Deepu has certain number of Flowers. It is not less than 15 and not more than 30. If she wants to give these flowers equally to two of her friends, then one flower remains. If she wants to give these flowers equally to three of her friends, then two flowers remain. If she wants to give these flowers equally to four of her friends, then three flowers remain. The number of Flowers with Deepu is

Options

A. 11
B. 35
C. 25
D. 23

Answer

D

Explanation

`15 lt` Number of Flowers `lt 30 ` (Given)
According to the question Number of flowers = `X (2) + 1 ... (i) `
Number of flowers = `X (3) + 2 ... (ii) `
and Number of flowers = `X (4) + 3 ... (iii) `
i.e. Number of flowers = `X (2)-1 `
So, it is equal to `{(L.C.M. of 2, 3, 4) x} - 1 `
or, `12x – 1`, where `x = 1, 2, 3 ` ...
or, 11, 23, 35,...
But, number of flowers must lies between 15 and 30. (Given)
So, Only 23 satisfies Therefore, required number of flowers with Deepu = 23
Another way : Hit and Trial Method:
`15 lt` Number of Flowers `lt 30 `(Given)
So, possible choices are 25 and 23
So, from the given choices, it is clear that only 23 satisfies all the conditions.
i.e.` 23/2 = 11 `and remainder 1,
`23/3 = 7 `and remainder 2
and `23/4 = 5 ` and remainder 3
So, required number of Flowers with Deepu = 23