Data Sufficiency
- 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.
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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 Option: A
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.
- 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.
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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)(n -1)
⇒ x + n = 57 .............(i)
Hence, the value of x cannot be found. So, I alone is not sufficient.
Consider statement II 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 sufficient as the value of x can be found by solving (i) and (ii)Correct Option: C
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)
- 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.
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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 Option: B
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.
Direction: are followed by two statements labelled as I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:
- 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]
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Given 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.Correct Option: E
Given 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.
- 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.
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Statement I alone is sufficient.
Statement II alone is not sufficient, for we can have more then one value of MN possible.Correct Option: A
Statement I alone is sufficient.
Statement II alone is not sufficient, for we can have more then one value of MN possible.
