Aman verma wrote:Q: A Domino was build using match-boxes.All the matchboxes were arranged in the form of an equilateral triangle i.e one matchbox in the front row , 2 matchboxes in the second row,3 matchboxes in the third row, 4 matchboxes in the fourth row and so on . If 669 more matchboxes are added in such a way that all the matchboxes are now in the form of a square and each of the sides now contain 8 matchboxes less than each side of the equilateral triangle, then ,initially ,how many matchboxes were there:
a) 2056
b)1540
c)1400
d)1220
e)1115
Note: I guess everybody knows what a domino is .
Let there be x matchboxes put in n such rows that made an equilateral triangle, so that
n/2 (n + 1) = x, the longest row here would be containing the maximum, n matchboxes to it, if 1 unit is the length of each matchbox (
may I assume that the matchboxes are put along its lengths and also that these are square?), then n is the side of the equilateral triangle so formed. Now we have to imagine a square of side (n - 8), such that
(n - 8)^2 = x + 669, and we're to find x.
Can we do n/2 (n + 1) = (n - 8)^2 - 669, first?
OK, so n^2 - 33 n - 1210 = 0
Or (n + 22) (n - 55) = 0
Or n = 55, and hence x = n/2 (n + 1) = 55 × 28 = [spoiler]
1540[/spoiler].
[spoiler]
B[/spoiler]
If that's the OA then the question really challanges our general awareness about all sorts of matchboxes in the world, too!
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
