Data Sufficiency problems
- 1. What are the number of teachers in the school?
I. The total number of teacher is less than the total number of student. There are different type of teachers in schools for Math, Science and English Subject.
II. The number of students for science are 20 and for math are 50. There are 300 students in school.
Options- A. If the Statement I alone is sufficient to answer the question but the Statement II alone is not sufficient
- B. If the Statement II alone is sufficient to answer the question but the Statement I alone is not sufficient
- C. If both Statement I and II together are needed to answer the question
- D. If either the Statement I alone or Statement II alone is sufficient to answer the question Discuss
Correct Answer:
Explanation:
The total number of student is given in the question.
Number of teachers are less than students, But we cannot tell exact how many teachers are there in school.
Data is insufficient, so we cannot get answer from all two statements.
- 2. In how many year can a simple interest of ?6570 be obtained on an amount of ? 36500?
I. The rate of simple interest is 6% per annum.
II. The difference between the simple interest and compound interest is ? 402.084.
Options- A. If the Statement I alone is sufficient to answer the question but the Statement II alone is jot sufficient
- B. If the Statement II alone is sufficient to answer the question but the Statement I alone is not sufficient
- C. If both Statement I and II together are needed to answer the question
- D. If either the Statement I alone or Statement II alone is sufficient to answer the question Discuss
Correct Answer: If the Statement I alone is sufficient to answer the question but the Statement II alone is jot sufficient
Explanation:
Apply the law of Simple Interest.
Simple Interest ( S.I ) = (P x R x T)/100
where Principal amount = P,
Rate of Interest = R% per year and
Time = T years.
Then
T = (S.I x 100)/P x R
From Statement I,
? T = 6570 x 100/36500 x 6
? T = 6570 x 1/365 x 6
? T = 1095 x 1/365
? T= 1095/365
? T= 3 yr
I statement is enough to answer the question. II statement is not enough alone to answer the question.
- 3. What is Raveena's age?
I. Raveena is half as old as Karishma.
ii. Raveena's age is three-fifth of her mother's age who is 45 yr old.
Options- A. If the Statement I alone is sufficient to answer the question but the Statement II alone is jot sufficient
- B. If the Statement II alone is sufficient to answer the question but the Statement I alone is not sufficient
- C. If both Statement I and II together are needed to answer the question
- D. If either the Statement I alone or Statement II alone is sufficient to answer the question Discuss
Correct Answer: If the Statement II alone is sufficient to answer the question but the Statement I alone is not sufficient
Explanation:
From Statement I,
Raveena is half as old as Karishma. But we don't know the age of Karishma.
From Statement II,
Age of Raveena = three-fifth of her mother's age
Age of Raveena = Age of her Mother x 3/5
Age of Raveena = 45 x 3/5 = 27 yr
- 4. What is the value of p2 + q + r?
I. 4p + 3q + 5r = 60, 2p = q, 2q = r
II. 3p + 3q + 2r = 34, 2p + 5q + 6r = 72
Options- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question
- C. If the data in either Statement I alone or in Statement II alone are sufficient to answer the question
- D. If the data in both the Statements I and II are not sufficient to answer the question Discuss
Correct Answer: If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question
Explanation:
From Statement I , given that
4p + 3q + 5r = 60...............(i)
2p = q
? p = q/2 ................(ii)
and 2q = r ....................(iii)
putting the value of p and r in terms of q in Eq. (i),
4 x q/2 + 3q + 5 x 2q = 60
15q = 60
? q = 4
put the value of q in Eq. (ii)
? p = q/2 = 4/2
p = 2;
put the value of q in Eq. (iii)
? r = 2q = 2 x 4
? r = 8
? value of p2 + q + r = (2)2 + 4 + 8 = 16
From Statement II,
3x + 3y + 2z = 34 ..............(a)
and 2x + 5y + 6z = 72 ....(b)
We cannot find the value of p, q and r from Eqs. (a) and (b)
- 5. What is the respective ratio between the length of a rectangle and side of square?
