Data Sufficiency

srcc25anu wrote:What is Sarah's annual income.

1. Sarah and Mary earn an annual income in the ratio of 4:3.

2. Sarah and Mary spend money in the ratio of 3:2 and together save $20,000, annually.

[spoiler]OA: E[/spoiler]

Target question: What is Sarah's annual income?

Let S = Sarah's annual income
Let M = Mary's annual income
Let x = the amount Sarah spends each year
Let y = the amount Mary spends each year

Rephrased target question: What is the value of S?

Statement 1: Sarah and Mary earn an annual income in the ratio of 4:3
In other words: S/M = 4:3
Cross multiply to get 3S = 4M
Simplify: 3S - 4M = 0
We can't find the value of S, so statement 1 is NOT SUFFICIENT

Statement 2: Sarah and Mary spend money in the ratio of 3:2 and together save $20,000, annually.

Sarah and Mary spend money in the ratio of 3:2
We get x/y = 3/2
Simplify to get: 2x - 3y = 0

Together they save $20,000 annually
Sarah's savings + Mary's savings = 20,000
(S - x) + (M - y) = 20,000

We can't find the value of S, so statement w is NOT SUFFICIENT

Statements 1 and 2 combined:
We now know that:
3S - 4M = 0
2x - 3y = 0
(S - x) + (M - y) = 20,000

Since we have 3 equations and 4 unknowns, we cannot solve this system for S.
So, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent