Data Sufficiency problems
- 1. Let PQRS be quadrilateral. Two circle 01 and 02 are inscribed in triangles PQR and PSR respectively. Circle 01 touches PR at M and circle 02 touches PR at N. Find the length of MN.
I. A Circle is inscribed in the quadrilateral PQRS.
II. The radii of the circles 01 and 02 are 5 and 6 units respectively.
Options- A. Statement I alone is sufficient to answer the question.
- B. Statement II alone is sufficient to answer the question.
- C. Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.
- D. Either Statement I or Statement I alone is sufficient to answer the question. Discuss
Correct Answer: Statement I alone is sufficient to answer the question.
Explanation:
Statement I alone is sufficient.
Statement II alone is not sufficient, for we can have more then one value of MN possible.
- 2. A, B, C, D, E and F are six integers such that E < F, B > A, A < D < B. C is the greatest integer. Is A the smallest integer?
I. E + B < A + D
II. D < F
Options- A. If statement I alone is sufficient to answer the question.
- B. If statement II alone is sufficient to answer the question.
- C. If statement I and statement II together are sufficient but neither of the alone is sufficient to answer the question.
- D. if either statement I or statement II alone is sufficient to answer the question. Discuss
Correct Answer: If statement I alone is sufficient to answer the question.
Explanation:
From statement I,
E + B < A + D, we easily say that E is less than A, because B>D and as the statement suggest E + B < A + D.
? E < A.
? A is not the smallest integer.
Statement I is sufficient to answer.
From statement II, D < F
This statement is not sufficient to find the relation between A and E.
- 3. Among six people P, Q, R, S, T and V each live on a different floor of a six storey building havng six floors numbered one to six (the ground floor is numbered 1, the floor above it, number 2 and so on and the topmost floor is numbered 6). Who lived on the topmost floor?
I. there is only one floor between the floors on which R and Q live, P lives on an even numbered floor.
II. T does not live on an even numbered floor. Q lives on an even numbered floor Q dose not live on the topmost floor.
III. S lives on an odd numbered floor. there are two floors between the floor on which S and P lives on a floor immediately above R'e floor .
Options- A. if the data is statement I and II are sufficient to answer the question while the data in statement II are not required to answer the question
- B. if the data statement I and II I are sufficient to answer the question, while the data in Statement II are not required to answer the question
- C. if the data in statements II and III are sufficient to answer the question, while the data in statement I are not required to answer
- D. if the data in all the Statement I, II and III together are necessary to answer the question Discuss
Correct Answer: if the data in all the Statement I, II and III together are necessary to answer the question
Explanation:
The data in Statement I, II and III together are necessary to answer the question .
- 4. Point D is in which direction with respect to point B?
I. Point A is to the West of point B. point C is to the North of point D is to the South of point C.
II. point G is to the south of point D. point G is 4m from point B. point D is 9 m from point B.
III. point A is to the west of point B. point B is exactly midway between point A and E. point F is to the South of point E. point D is to the West of point F.
Options- A. if the data is statement I and II are sufficient to answer the question while the data in statement II are not required to answer the question
- B. if the data statement I and III are sufficient to answer the question, while the data in Statement II are not required to answer the question
- C. if the data in statements II and III are sufficient to answer the question, while the data in statement I are not required to answer
- D. if the data in all the Statement I, II and III together are necessary to answer the question Discuss
Correct Answer: if the data in all the Statement I, II and III together are necessary to answer the question
Explanation:
The data given both the Statement I, II and II together are not sufficient to answer the question.
- 5. The re are six letter W, A, R, S, N, aad E. Is 'answer'the word formed after performing the following operations using these six letter only?
I. E is placed fourth to the right of A. S is not placed immediately next to either A or E.
II. R is placed immediately next (either left or right to E. W is placed immediately next (either left or right) to S.
III. Both N and W are placed immediately next to S. the word dose not begin with R. A is not placed immediaiately next to W.
