Data Sufficiency problems
- 1. Five letter A, E, G, N and R are arranged left to right according to certain conditions. Which letter is placed third?
I. G is placed second to the right of A. E is to the immediate right of G . There are only two letter between Rand G.
II. N is exactly between A and G, neither A nor G is at the extreme end of the arrangement.
Options- A. if the data in statement I alone are sufficient to answer the question , which 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 statement I alone or Statement II alone are sufficient to answer the question
- D. if the data neither in Statement I nor II together are sufficient to answer the questions Discuss
Correct Answer: if the data either in statement I alone or Statement II alone are sufficient to answer the question
Explanation:
Form Statement I,
R A G E
Clearly , the left place or empty place is filled by N .
From Statement II ,
A N G
G N A
Clearly N is at third place ,
Hence, the data in Statement I alone or in Statement II alone are sufficient to answer the question .
- 2. In how many days will B alone complete the work?
I. A and B together can complete the work in 8 days.
II. B and C together can complete the work in 10 days.
III. A and C together can complete the work in 12 days.
Options- A. Only I and II
- B. Only II and III
- C. I, II and III
- D. Data is insufficient Discuss
Correct Answer: I, II and III
Explanation:
(A + B)'s 1 day's work = 1/8 ..........(i)
(B + C)'s 1 day's work = 1/10 ..........(ii)
(C + A)'s 1 day's work = 1/12 ............(iii)
Add the equation (i), (ii), (iii)
2(A + B + c)'s 1 day's work = 1/8 + 1/10 + 1/12
(A + B + C)'s 1 day's work = 1/2[1/8 + 1/10 + 1/12] ..........(iv)
Subtracting Eq. (iii) from Eq. (iv), we get B's 1 day's work.
then, required number of days = 1/(B's 1 day's work) .
So we need all above 3 statements to solve the given question.
- 3. What is the rate of interest percentage per annum?
I. An amount doubles itself at simple interest in 10 yr.
II. Difference between the compound interest and simple interest on an amount of ? 15000 in 2 yr is ? 150.
III. The compound interest calculated after 8 yr is more than the amount principle.
Options- A. Only I
- B. Only II
- C. Ii and III
- D. I and III Discuss
Correct Answer:
Explanation:
From Statement I,
SI = PRT/100
? P = (P x R x 10)/100
? R = 10%
From Statement II,
Difference (D) = PR2/(100)2
? 150 = (15000 x R2)/10000
? R = 10%
Thus, either Statement I or II is sufficient.
- 4. What is the mark scored by Abhijit in English?
I. Marks scored by Abhijit In Mathematics are more than his marks in Science by 20.
II. Total marks scored by Abhijit in Mathematics, Science and English are 197.
III. Marks scored by Abhijit in Science are more than his marks in English by 12.
Options- A. Any two of the three
- B. II and III
- C. I, II and III
- D. Data is insufficient Discuss
Correct Answer: I, II and III
Explanation:
From Statement I and III,
Let marks in English be x
Marks in Science = x + 12
and marks in Mathematics = x + 32
From Statement II,
E + S + M = 197
x + x + 12 + x + 32 = 197
? 3x + 44 = 197
? 3x = 197 - 44 = 153
? x = 51
? Marks in English = 51
- 5. In how many days will Y alone complete the work?
I. X and Y together can complete the wok in 8 days.
II. Y and Z together can complete the work in 10 days.
III. X and Z together can complete the work in 12 days.
Options- A. Only I and II
- B. Only II and III
- C. I, II and III
- D. Data is insufficient Discuss
Correct Answer: I, II and III
Explanation:
(X + Y)'s 1 day's work = 1/8 ..(i)
(Y + Z)'s 1 day's work = 1/10 ...(ii)
(Z + X)'s 1 day's work = 1/12 ..(iii)
Adding equations i , ii , iii
2(X + Y + Z)'s 1 day's work = 1/8 + 1/10 + 1/12
(X + Y + Z)'s 1 day's work
= 1/2[1/8 + 1/10 + 1/12] ..(iv)
Subtracting Eq. (iii) from Eq. (iv), we get Y's 1 day's work,
Then, required number of days
= 1/Y's 1 day's work
- 6. What is Supriya's present age?
