Good one

[yalanand]

If a, b, and c are postitive numbers, is (a^2)(b + c) > (c^2)(b + a) ?

(1) a > b > c
(2) b = 10 and a + c = 1

[ontopofit]

I think its A.
wat is OA?

[yalanand]

correct but explaination?

[ontopofit]

yeah.
we have an equation with a,b and c +ve.

a^2b + a^2c > c^2a + c^2b

statement 1) - a>b>c
a>c (both being positive)
so a^2b > c^2b and a^2c > c^2a ,hence suff.

2) b=10, a+c = 1

here we know the value of b is 10 but we cant figure out which is greater of a and c.
so this statement is insuff.

hence A.

[Bidisha800]

a^2)(b + c) > (c^2)(b + a)
= (a-c)(ab+bc+ca)

if a>b>c then (a-c) >0 and (a-c)(ab+bc+ca) >0

(A) suff

b=10 and a+c=1
can't derive the value of (a-c)(ab+bc+ca) insuff


(A)

[vikram_k51]

If a, b, and c are postitive numbers, is (a^2)(b + c) > (c^2)(b + a) ?

(1) a > b > c
(2) b = 10 and a + c = 1

Question Rephrase:

Is (a^2)(b + c) > (c^2)(b + a)?

Or Is a^2*b+a^2*c>c^2*b+c^2*a

Or Is a^2*b-c^2*b>c^2*a-a^2*c

Or Is b(a^2-c^2)>ca(c-a)

Or Is b(a+c)(a-c)>ca(c-a)

Or Is b(a+c)<ac? or is ab+bc<ac?

From A:a>b>c Hence ab+ac >ac Thus Sufficient.

From B:b= 10;a+c=1;

Now A.M>=G.M

Or a+c/2>Root ac

or 1/2 > Root ac

or 1/4 > ac

Hence 10*1 >1/4 ;Thus b(a+c)>ac And sufficient

Hence D