Data Sufficiency MCQ Quiz - Objective Question with Answer for Data Sufficiency - Download Free PDF
Last updated on May 27, 2025
Latest Data Sufficiency MCQ Objective Questions
Data Sufficiency Question 1:
In questions numbered a question is followed by data in the form of two statements labelled as (I) and (II). You must decide whether the data given in the statements are sufficient to answer the questions. Using the data make an appropriate choice from (1) to (4) as per the following guidelines:
(a) Mark choice (1) if the statement (I) alone is sufficient to answer the question.
(b) Mark choice (2) if the statement (II) alone is sufficient to answer the question.
(c) Mark choice (3) if both the statements (I) and (II) are sufficient to answer the question but neither statement alone is not sufficient.
(d) Mark choice (4) if both the statements (I) and (II) together are not sufficient to answer the question and additional data are required.
Consider the given question and decide which of the following statement is sufficient to answer the question.
The lengths of two longer sides of the triangle Δ are 25 cm and 24 cm.
Question: What is the length of the shortest side ?
Statement I: The angles of Δ are in the ratio 1 : 2 : 3.
Statement II: The length of the perpendicular drawn on the longest side of Δ from its opposite vertex is 6.72 cm.
Answer (Detailed Solution Below)
Data Sufficiency Question 1 Detailed Solution
Concept:
1) If in a right-angle triangle
Ratio of three angle = 30° : 60° : 90° (or 1 : 2 : 3), then
The ratio of it's side opposite to this angle = 1: √3 : 2
2) AC × BD = AB × AD
Calculation:
Statement I:
The angles of Δ are in the ratio 1 : 2 : 3
As we know in a triangle sum of all the angles is 180°
So, The angles of Δ are 30°, 60°, 90°
Therefore,
So, the sides should be in the ratio 1: √3 : 2
By using the Pythagoras' theorem
x2 + 242 = 252
⇒ x2 + 576 = 625
⇒ x2 = 625 - 576
⇒ x2 = 49
⇒ x = 7
So, the shortest side = 7 cm
But, 7, 24 & 25 are not in the ratio 1 : √3 : 2, but as per the property,
If the ratio of angle = 1 : 2 : 3 then the ratio of side = 1 : √3 : 2.
Therefore, the information given in Statement I is not sufficient.
Statement II:
From the Pythagoras theorem, we got x = 7
By using the above property
BC × AD = AB × AC
7 × 24 = 25 × AD
AD = 168/25 = 6.72
Therefore, if we take the length of the shortest side equal to 7 cm, we got the length of the perpendicular drawn on the longest side of Δ from its opposite vertex is 6.72 cm.
Statement 2 is sufficient to answer this question.
∴ Option (2) is correct.
Data Sufficiency Question 2:
In questions numbered a question is followed by data in the form of two statements labelled as (I) and (II). You must decide whether the data given in the statements are sufficient to answer the questions. Using the data make an appropriate choice from (1) to (4) as per the following guidelines:
(a) Mark choice (1) if the statement (I) alone is sufficient to answer the question.
(b) Mark choice (2) if the statement (II) alone is sufficient to answer the question.
(c) Mark choice (3) if both the statements (I) and (II) are sufficient to answer the question but neither statement alone is not sufficient.
(d) Mark choice (4) if both the statements (I) and (II) together are not sufficient to answer the question and additional data are required.
In each of the question, a question is followed by two statements I and II. Give your answer as
What is the range of y?
I. 13 ≤ x + y ≤ 19
II. 4 ≥ x - y ≥ -5
Answer (Detailed Solution Below)
Data Sufficiency Question 2 Detailed Solution
Solution:
Statement I - alone cannot give the answer to the question, because it does not specify any relationship between x and y. For example, if x = 12 and y = 1, then both of the inequalities in statement I are satisfied, but the range of y is only 1.
Statement II - alone cannot give the answer to the question, because it does not specify any bounds on x + y. For example, if x = -3 and y = 7, then both of the inequalities in statement II are satisfied, but the range of y is 10.
However, statements I and II together can be used to determine the range of y. If we add the two inequalities in statement I, we get:
13 ≤ x + y ≤ 19
4 ≥ x - y ≥ -5
--------------
17 ≤ 2y ≤ 24
--------------
8.5 ≤ y ≤ 12
Therefore, the range of y is [8.5, 12].