I. Supriya is 3 yr older than Priya.
II. The ratio of Priya's, Reshma's age is 3 : 4
Options- A. If the data given in Statement I alone is sufficient to answer the question whereas the data given in Statement II alone is not sufficient to answer the question
- B. If the data given in Statement II alone is sufficient to answer the question whereas the data given in Statement I alone is 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 Statement I and II are not sufficient to answer the question Discuss
Correct Answer: If the data in both the Statement I and II are not sufficient to answer the question
Explanation:
Data are not sufficient even from Statement I and II both.
- 7. What is the rate of interest percentage per annum?
I. An amount of ? 6200 fetches simple interest of ? 1736 in 2 yr.
II. An amount of ? 4500 fetches compound interest of ? 1348.20 in 2 yr.
Options- A. If the data given in Statement I alone are sufficient to answer the question whereas the data given in Statement II alone are not sufficient to answer the question
- B. if the data given in Statement II alone are sufficient to answer the question whereas the data given 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 Statement 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,
R = (SI x 100) / (P x T)
? (1736 x 100)/(6200 x 2) = 14%
From Statement II,
1348.2 4500(1 + r/100)2 - 4500
? 1348.2 + 4500 = 4500(1 + r/100)2
? 5848.2 = 4500((1 + r/100)2
? 5848.2/4500 = (1 + r/100)2
? 3249/2500 = (1 + r/100)2
? (57/50)2 = (1 + r/100)2
? 1 + r/100 = 57/50
? r/100 = 57/50 - 1 = 7/50
? r = 7 x 100/50
? r = 14%
Both statement are alone sufficient.
- 8. How many marks did Nigam get in Biology?
I. Nigam got 42 marks in English which were half the marks he got in Biology.
II. Nigam's marks in Biology were 14% of the total marks he got in all the subjects together.
Options- A. If the data given in Statement I alone are sufficient to answer the question whereas the data given in Statement II alone are not sufficient to answer the question
- B. if the data given in Statement II alone are sufficient to answer the question whereas the data given 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 Statement I and II are not sufficient to answer the question Discuss
Correct Answer: If the data given in Statement I alone are sufficient to answer the question whereas the data given in Statement II alone are not sufficient to answer the question
Explanation:
Data given in Statement I alone are sufficient to answer the question
- 9. What is the speed of the boat in still water?
I. The boat travels at the speed of 4km/h upstream.
II. The boat travels at the speed of 6km/h downstream.
Options- A. If the data given in Statement I alone are sufficient to answer the question whereas the data given in Statement II alone are not sufficient to answer the question
- B. if the data given in Statement II alone are sufficient to answer the question whereas the data given 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 Statement I and II are not sufficient to answer the question Discuss
Correct Answer:
Explanation:
We know that,
Speed of boat in still water
= (Speed upstream + Speed downstream)/2
From Statements I and II,
Speed = (6 + 4)/2 = 10/2 = 5 km/h
So, answer can be determined from both statements.
- 10. The ages of Anand and Sujeet are in the ratio of 6 : 5. What is the age of Anand?
I. The ages of Anand and Sandeep are in the ratio of 10 : 7 .
II. After 5 yr, the ratio of Anand's and Sujeet's ages will be 7 : 6 .
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 II alone is sufficient to answer the question but the Statement I alone is not sufficient
Explanation:
From Statement II,
The ratio of their ages after 5 yr is 7 : 6
So, (6k + 5) / (5k + 5) = 7/6
? 36k + 30 = 35k + 35
? 36k - 35k = 35 - 30
? k = 5
? Age of anand = 6 x 5 = 30 yr
So, Statement II is alone sufficient.
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