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- Question
- Given below is an equation where the letters represent digits. (PQ) . (RQ) = XXX. Determine the sum of P + Q + R + X.
I. X = 9.
II. The digits are unique. [3]
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.
- Correct Answer
-
ExplanationGiven relationship is (PQ)(RQ) = XXX
Since X can take 9 values from 1 to 9 hence we have 9 possibilities
111 = 3 x 37 444 = 12 x 37 777 = 21 x 37
222 = 6 x 37 555 = 15 x 37 888 = 24 x 37
333 = 9 x 37 666 = 18 x 18 999 = 27 x 37
But out of these 9 cases only in 999, we get the unit's digit of two numbers the same. Since it is a unique value, hence we need neither statement I nor statement II to answer the question. - 1. Ram is taller than Shyam and Jay is shorter than Vikram. Who is the shortest among them?
I. Ram is the tallest.
II. Shyam is taller than Vikram.
Options- A. if the data in Statement I alone is sufficient to answer the question but the data in Statement II alone is not sufficient to answer the question.
- B. if the data in Statements II alone is sufficient to answer the question but the data in Statement I alone is not sufficient to answer the question.
- C. if the data in Statement I and II together are necessary to answer the question.
- D. if the data in Statement I and II together are not sufficient to answer the question. Discuss
- 2. What is the average height of the class?
I. Average height of the class decreases by 1 cm i we exclude the tallest person of class whose height is 56 cm.
II. Average height of the class increase by 1 cm if we exclude the shortest person o the class whose height is 42 cm.
Options- A. if the data in Statement I alone is sufficient to answer the question but the data in Statement II alone is not sufficient to answer the question.
- B. if the data in Statements II alone is sufficient to answer the question but the data in Statement I alone is not sufficient to answer the question.
- C. if the data in Statement I and II together are necessary to answer the question.
- D. if the data in Statement I and II together are not sufficient to answer the question. Discuss
- 3. Salary of A and B is in ration 3:4 and expenditure is in ratio 4:5. What is the ratio of their saving?
I. B's saving is 25% of his salary.
II. B's salary is ? 2500.
Options- A. if the data in Statement I alone is sufficient to answer the question but the data in Statement II alone is not sufficient to answer the question.
- B. if the data in Statements II alone is sufficient to answer the question but the data in Statement I alone is not sufficient to answer the question.
- C. if the data in Statement I and II together are necessary to answer the question.
- D. if the data in Statement I and II together are not sufficient to answer the question. Discuss
- 4. ?ABC and ?PQR are congruent
I. Area of ?ABC and ?pPQR are same
II. ?ABC and ?PQR are right angle Triangles.
Options- A. if the data in Statement I alone is sufficient to answer the question but the data in Statement II alone is not sufficient to answer the question.
- B. if the data in Statements II alone is sufficient to answer the question but the data in Statement I alone is not sufficient to answer the question.
- C. if the data in Statement I and II together are necessary to answer the question.
- D. if the data in Statement I and II together are not sufficient to answer the question. Discuss
- 5. Is 'Ube' positive?
I. a + b is positive.
II. a - b is positive.
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 both statement I and II together are necessary to answer the question.
- D. if both statement I and II together are not sufficient to answer the question. Discuss
- 6. 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
- 7. 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
- 8. 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
- 9. 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
- 10. 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
Data Sufficiency problems
Search Results
Correct Answer: if the data in Statements II alone is sufficient to answer the question but the data in Statement I alone is not sufficient to answer the question.
Explanation:
Given that Ram > Shyam, Vikram > Jay.
Hence from this we can conclude that neither Ram nor Vikram is the shortest. And we have to find the shortest. And we have to find the shortest among them:
Consider statement alone:
We know that that Ram is not the shortest, either Shyam or Jay is the shortest.
Hence (I) alone is not sufficient.
Consider statement I alone Shyam > Vikram.
From the given information and the information in (II), we get Ram > Shyam > Vikram > Jay.
Hence, (II) alone is sufficient.
Correct Answer: if the data in Statement I and II together are necessary to answer the question.
Explanation:
Let x be the average height of the class and n be the number of students in the class.
Consider statements I alone
xn - 56 = (x + 1)(x -1)
? x + n = 57 .............(i)
Hence, the value of x cannot be found. So, I alone is not sufficient.
Consider statement I alone:
xn - 42 = (x + 1)(n - 1)
? x - n = 41 .............(ii)
Hence, the value of x cannot be found. So, II alone is not sufficient.
Both the statements together are suficient as the value of x can be found by solving (i) and (ii)
Correct Answer: if the data in Statement I alone is sufficient to answer the question but the data in Statement II alone is not sufficient to answer the question.
Explanation:
Given that their salaries are in the ratio of 3:4 and expenditure is in the ratio of 4:5 hence we can assume that salary of A and B are 3x and 4x and their expenditures are 4y and 5y.
Now we need to find the ratio of (3x - 4y)/(4x - 5y)
Consider statement I alone:
Giving of B is 25% of his salary hence his expenditure must be 75% so 3/4(4x) = 5y or 3x = 5y from this we can find the required ratio hence this statement is sufficient.
Consider statement II alone :
Given that 4x = 2000 or x = 500 but from this we can not find the value of y and hence we can not find the ratio of their savings.
Correct Answer: if the data in Statement I and II together are not sufficient to answer the question.
Explanation:
Consider Statement I alone
Given that Area (?ABC) = Area(?PQR) since nothing about the sides or angles is mentioned, we can not say if they are congruent.Hence, I alone is not sufficient.
Consider Statement II alone
?ABC and ?PQR are right triangles. Nothing about the sides is given, Hence, II alone is not sufficient. Now using both I and II
Now we have two right angled triangle k with same area we may have different combination as only product of base and height is same. Hence even by using both the statement we can not find the answer.
Correct Answer: if both statement I and II together are not sufficient to answer the question.
Explanation:
If we look at statement I then we will get
If a = 3 and b = 2, a + b > 0. Here b > 0
If a = 3 and b = -2, a + b > 0. Here b < 0
Hence I alone is not sufficient.
Now if we look at Statement II only then we will get
if a = 3 and b 2, a - b > 0. Here b > 0
If a = 3 and b = -2, a - b > 0. Here b < 0
Hence II alone is not sufficient.
Now by using statements I and II together
If a = 3 and b = 2, a - b > 0 and a + b > 0. Here b > 0
If a = 3 and b = -2, a - b > 0. and a + b > 0. Here b < 0.
Hence I and II together are also insufficient.
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.
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.
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 .
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.
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
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