data Sufficiency Questions and Answers updated daily – Logical Reasoning



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Data Sufficiency Questions

1. Average age of employees working in a department is 30 years. In the next year, 7 workers will retire. What will be the average age in the next year?
I. Retirement age is 60 years.
II. There are 50 employees in the department. 



SHOW ANSWER
Correct Ans:Both I and II are necessary to answer
Explanation:
EXPLANATION:
Given, Average age of employees = 30 years.

From StatementI:
Retirement age = 60 years.

From StatementII:
Number of employees in the department =​​​​​​ 50
Average age of 50 employees = 30years.
Total age of 50 employees = (50 x 30) years = 1500 years

From Both Statements I andII:
Number of employees in the next year = 43. (since 7 workers retire)
Total age of 43 employees next year = (1500 + 43 - 60 x 7) = 1123
Average age in the next year = 1123/ 43 = 26.12 years
Thus, Both StatementsI and II are necessary to answer


2. Average age of employees working in a department is 30 years. In the next year, 8 workers will retire. What will be the average age in the next year?
I. Retirement age is 60 years.
II. There are 50 employees in the department. 



SHOW ANSWER
Correct Ans:Both I and II are necessary to answer
Explanation:
Given, Average age of employees = 30 years

From Statement I:
Retirement age = 60 years.

From Statement II:
Number of employees in the department = 50
=> Average age of 50 employees = 30 years.
=> Total age of 50 employees = (50 x 30) years = 1500 years

Number of employees next year = 42. (since 8 workers retire)

From Both Statements I and II:
Total age of 42 employees in the next year (1500 + 42 - 60 x 8) = 1062.
Average age in the next year = 1062/ 42 = 25.29

Therefore, Both statements I and II are necessary to answer.


3. Average age of employees working in a department is 30 years. In the next year, 15 workers will retire. What will be the average age in the next year?
I. Retirement age is 60 years.
II. There are 50 employees in the department.



SHOW ANSWER
Correct Ans:Both I and II are necessary to answer
Explanation:
Given, Average age of employees = 30 years
From Statement I:
Retirement age = 60 years.
From Statement II:
Number of employees in the department = 50
=> Average age of 50 employees = 30 years.
=> Total age of 50 employees = (50 x 30) years = 1500 years

Number of employees next year = 35. (since 15 workers retire)

From Both Statements I and II:
Total age of 35 employees in the next year (1500 + 35 - 60 x 15) = 635.
Average age in the next year = 635 / 35 = 18.14
Therefore, Both statements I and II are necessary to answer.


4. Average age of employees working in a department is 30 years. In the next year, 20 workers will retire. What will be the average age in the next year?
I. Retirement age is 60 years.
II. There are 40 employees in the department.



SHOW ANSWER
Correct Ans:Both I and II are necessary to answer
Explanation:
Given, Average age of employees = 30 years
From Statement I:
Retirement age = 60 years.
From Statement II:
Number employees in the department = 40
=> Average age of 40 employees = 30 years.
=> Total age of 40 employees = (40 x 30) years = 1200 years

Number of employees next year = 20. (since 20 workers retire)

From Both Statements I and II:
Total age of 20 employees in the next year (1200 + 20 - 60 x 20) = 20.
Average age in the next year = 20/ 20 = 1
Therefore, Both statements I and II are necessary to answer.


5. Average age of employees working in a department is 30 years. In the next year, 10 workers will retire. What will be the average age in the next year?
I. Retirement age is 60 years.
II. There are 50 employees in the department. 



SHOW ANSWER
Correct Ans:Both I and II are necessary to answer
Explanation:
Given, Average age of employees = 30 years.

From StatementI:
Retirement age = 60 years.

From StatementII:
Number of employees in the department =​​​​​​ 50
Average age of 50 employees = 30years.
Total age of 50 employees = (50 x 30) years = 1500 years

From Both Statements I andII:
Number of employees in the next year = 40. (since 10 workers retire)
Total age of 40 employees next year = (1500 + 40 - 60 x 10) = 940
Average age in the next year = 940/ 40 = 23.5 years
Thus, Statements I and II together give the answer.


6. What is the two-digit number whose first digit is "a" and the second digit is "b"?. The number is greater than 9.
I. The number is multiple of 9.
II.The number is multiple of 3



SHOW ANSWER
Correct Ans:Both I and II are not sufficient to answer
Explanation:
What is the two-digit number whose first digit is "a" and the second digit is "b"?. The number is greater than 9.
I. The number is multiple of 9.
II.The number is multiple of 3
We cannot find out the number with the given course of action.
So,Both I and II are not sufficient to answer.


7. What is the two-digit number whose first digit is "a" and the second digit is "b"?. The number is greater than 9.
I. The number is multiple of 61.
II. The sum of the digits "a" and "b" is 7. 



