Symbiosis National Aptitude Test SNAP 2012 Paper

Question : 31 of 150

Marks: +1, -0

Balls are arranged in rows to form an equilateral triangle.
The first row consists of one ball, the second row consists of two balls and so on. If 669 more balls are added, then all the balls can be arranged in the shape of a square and each of the sides contains 8 balls less than each side of the triangle had. The initial number of balls is

1600
1500
1540
1690

Validate

Solution:

1600 + 669 = 2269 = Not a perfect square
1500 + 669 = 2169 = Not a perfect square
1540 + 669 = 2209 = Square of 47
1690 + 669 = 2359 = Not a perfect square
Thus, by adding 669 to each of the alternatives, we note that 1540 + 669 = 2209, and this is the only square number.
So each side of the square contains

√{2209}

= 47 balls
∴ Each side of the triangle will contain 55 balls.
Thus the triangle will contain
1 + 2 + 3 + ... + 55 =

{55(55+1)}/2

= 1540 balls

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