Beth and Jim each received a salary increase. If Jim's salary was inc

The answer is B.

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

Lets 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 lets 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) x Beth's Salary
Lets assume if Beth's salary is 100 then Jim's salary is (4/5)*100 = 80
The question also tells us that both received the same percentage increase in salary.
Lets 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.

Conceptually...Stmt 2 tells us Beth's salary is greater than Jim's salary. If you increase two numbers (one larger than the other) by the same percent then the larger number will see a greater increase then the smaller number.

1) no info on Beth, insuff

2) you dont have to do any calculation here. you know that Beths salary was already bigger than Jims because Jims salary was 4/5 Beths. They percent of the raises were the same so x% of the bigger salary will yeild more dollars than x% of the smaller number

IMO B.

from the second statement its clear that Jims salary is less than Beth salary.

whatever be the percentage, as long as they are equal, the above statement stays the same and also, increases.

J < S.

hence x%S is always greater than x%J.

In crispy manner it can be said :-

first statement gives us no information on Beth's Salary and it actually doesn't say anything other than Jim makes more than 25k so he could make 26k or 275k.

second statement tells us who makes more money so we know who gets the bigger raise.

Hence B.
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Question : Is B's salary increase > J's
Since both the have same % of increase hence B's salary increase is > then J's increase only WHEN B's salary > J's salary

1 ) J > 25000 we dont know B. Hence Insufficient.

2) J = 4/5 B => B's salary is always > than J's which is what the question is asking. Hence B.
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If Beth’s and Jim’s salaries were increased by the same percent, the only way Beth’s increase (in dollar amount) is more than Jim’s is if Beth’s salary is more than Jim’s.

Statement One Alone:

Before the increases, Jim's salary was greater than $25,000.

Since we know nothing about Beth’s salary, we can’t determine whether Beth’s salary is more than Jim’s. Statement one is not sufficient to answer the answer.

Statement Two Alone:

Before the increases, Jim's salary was 4/5 of Beth's salary.

Since Jim's salary was 4/5 of Beth's, Beth’s salary is more than Jim’s. Statement two is sufficient to answer the question.

Answer: B
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\(B,J\,\, > 0\,\,\,\,\left[ \$ \right]\,\,\,\,\,\left\{ \matrix{\\
\,B \to \left( {1 + x} \right)B \hfill \cr \\
\,J \to \left( {1 + x} \right)J \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\left( {{\rm{increase}}:\,\,x\,\,\left( \% \right)\,\, > 0} \right)\)

\(xB\mathop > \limits^? xJ\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{x\, > \,0} \,\,\,\,\,\,\boxed{\,\,B\mathop > \limits^? J\,\,}\,\)


\(\left( 1 \right)\,\,\,\,J > 25000\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {B,J} \right) = \left( {26000,26000} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \\
\,{\rm{Take}}\,\,\left( {B,J} \right) = \left( {27000,26000} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\)


\(\left( 2 \right)\,\,J = {4 \over 5}B\,\,\mathop < \limits^{B\, > \,\,0} \,\,B\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle\)


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

Regards,
Fabio.
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