SHOW ANSWER
Correct Ans:I alone sufficient while II alone not sufficient to answer
Explanation:
EXPLANATION:
From statement I:
A two digit number, greater than 9 and multiple of 61 should be 61 itself.
Because, 2 x 61 = 122 (3 digit number).
Therefore, I alone sufficient to answer.

From statement II:
A two digit number, greater than 9 and sum of the digit is 7.
It can be 16, 25, 34, 43, 52, 61.
So we cannot determine the required answer from the statement II alone.

Thus, I alone give the answer while II alone not sufficient to answer.


8. What is the two-digit number whose first digit is "a" and the second digit is "b"? The number is greater than 9.
I. The number is multiple of 52.
II. The sum of the digits "a" and "b" is 7.



SHOW ANSWER
Correct Ans:I alone sufficient while II alone not sufficient to answer
Explanation:

From statement I:

A two digit number, greater than 9 and multiple of 52 should be 52 itself.

Because, 2 x 52 = 104(3 digit number).

Therefore, I alone sufficient to answer.

From statement II:

A two digit number, greater than 9 and sum of the digit is 7.

It can be 16, 25, 34, 43, 52, 61.

So we cannot determine the required answer from the statement II alone.

Thus, I alone give the answer while II alone not sufficient to answer.



9. What is the two-digit number whose first digit is "a" and the second digit is "b"?. The number is greater than 9.
I. The number is multiple of 51.
II. The sum of the digits "a" and "b" is 6.



SHOW ANSWER
Correct Ans:I alone sufficient while II alone not sufficient to answer
Explanation:

From statement I:

A two digit number, greater than 9 and multiple of 51 should be 51 itself.

Because, 2 x 51 = 102 (3 digit number).

Therefore, I alone sufficient to answer.

From statement II:

A two digit number, greater than 9 and sum of the digit is 6.

It can be 15, 24, 33, 42, 51, 60.

So we cannot determine the required answer from the statement II alone.

Thus, I alone give the answer while II alone not sufficient to answer.



10. What is the two-digit number ?
I. The difference between the two digits is 9.
II. The sum of the digits is equal to the difference between the two digits.



SHOW ANSWER
Correct Ans:Both I and II are necessary to answer
Explanation:

Let the tens and unit digits bexandyrespectively. Then,

From StatementI.x-y= 9.

From Statement II.x+y=x-y.

From I and II, we getx-y= 9 andx+y= 9.

On solving, we getx= 9 andy= 0.

Therefore, Required number is 90.

Thus, both StatementsI and II are necessary to answer.



11. What is the two-digit number ?
I. The difference between the two digits is 8.
II. The sum of the digits is equal to the difference between the two digits. 



SHOW ANSWER
Correct Ans:Both I and II are necessary to answer
Explanation:
Given
Difference between two digits = 8
Sum of the digits =Difference between two digits
Let unit digit be b
Let tenth digit be a
Let difference between the digits be
a - b = 8 ---> 1)
LetSum of the digits be
a + b = 8 ----> 2)
Solving 1 and 2
2a = 16
a = 16 / 2
a = 8.
Substuting a = 8 in eqn 2
a + b = 8
8 + b = 8
b = 8 - 8
= 0
Two digit number = 80.
Here both I & II are needed to solve the questions.


12. What is the two-digit number ?
I. The difference between the two digits is 7.
II. The sum of the digits is equal to the difference between the two digits.



SHOW ANSWER
Correct Ans:Both I and II are necessary to answer
Explanation:


13. What is the two-digit number?
I. The difference between the two digits is 6.
II. The sum of the digits is equal to the difference between the two digits.



SHOW ANSWER
Correct Ans:Both I and II are necessary to answer
Explanation:

Let the tens and units digit of a two digit number be X and Y respectively.
From Statement I:
X - Y = 6 --> (eqn 1)

From Statement II:
X + Y = X - Y = 6
=> X + Y = 6--> (eqn 2)

From Both Statements I and II:
On Adding eqn (1) and (2), we get,
2X = 12
=> X = 6---> subs in X -Y = 6
=> Y = 6- 6
=> Y = 0
Therefore the two digit number is 60.
Hence, Both statement I and II are necessary to answer.



14. What is the two-digit number?
I. The difference between the two digits is 5.
II. The sum of the digits is equal to the difference between the two digits. 



SHOW ANSWER
Correct Ans:Both I and II are necessary to answer
Explanation:
Let the tens and units digit of a two digit number be X and Y respectively.
From Statement I:
X - Y = 5 --> (eqn 1)

From Statement II:
X + Y = X - Y = 5
=> X + Y = 5 --> (eqn 2)

From Both Statements I and II:
On Adding eqn (1) and (2), we get,
2X = 10
=> X = 5---> subs in X – Y = 5
=> Y = 5 – 5
=> Y = 0

Therefore the two digit number is 50.
Hence, Both statement I and II are necessary to answer.