Therefore, the correct answer is option 3, if the statements I and II together are necessary to give the answer to the question.
Data Sufficiency Question 3:
In questions numbered a question is followed by data in the form of two statements labelled as (I) and (II). You must decide whether the data given in the statements are sufficient to answer the questions. Using the data make an appropriate choice from (1) to (4) as per the following guidelines:
(a) Mark choice (1) if the statement (I) alone is sufficient to answer the question.
(b) Mark choice (2) if the statement (II) alone is sufficient to answer the question.
(c) Mark choice (3) if both the statements (I) and (II) are sufficient to answer the question but neither statement alone is not sufficient.
(d) Mark choice (4) if both the statements (I) and (II) together are not sufficient to answer the question and additional data are required.
In each of the question, a question is followed by two statements I and II. Give your answer as
Is the positive integer m odd?
I. m2 + 2m is even
II. m2 + m is even
Answer (Detailed Solution Below)
Data Sufficiency Question 3 Detailed Solution
Statements I :
Let the value of m = 5, 6, ---
If m = 5 (Odd)
m2 + 2m = 25 + 10 = 35 (Odd)
If m = 6 (Even)
m2 + 2m = 36 + 12 = 48 (Even)
If m is odd than 'm2 + 2m' is odd and m is even than 'm2 + 2m' is even
Statements II :
Let the value of m = 5, 6, ---
If m = 5 (Odd)
m2 + m = 25 + 5 = 30 (Even)
If m = 6 (Even)
m2 + m = 36 + 6 = 42 (Even)
So, we can't say m is odd or even
∴ The statement I alone can give the answer to the question
Data Sufficiency Question 4:
In questions numbered a question is followed by data in the form of two statements labelled as (I) and (II). You must decide whether the data given in the statements are sufficient to answer the questions. Using the data make an appropriate choice from (1) to (4) as per the following guidelines:
(a) Mark choice (1) if the statement (I) alone is sufficient to answer the question.
(b) Mark choice (2) if the statement (II) alone is sufficient to answer the question.
(c) Mark choice (3) if both the statements (I) and (II) are sufficient to answer the question but neither statement alone is not sufficient.
(d) Mark choice (4) if both the statements (I) and (II) together are not sufficient to answer the question and additional data are required.
In each of the question, a question is followed by two statements I and II. Give your answer as
Is 10, a factor of n + 5 ?
I. n is odd and divisible by 9
II. n is even and divisible by 5
Answer (Detailed Solution Below)
Data Sufficiency Question 4 Detailed Solution
Statements I
n is odd and divisible by 9 → 9, 27, 45,63 -----
If we take n = 45
than, n + 5
⇒ 50 is divisible by 10
The statement I can give the answer to the question
Statements II
n is even and divisible by 5 → 10, 20, 30, 40, -----
If we add 5 than that number is not divisible by 10
The statement II can't give the answer to the question
∴ If the statement I alone can give the answer to the question.
Data Sufficiency Question 5:
In questions numbered a question is followed by data in the form of two statements labelled as (I) and (II). You must decide whether the data given in the statements are sufficient to answer the questions. Using the data make an appropriate choice from (1) to (4) as per the following guidelines:
(a) Mark choice (1) if the statement (I) alone is sufficient to answer the question.
(b) Mark choice (2) if the statement (II) alone is sufficient to answer the question.
(c) Mark choice (3) if both the statements (I) and (II) are sufficient to answer the question but neither statement alone is not sufficient.
(d) Mark choice (4) if both the statements (I) and (II) together are not sufficient to answer the question and additional data are required.
In each of the question, a question is followed by two statements I and II. Give your answer as
What is the sum of the first 21 terms of the AP?
I. The common difference of the A.P. is 3
II. The 11th term of the A.P. is 31.
Answer (Detailed Solution Below)
Data Sufficiency Question 5 Detailed Solution
Formula used:
Sn = \(\frac {n}{2}\) [2a + (n - 1)d]
Tn = a + (n - 1)d
n → Number of terms
a → First term
d → common difference
Statements I
Common difference of the A.P. (d) = 3
The statement I alone can not give the answer to the question
Statements II
11th term of the A.P. = 31
⇒ a + (n - 1)d = 31
⇒ a + 10d = 31
The statement II alone can not give the answer to the question
Now, if both statements are used than,
⇒ a + 10d = 31
⇒ a + 10 × 3 = 31
⇒ a = 1
Sn = \(\frac {n}{2}\) [2a + (n - 1)d], now if we put all the value than i will find the actual value.