Options- A. if the data is statement I and II are sufficient to answer the question while the data in statement II are not required to answer the question
- B. if the data statement I and II I are sufficient to answer the question, while the data in Statement II are not required to answer the question
- C. if the data in statements II and III are sufficient to answer the question, while the data in statement I are not required to answer
- D. if the data in all the Statement I,II and III together are necessary to answer the question Discuss
Correct Answer: if the data in all the Statement I,II and III together are necessary to answer the question
Explanation:
if the data in all the Statement I,II and III together are necessary to answer the question
- 6. Whose body weight is scored highest among the five boys Arun, Vinay, suraj, Raju and Pratap?
I. Average weight of Arun, Suraj and Vinay is 68 kg and average weight of Raju and Pratap is 72 kg. Also, Suraj is 78 kg, Raju is 68 kg and Vinay is 46 kg.
II. Average weight of Arun, Surai, Vinay and Raju is 68 kg and also Suraj is 78 kg, Raju is 68 kg and Vinay is 46 kg. All of them have different weight.
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,
Total weight of Arun, Suraj and Vinay = 3 x Average weight = 3 x 68 kg
? Arun's weight = 3 x 68 - (78 + 46) = 80 kg
Now, total weight of Raju and Pradeep = 2 x 72 = 144 kg
? Pratap's weight = 144 - 68 = 76 kg
? Second highest weight = 78 kg
(Suraj's weight)
From statement II,
Total weight of Arun, Suraj, Vinay and Raju = 4 x 68 = 272 kg
? Arun's weight = 272 - (78 + 68 + 46)
? Arun's weight = 272 - 192 = 80 kg
? Second highest weight = 78 kg (Suraj's weight)
- 7. What is the price of 1 dozen oranges?
I. Price of 2 dozen oranges and 1 dozen banana is $110.
II. Price of 3 dozen apples and 1 dozen banana is $170.
III. Price of 1 dozen oranges and 1 dozen apples is $95.
Options- A. Only I and II or only I and III
- B. Only I and III or only II and III
- C. Only I and II or only II and III
- D. Only II and III Discuss
Correct Answer:
Explanation:
As per given above statements , we have
Let, the price of 1 dozen oranges, 1 dozen banana and 1 dozen apples be x, y and z, respectively.
I. Price of 2 dozen oranges and 1 dozen banana = $110
? 2x + y = 110
II. Price of 3 dozen apples and 1 dozen banana = $170
? 3z + y = 170
III. Price of 1 dozen oranges and 1 dozen apples = $95
? x + z = 95
we find the price of 1 dozen oranges .So, by combining all, we get the values of x = 45.
- 8. What was the amount of profit earned?
I. 10% discount was offered on the labelled price.
II. Had there been not discount, profit would have been 30%
III. Selling price was more than the cost price by 20%
Options- A. I and either II or III
- B. Any two of the three
- C. All I, II and III
- D. Either I or II and III Discuss
Correct Answer:
Explanation:
None of the statements give the amount of labelled price or SP. So, even by combining all the statements together, question cannot be answered.
Hence ,we cannot find the amount of profit earned because all the above given information are not sufficient .
- 9. What is the cost of flooring a rectangular hall?
I. Perimeter of the hall is 76 m
II. Area of the hall is 336 m 2.
III. Cost of flooring per square metre is $550.
Options- A. I and III only
- B. II and III only
- C. Any two of the three
- D. All I, II and III Discuss
Correct Answer: II and III only
Explanation:
From above given statement , we can see that
I. Perimeter of the rectangular hall = 2 ( length + breadth ) = 76 m
? 2 ( L + B ) = 76
? L+ B = 38
II. Area of the hall = 336 m2
? length x breadth = 336 m2
III. Cost of flooring per square metre = $550.
Combining (II) and (III),
Total cost = Area of the hall x Cost of flooring per square metre
= 336 × 550 = $184800.
- 10. What is the rate of interest p.c.p.a.?
I. The amount doubles itself in 5 years on simple interest.
II. Difference between the compound interest and the simple interest earned on this amount in two years is $400.
III. Simple interest earned per annum is $2000.
Options- A. Only I
- B. Only II and III
- C. Any two of the three
- D. All I, II and III Discuss
Correct Answer:
Explanation:
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