15. What is the two-digit number ?
I. The difference between the two digits is 4.
II. The sum of the digits is equal to the difference between the two digits.



SHOW ANSWER
Correct Ans:Both I and II are necessary to answer
Explanation:
Given
Difference between two digits = 4
Sum of the digits =Difference between two digits
Let unit digit beb
Let tenth digit bea
Let difference between the digits be
a - b = 4 ---> 1)
LetSum of the digits be
a + b = 4 ----> 2)
Solving 1 and 2
2a = 8
a = 8 / 2
a = 4
Substuting a = 8 in eqn 2
a + b = 4
4 + b = 4
b = 4 - 4
b= 0
Two digit number = 40.
Here both I & II are needed to solve the questions.


16. What is the two-digit number?
I. The difference between the two digits is 3.
II. The sum of the digits is equal to the difference between the two digits.



SHOW ANSWER
Correct Ans:Both I and II are necessary to answer
Explanation:
Let the tens and units digit of a two digit number be X and Y respectively.
From Statement I:
X - Y = 3 --> (eqn 1)

From Statement II:
X + Y = X - Y = 3
=>X + Y = 3--> (eqn 2)

From Both Statements I and II:
On Adding eqn (1) and (2), we get,
2X = 6
=> X = 3---> subs in X – Y = 3
=> Y = 3 – 8
=> Y = 0

Therefore the two digit number is 30.
Hence, Both statement I and II are necessary to answer.


17. What is the two-digit number ?
I. The difference between the two digits is 2.
II. The sum of the digits is equal to the difference between the two digits.



SHOW ANSWER
Correct Ans:Both I and II are necessary to answer
Explanation:


18. What is the number?
I . The sum of the digits is 35. The ratio of the two digits is 1 : 6.
II. The product of the two digit number is 150. The quotient is 6. 



SHOW ANSWER
Correct Ans:Both I and II are not sufficient to answer
Explanation:

Letthe tens and units digit bexandyrespectively. Then,
From Statement I:
x + y = 35
x : y = 1 : 6
=>x = z, y = 6z-->subs inx + y = 35
=> z + 6z = 35
=> 7z = 35
=> z = 5
so, x = 5,
and,y = 6z = 30

Thus the two digit number can't be formed with the data given in Statement I.

From Statement II:
xy = 150
x/y = 6/1 ==> x = 6y ---> subs inxy = 150
=> 6y * y = 150
=> 6y2= 150
=>y2= 25
=> y = 5
and, x = 6y = 6* 5= 30

Thus the two digit number can't be formed with the data given in Statement II.

Therefore, Both statements I and II are not sufficient to answer.



19. What is the number?
I . The sum of the digits is 44. The ratio of the two digits is 1 : 10.
II. The product of the two digit number is 160. The quotient is 10.



SHOW ANSWER
Correct Ans:Both I and II are not sufficient to answer
Explanation:

Letthe tens and units digit bexandyrespectively. Then,
From Statement I:
x + y = 44
x : y = 1 : 10
=>x = z, y = 10z-->subs inx + y = 44
=> z + 10z = 44
=> 11z = 44
=> z = 4
so, x = 4,
and,y = 10z = 40

Thus two digit number cannot be formed with the data given in statement I.

From Statement II:
xy = 160
x/y = 10/1 ==> x = 10y ---> subs inxy = 160
=> 10y * y = 160
=> y2= 16
=>y= 4
and, x = 10y = 40
Thus two digit number cannot be formed with the data given in statement II.

Therefore, Both I and II are not sufficient to answer.



20. What is the number?
I . The sum of the digits is 21. The ratio of the two digits is 1 : 6.
II. The product of the two digit number is 54. The quotient is 6.



SHOW ANSWER
Correct Ans:Both I and II are not sufficient to answer
Explanation:

Letthe tens and units digit bexandyrespectively. Then,
From Statement I:
x + y = 21
x : y = 1 : 6
=>x = z, y = 6z-->subs inx + y = 21
=> z + 6z = 21
=> 7z = 21
=> z = 3
so, x = 3,
and,y = 6z = 18

Thus the twodigit number cannot be formed with the data given instatement I alone.

From Statement II:
xy = 54
x/y = 6/1 ==> x = 6y ---> subs inxy = 54
=> 6y * y = 54
=> 6y2= 54
=>y2= 9
=> y = 3
and, x = 6y = 6* 3= 18

Thus the twodigit number cannot be formed with the data given instatement II alone.

Therefore, Both statements I and II are not sufficient to answer.




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