LUANDATO wrote:Balls of equal size are arraged in two rows to form an equilateral triangle. The top most row consist of one ball, the second row of two balls and so on. If 669 balls are added, then all the balls can be arreged in the shape of square and each of the sides of the square contain 8 balls less than the each of the side of the triangle did. How many balls made up the triangle?

A. 1540
B. 2209
C. 2878
D. 1210
E. 1560

The OA is A.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

Clearly by adding 669 to the area of triangle we should get a perfect square number
Let us try from top
Biggest number is 2878
2878+ 669 gives a number whose units digit would be 7 and there cannot be any number whose perfect square has 7 as its units digit. Therefore 2878 is ruled out.
Next is 2209
2209 + 669 gives a number whose units digit would be 8 and there cannot be any number whose perfect square has 8 as its units digit. Therefore 2209 is ruled out.
Left over numbers are 1560, 1540 and 1210
Adding 669 we will get 2229, 2209 and 1879. Here we will check which one is perfect square. Here units digit is 9 which means the number should have units digit as 7 or 3.
Now we know 50^2 is 2500 so number should be less than 50 and ending in 7 or 3
So let us check 47 and 43
47^2= 2209 which exactly matches with our option A =1540 because 1540+669=2209
and 43^2 is 1849 which does not with any of the options .
hence A is correct option.

[for your satisfaction you may check the number of balls in the triangle also whose each side=47+8=55
No. of balls in the triangle= (55/2)*(1+55)= 55*28= 1540]