Data Sufficiency

BTGmoderatorDC wrote:Beth and Jim each received a salary increase. If Jim's salary was increased by the same percent as Beth's salary, did Beth receive a greater dollar increase in salary than Jim?

(1) Before the increases, Jim's salary was greater than $25,000.
(2) Before the increases, Jim's salary was 4/5 of Beth's salary.
Source: GMAT Prep

$$B,J\,\,\, > 0\,\,\,\,\left[ \$ \right]\,\,\,\,\,\left\{ \matrix{
\,B \to \left( {1 + x} \right)B \hfill \cr
\,J \to \left( {1 + x} \right)J \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\left( {{\rm{increase}}:\,\,x\,\,\left( \% \right)\,\, > 0} \right)$$
$$xB\mathop > \limits^? xJ\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{x\, > \,0} \,\,\,\,\,\,\boxed{\,\,B\mathop > \limits^? J\,\,}\,$$
$$\left( 1 \right)\,\,\,\,J > 25000\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {B,J} \right) = \left( {26000,26000} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {B,J} \right) = \left( {27000,26000} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$
$$\left( 2 \right)\,\,J = {4 \over 5}B\,\,\mathop < \limits^{B\, > \,\,0} \,\,B\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

First, it is a 'Yes/No' question. We are not looking for an exact value.

Let's look at:
1) Before the increases, Jim's salary was greater than $25,000.

It does not provide any information about Beth's salary. Not sufficient.

Now, let's look at:
2) Before the increases, Jim's salary was 4/5 of Beth's salary.

It tells you a relationship between the two salaries.

Jim's salary = 4/5 * Beth's salary

Let's assume if Beth's salary is 100 then Jim's salary (4/5)*100 = 80.

The question also tells us that both received the same percentage increase in salary.

Let's say they both received a 10% raise that would mean Beth received a raise of 10 and Jim received a raise of 8 dollars.

The question asks us who received a greater increase in salary. From above it is clear Beth did.

Hence Statement 2 is sufficient. Hence, B is the correct answer.