The data in Statement I, II and III together are necessary to answer the question .
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.
Statement I alone is sufficient.
Statement II alone is not sufficient, for we can have more then one value of MN possible.
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.
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.
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)
The data given both the Statement I, II and II together are not sufficient to answer the question.
if the data in all the Statement I,II and III together are necessary to answer the question
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)
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.
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 .
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