I. Area of the square is 576 sq cm and the area of the rectangle is 600 sq cm
II. Breadth of the rectangle is half the side of the square.
Options- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question
- C. If the data in either Statement I alone or in Statement II alone are sufficient to answer the question
- D. If the data in both the Statements I and II are not sufficient to answer the question Discuss
Correct Answer:
Explanation:
From Statement I,
Area of square = 576 sq cm
? Side of square = Square root of Square's area
? Side of square = Square root of 576 = 24 cm
and area of rectangle = 600 sq cm
area of rectangle = ( length x breadth ) of rectangle
We cannot find the length of rectangle
From Statement II,
Breadth of rectangle = side of square x 1/2
Breadth of rectangle = 24 x 1/2 = 12 cm
? Length of rectangle = 600/12 = 50 cm
? Ratio = Length of rectangle/ Side of square = 50/24
= 25/12
- 6. What is the smaller angle of a parallelogram?
I. Ratio between the angles of a triangle is 3 : 5 : 4 and the larger angle, of the parallelogram is 34 ° more than the largest angle of the triangle.
II. Larger angle of the parallelogram is 38° more than its smaller angle.
Options- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question
- C. If the data in either Statement I alone or in Statement II alone are sufficient to answer the question
- D. If the data in both the Statements I and II are not sufficient to answer the question Discuss
Correct Answer: If the data in either Statement I alone or in Statement II alone are sufficient to answer the question
Explanation:
From Statement I.
Let the ratio proportion is x.
some of angle of triangle = 180 °
3x + 5x + 4x = 180 °
12x = 180 °
x = 180 ° /12
x = 15 °
Largest angle of triangle
= 5x = 5 x 15
= 75 °
? Larger angle of parallelogram
= 75 ° + 34 °
= 109 °
? Smaller angle of parallelogram
= 180 ° - 109 °
= 71 °
From Statement II,
Let the smaller angle of parallelogram be = x
and the larger angle of parallelogram = x + 38 °
Sum of two opposite angles of a parallelogram = 180 °
x + x + 38 ° = 180 °
? 2x = 180 ° - 38°
? 2x = 142°
? x = 142° / 2
? x = 71 °
- 7. What will be the number?
I. One-fifth of a number is equal to 20% of that number.
II. Thirty-five percent of a number is 7 / 20 of that number.
Options- A. If the data in statement I alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
- B. If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
- C. If the data either in statement I alone or in statement II alone are sufficient to answer the question.
- D. If the data even in both statements I and II together are not sufficient to answer the question. Discuss
Correct Answer: If the data even in both statements I and II together are not sufficient to answer the question.
Explanation:
Data in both statements I and II together are not sufficient to answer the question. Hence, required answer is option D .
- 8. Who amongst L, M, N, O and P is the shortest?
I. O is shorter than P but taller than N.
II. M is not as tall as L.
Options- A. if the data in statement I alone is sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
- B. if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
- C. if the data either in statements I alone or in statement II alone are sufficient to answer the question; and
- D. if the data given in both the statement I and II together are not sufficient to answer the question; and Discuss
Correct Answer: if the data in statement I alone is sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
Explanation:
From I: P > O > N
From II: L > M From I and II, either M or N is the shortest. We can't determine who is shorter between the two of them.
- 9. Are all the five friends, viz, Leena, Amit, Arun, Ali and Ken, who are seated around a circular table, facing the centre?
I. Leena sits second to the left of Amit. Amit face the centre. Arun sits second to the right of Leena.
II. Ali sits on the immediate left of Ali but Ken is not an immediate neighbour of Amit.
Options- A. if the data in statement I alone is sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
- B. if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
- C. if the data either in statements I alone or in statement II alone are sufficient to answer the question; and
- D. if the data given in both the statement I and II together are not sufficient to answer the question; and Discuss
Correct Answer: if the data either in statements I alone or in statement II alone are sufficient to answer the question; and
Explanation:
From I: If all of them face the centre, it means if A sits second to the left of B, then B should sit second to the right of A. But here Amit and Arun are different persons. Hence all of them do not face the centre
From II: Again suppose of them face the centre like KEN. Ali sits third to the left of ken. Now, if Amit sits on the left of Ali obviously ken should be his neighbour. But the statement says otherwise. Hence our assumption is disproved. All of them do not face the centre.
- 10. Is T grandmother of Q?
I. P is the mother Q. Q is the son of R. R is the son of T.
II. L is father of N and N is daughter of T.
Options- A. if the data in statement I alone is sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
- B. if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
- C. if the data either in statements I alone or in statement II alone are sufficient to answer the question; and
- D. if the data given in both the statement I and II together are not sufficient to answer the question; and Discuss
Correct Answer:
Explanation:
In I, Sex of T is not known. In II, Q does not figure. Hence we need both the statements to establish the relationship.
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