The statements I and II together are necessary to give the answer to the question.
Top Data Sufficiency MCQ Objective Questions
You are given a question followed by two statements numbered I and II. You have to decide whether the data provided on the statements are sufficient to answer the question.
What is the value of 'x'?
Statements :
I. x + 2y = 6
II. 3x + 6y = 18
Answer (Detailed Solution Below)
Data Sufficiency Question 6 Detailed Solution
Download Solution PDFStatement I:
⇒ x + 2y = 6
Here, we cannot find the value of x with the help of only one equation
Hence, Statement I alone is insufficient
Statement II:
⇒ 3x + 6y = 18
Here, we cannot find the value of x with the help of only one equation
Hence, Statement II alone is insufficient
From Statement I and II:
⇒ x + 2y = 6 ----(1)
⇒ 3x + 6y = 18 ----(2)
Multiplying equation (1) by 3 we get
⇒ 3(x + 2y) = 6 × 3
⇒ 3x + 6y = 18 ----(3)
Here, both equations (2) and (3) is same so we can not find the value of x
∴ Statements I and II together are not sufficient
Confusion Points
The second equation is only the multiple of first, so we cannot find the values of x and y
Consider the given question and decide which of the following statement(s) is/are sufficient to answer the question.
What is the average daily wage of X, Y and Z?
Statements:
- Y’s salary is half of (X + Z)
- X and Y together earn Rs. 40 more than Z and Z earns Rs. 500
Answer (Detailed Solution Below)
Data Sufficiency Question 7 Detailed Solution
Download Solution PDFFrom statement 2,
Earning of Z = Rs. 500
Earning of X and Y = Rs. 500 + 40 = Rs. 540.
⇒ Required average of daily wages = (X + Y + Z)/3 = (540 + 500)/3 = Rs. 1040/3
∴ 2 alone is sufficient while 1 alone is insufficient.Given below are two quantities named A & B. Based on the given information; you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.
Quantity A: If x is 20% more than y and y is 62.5% less than 840, then find the value of x.
Quantity B: 420
Answer (Detailed Solution Below)
Data Sufficiency Question 8 Detailed Solution
Download Solution PDFQuantity A:
⇒ y = (100 – 62.5)% of 840
⇒ y = 37.5% of 840
⇒ y = 3/8 × 840 = 315
Now,
⇒ x = (100 + 20)% of y
⇒ x = 1.2 × 315 = 378
⇒ Quantity A = 378
Quantity B: 420
∴ Quantity A < Quantity B
The question below consists of a question followed by two statements labeled as 1 and 2. You have to decide whether these statements are sufficient to answer the question.
Question: What is the value of X+Y ?
Statements:
1. X - 2Y = 5
2. X2 – 25 = 4XY - 4Y2
Answer (Detailed Solution Below)
Data Sufficiency Question 9 Detailed Solution
Download Solution PDFFrom Statement 1: X - 2Y = 5
cannot find the value of X and Y.
From statement 2: X2 – 25 = 4XY - 4Y2
X2 – 25 = 4XY - 4Y2 -------(1)
X2 - 4XY + 4Y2 = 25
(X - 2Y)2 = 25
X - 2Y = 5
cannot find the value of X and Y.
So, same equation in both the statements.
Hence, option (3) is the correct answer.
Confusion PointsHere, after calculation, we got only 1 equation, hence we cannot conclude the exact values of X and Y.
Consider the given question and decide which of the following statement(s) is/are sufficient to answer the question.
Is (X – 5) even? X is a real number.
Statement:
- X – 15 belongs to integer
- X – 10 is an odd integer
Answer (Detailed Solution Below)
Data Sufficiency Question 10 Detailed Solution
Download Solution PDFStatement 1:
X – 15 = integer
⇒ X is also an integer
Statement 2:
X – 10 = odd integer
⇒ X is an odd integer.
⇒ (X – 5) is even.
