Data Sufficiency problems
- 1. What is the three digit number?
I. Three-fifth of that number is less than that number by 90.
II. One-fourth of that number is 25% of that number
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 the 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 not sufficient
Explanation:
From Statement II,
Suppose the number be N.
N - 3N/5 = 90,
? 2N/5 = 90
N = 225
From Statement II,
N/4 = (25 x N)/100
? N/4 = N/4
So, Statement i is required.
- 2. What is the salary of A, in a group of A, B, C, D and E whose average salary is ? 65780?
I. Total of the salaries of B and C is ? 88545.
II. Total of the salaries of D and E is ? 59020.
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 the 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 both the Statement I and II together are needed to answer the question
Explanation:
From the Statement I and II.
Salary of A = 5 x 65780 - (88545 + 59020)
= 328900 - 147565 = ? 181335
Both Statement are required.
- 3. What is the profit earned by selling a watch for ? 15675?
I. Total cost price of 5 such watches is equal to selling price of 4 such watches.
II. 25% profit is earned by selling each watch.
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 the 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 either the Statement I alone or Statement II alone is sufficient to answer the question
Explanation:
From Statement I,
Selling price of watch = ? 15675
and the cost price of a watch = 15675 x 4/5
= ? 12540
? Profit = 15675 - 12540 = ? 3135
From Statement II,
Cost price of a watch
= 15675/100 + 25 x 100 = ? 12540
? Profit = 15675 - 12540 = ? 3135
- 4. What is the three digit number?
I. Two-fifth of the number is half of 204.
II. 20% of the number is 51.
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 either the Statement I alone or Statement II alone is sufficient to answer the question
Explanation:
Suppose the number be P.
From Statement I.
P x 2/5 = 1/2 x 204
? P x 2/5 = 102
? P = 102 x 5/2
? P = 255
From Statement II.
P x 20/100 = 51
? P = 51 x 100/20
? P = 255
Both statements alone are sufficient to answer the above question.
- 5. What is the area of the rectangular plot?
I. The length of the plot is 375 m.
II. The length of the plot is thrice its breadth.
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: If both Statement I and II together are needed to answer the question
Explanation:
From Statement I and II,
Length of plot = 375 m
Breadth of plot = 375/3 m = 125 m
Area of rectangular plot = Length x Breadth
Area of rectangular plot = 375 x 125 sq m = 46875 sq m
- 6. What is the minimum passing percentage in a test?
I. Raman scored 25% marks in the test and Sunil scored 288 marks which is 128 more than Raman.
II. Raman scored 64 marks less than the minimum passing marks.
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,
Marks scored by Sunil = 288 and marks scored by Raman = 288 - 128 = 160
? Maximum marks = 160 x100/25 = 640
From Statement II,
Minimum passing Marks = 160 + 64 = 224
? Minimum passing percentage
= 224 x 100 /640 = 35%
Hence, the data in both the statements necessary to answer the question.
- 7. Is granddaughter of B?
B is the father of M. M is the sister of T. T is the mother of F.
II. S is the son F. V is the daughter of F.R is is the brother of T.
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 Statements 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 given in both the Statement I and II together are not sufficient to answer the question. Discuss
Correct Answer: if the data given in both the Statement I and II together are not sufficient to answer the question.
Explanation:
Using Statement I: The gender of F is not known So, we cannot says if F is granddaughter or grandson of B.
Using Statement II: The name of B has not even been mentioned. Using both statements together.
- 8. Is it 9 o'clock now?
I. After half an hour, the minute and the hour hands of the clock will make an angle of exactly 90° with each other.
II. Exactly 15 minutes ago, the minute and the hour hands of the clock coincided with each other.
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 Statements 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 given in both the Statement I and II together are not sufficient to answer the question. Discuss
Correct Answer: if the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
Explanation:
Using Statement I: If the time is 9 o'clock now then after 30 minutes ie at 9:30 the angle between the minute and hour hand cannot be 90°. So, now time is not 9 o'clock.
Using Statement II: If the time is 9 o'clock now then after 15 minutes before the hour and minute hand of the clock can never coincide with each other Instead they will have an angle of 7.5°. So, the time now is not 90°' clock.
- 9. Are all the five friends - A, B, C, D and E - who are seated around a circular table facing the centre?
I. A sites to the left of B. B faces the centre. D and E are immediate neighbours of each other. C sits second to the right of E.
II. D sits second to right of C. C faces the centre. Both E and A are immediate neighbours of D. B sits second to the right of A.
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 Statements 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 given in both the Statement I and II together are not sufficient to answer the question. Discuss
Correct Answer: if the data in Statements II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
Explanation:
Using Statement I: We cannot determine if all the fiends are facing the centre.
A is the facing outside of C is facing the centre of circle. So, all friends are not facing the centre.
- 10. Which Bag amongst P, Q, R, S and T is the heaviest?
I. Bag Q is heavier than R and S. Bag T is heavier than only bag P.
II. Only three bags are lighter than R. The weight of bag Q is 50 kg, which is 2 kg more than bag R.
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 Statements 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 given in both the Statement I and II together are not sufficient to answer the question. Discuss
Correct Answer: if the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
Explanation:
Using Statement I:
Q > R > S > T > P,
Q is the heaviest
Using Statement II:
Q > R > S > T > P,
Q is the heaviest.
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