GMATClub m17 DS

[mmslf75]

Are all angles of triangle ABC smaller than 90 degrees?

1. 2AB = 3BC = 4AC
2. AC^2 + AB^2 > BC^2


OA A

pls explain !!!

[ramsharma]

Are all angles of triangle ABC smaller than 90 degrees?

1. 2AB = 3BC = 4AC
2. AC^2 + AB^2 > BC^2


OA A

pls explain !!!

Statement 1.
Consider 2AB=3BC=4AC=12K WHERE K IS CONSTANT

NOW 2AB=12K;AB=6K SIMILARLY BC=4K AND AC=3K

SO AB:BC:AC=6:4:3

THIS IMPLIES ANGLE ACB IS MORE THAN 90 DEG(THIS ANGLE WOULD HAVE BEEN 90DEG IF THE RATIO WAS 5:4:3 AND LESS THAN 90DEG IF RATIO FIRST FIGURE WOULD HAVE BEEN LESS THAN 5)
hence statement 1 is sufficient

Statement 2.

AC^2 + AB^2 > BC^2

consider AC=AB=BC, given condition satisfied.All angle less than 90deg
now consider AC=7,AB=3,BC=5 given condition satisfied ,Angle B will be more than 90Deg

So Insufficient