DS Ratio GMATPrep CAT

[myfish]

This one bothers me.
(1) If the ratio increases (1/2 > 1/4) means both the numerator and the denominator could change, just one more than the other, which is insufficient.
(2) The increased sum does not say what increases, insufficient.
(T) ?? This is where I lose it....

Anyone?

[Anurag@Gurome]

Refer to the post here >> https://www.beatthegmat.com/shares-of-st ... tml#461933

[jcnasia]

Si = stocks initial
Sf = stocks final
Bi = bonds initial
Bf = bonds final

The question is: Is Sf > Si?

Statement 1:
Sf / (Sf + Bf) > Si / (Si + Bi)

Let Sf = 1, Bf = 0, Si = 1, and Bi = 1,000,000, then the above statement is true, but Sf = Si.
Let Sf = 2, Bf = 0, Si = 1, and Bi = 1,000,000, then the above statement is true, and Sf > Si.
So, statement 1 is insufficient.

Statement 2:
Sf + Bf > Si + Bi

Let Sf = 1, Bf = 1,000,000, Si = 1, and Bi = 0, then the above statement is true, but Sf = Si.
Let Sf = 2, Bf = 1,000,000, Si = 1, and Bi = 0, then the above statement is true, and Sf > Si
So, statement 2 is insufficient.

Statement 1 and 2:
Sf / (Sf + Bf) > Si / (Si + Bi) => Sf/Si > (Sf + Bf)/(Si + Bi)

Sf + Bf > Si + Bi => (Sf + Bf)/(Si +Bi) > 1

Thus, Sf/Si > 1 which means Sf > Si.

This will hold true for all positive values of Si, Sf, Bi, and Bf, so Statements 1 & 2 are sufficient together.