∴ Statement 2 alone is sufficient while statement 1 alone is insufficient.Directions: In the following question, two quantities A and B are given. You have to use your knowledge of mathematics to find the values of both A and B and choose the most appropriate relationship between the magnitudes of A and B from the given options.
Quantity A: Pipes X and Y can fill a tank in 15 hours and 20 hours respectively. There is a hole at 3/4th of the height of the tank which can drain water in 12 hours if it is at the bottom of the tank. How much time will it take to fill the tank?
Quantity B: 14 hours.
Answer (Detailed Solution Below)
Data Sufficiency Question 11 Detailed Solution
Download Solution PDFQuantity A -
Let the volume of tank = LCM of (15, 20, 12) = 60 units.
X's capacity = 60 / 15 = 4 units.
Y's capacity = 60 / 20 = 3 units.
Hole's emptying capacity = 60 / 12 = 5 units.
Time taken to fill (3 / 4)th tank = 45 / (4 + 3) = 6.42 units
Time taken for remaining (1 / 4)th tank = 15 / (4 + 3 - 5) = 7.5 units
Total time = 6.42 + 7.5 = 13.92 hours
Quantity B - 14 hours.
Hence, Quantity A < Quantity B
Confusion Points The statement that a hole at the bottom would have caused the tank to empty in 12 hours was made to give readers a sense of the pipe's flow rate, not to imply that the hole is at the bottom.
Consider the following question and decide which of the statements is sufficient to answer the question.
Question:
Find the value of m, slope of a line.
Statements:
1) y = mx + 2
2) Line passes through (2, 1)
Answer (Detailed Solution Below)
Data Sufficiency Question 12 Detailed Solution
Download Solution PDFStatement 1∶
y = mx + 2
We cannot find anything with statement 1.
Statement 2∶
Line passes thgough (2, 1)
We cannot find anything with statement 2.
Combining statement 1 and 2∶
∵ Line passes through (2, 1), it will satisfy the equation of line y = mx + 2
∴ Putting x = 2 and y = 1 in the equation of line
⇒ 1 = 2m + 2
⇒ m = -1/2
∴ Both statements 1 and 2 are sufficient.
Read the given question and decide which of the following information is sufficient to answer the question.
What is the value of ∠ACB?
Informations
| 1 | |
| 2 | ∠D = 60° |
Answer (Detailed Solution Below)
Data Sufficiency Question 13 Detailed Solution
Download Solution PDFCalculation:
Since angles by a chord on two different points on the same segment of a circle are equal.
∵ ∠D = 60°
So, ∠ACB = ∠D = 60°
Hence, Both 1 and 2 are sufficient (Option 2 is correct)
Consider the following question and statements and decide which of the statements is sufficient to answer the question.
What is the total weight of six boxes? Each of them is equal in weight.
Statements:
A. One-third of each boxes’ weight is 2 kg
B. The total weight of four boxes is 12 kg more than the total weight of two boxes.Answer (Detailed Solution Below)
Data Sufficiency Question 14 Detailed Solution
Download Solution PDFStatement A:
⇒ One-third of each boxes’ weight is 2 kg
⇒ Weight of each box = 6 kg
⇒ So, the total weight of 6 boxes = 36 kg
Statement B:
The total weight of four boxes is 12 kg more than the total weight of two boxes
Let the weight of 1 box be x.
⇒ Given, 4x - 12 = 2x
⇒ x = 6 kg
⇒ So, the total weight of 6 boxes = 36 kg
∴ Both Statements 1 and 2 alone are sufficientQuestion given below is followed by two statements
Is ‘a’ positive?
I) a + b is positive
II) a – b is positive.
Answer (Detailed Solution Below)
Data Sufficiency Question 15 Detailed Solution
Download Solution PDFFrom I
We know that a + b is positive ⇏ a is positive as b can be a large positive value when a is negative
For example,
Let the number of b be 2,
Then the number of a be -3
so, according to the statement
a + b = 2 + (-3) = -1 is negative
From II
We know that a - b is positive ⇏ a is positive as b can be a large negative value when a is negative
For example,
Let the number of b be 2,
Then the number of a be -3
so, according to the statement
a - b = 2 - (-3) = 5 is positive
Now, adding both i.e. I + II
(a + b) + (a - b) = positive
a is positive
Both the statements prove a is positive.