# Official Quant Thread for CAT 2012Quantitative Report

Please continue here for all the Quant queries and discussions.
Part 1
Part 2
http://www.pagalguy.com/forum/quantitative-questions-and...
59 59
Page 3493 of 3737
Page 3494 of 3737
@Stoicalme said: 1) a and b are natural numbers such that a > b > 1. If 8! is divisible by a^2 â€” b^2, then how many such sets (a, b) are possible? a 5 b 6 c 7 d 8 2) The lines y = 3x and x + y = 40 and the x axis bound a triangular area. Find the total number of points on or inside this triangle with integral coordinates. a 600 b 641 c 655 d 662 e 625 _____/\_____
8! = 2*2^2*2^2*2^2*3^2*5*7
3^2*2^2, 4^2*2^2, 4^2*3^2, 8^2*3^2, 6^2*2^2, 6^2*4^2, 12^2*2^2 =>7 pairs

2-
after solving 3 equations we got vertices of triangle as (0,0), (40,0), (10, 30)

draw a line from (10,30) perpendicular to x axis

we got 2 triangles (0,0), (10,0), (10,30) and (10,0) (40,0) and (10,30)

so required coordinates will be
[(11*31 - hcf(10 30)+1)/2 + hcf(10 30)+1] + [(31*31 - hcf(30 30)+1)/2 + hcf(30 30)+1)] - 31 points counted twice

= 176 + 496 - 31 = 641
I don't have time to hate people who hate me, because I am too busy in loving people who love me.
Page 3495 of 3737