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Bunuel
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Both of the answers above already got E, and they're right, but I think this question is worth slowing down on, because the trap is subtle in a specific way.

Set it up: Steven's raw increase each year is some fixed amount, call it d. Stuart's increase in year 2 is T0(1+r)r, where T0 is his starting salary and r is his fixed growth rate. The question stem gives you one equation connecting them: d equals T0(1+r)r. That's the only bridge between the two people, and neither statement touches it directly.

1. Statement 1 says Steven's salary after 2 years was 20 percent more than his starting salary. So S0 + 2d = 1.2 S0, which gives d = 0.1 S0, or S0 = 10d. Now you know Steven's starting salary in terms of d. You know nothing about Stuart. Not sufficient.

2. Statement 2 says Stuart's year-2 increase was 11 percent of his starting salary. So T0(1+r)r = 0.11 T0, which simplifies to (1+r)r = 0.11, giving r = 0.1. Notice T0 cancels out completely, so you get Stuart's growth rate but never his salary. Not sufficient.

3. Combine them. Now S0 = 10d, and from the stem equation, T0 = d divided by 0.11. So S0 minus T0 works out to d times 10/11. That's a clean relationship, but d itself was never pinned to an actual dollar figure anywhere in the problem, and every number in this question is a percentage. Scale every salary by any constant and both statements still hold. E.

One-line takeaway: when a DS question is built entirely out of percentages with no dollar figure anywhere, check whether you actually have a value or just a relationship between values.
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Stevens salary A, increasing by $x each year
Stuarts salary B, increasing by y% each year.
We know that stuards increase at the end of the third year is the same as the first year, so just x. And we know that Stuards increase is his percent comounded.
We want to find the difference in salaries from their starting postitions, meaning we have to somehow solve for A and B.

X=B(1 + y/100)(1 + y/100)


I) (A+2x-x)/x = (1) equation, (2) unknowns, N.S.

II) (B(1 + y/100)(1 + y/100))-B / B = (1) equation, (2) unknowns, N.S.

I+II) = (2) equation, (2) unknowns, N.S.
Bunuel
­Steven and Stuart took a job in different companies at the same time. Steven’s salary increased by a fixed amount at the end of every year and Stuart’s salary increased by a fixed percentage at the end of every year. If the increase in the salary of Steven at the end of the third year was equal to the increase in the salary of Stuart at the end of the second year, what was the difference in the salaries of Steven and Stuart when they took the job?

(1) Steven’s salary after 2 years was 20% more than the salary at which he took the job

(2) The increase in the salary of Stuart at the end of the second year was 11% of the salary at which he took the job.


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