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Please provide a detailed solution for this problem

by Architj » Tue Apr 21, 2015 6:19 am
In a certain mattress store, each week fiona earns a salary of $360 plus 5 percent of the amount of her sales which exceeds $900 for that week. what is the difference in the amounts of sales of fiona in week W1 and week W2?

I. the difference of fiona's earnings in W1 and W2 was $60.
II. in W1 as well as in W2, the amount of fiona's sales exceeded $900.
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Source: — Data Sufficiency |
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by MartyMurray » Mon May 25, 2015 8:57 am
Architj wrote:In a certain mattress store, each week fiona earns a salary of $360 plus 5 percent of the amount of her sales which exceeds $900 for that week. what is the difference in the amounts of sales of fiona in week W1 and week W2?

I. the difference of fiona's earnings in W1 and W2 was $60.
II. in W1 as well as in W2, the amount of fiona's sales exceeded $900.
This question is cool because one can be tempted to think that Statement 1 is sufficient, when actually it's not.

Statement 1 basically says that in at least one of the weeks she earned more than $900. That's the only way her pay can go up. In addition, she had to earn enough over $900 that she got $60 in commission.

$60/.05 = $1200. So to get $60 in commission, she needed to earn at least $1200 more than $900.

However we can't determine exactly what she made in either week.

She could have made ANY AMOUNT less than $900 in sales in one week and $900 + $1200 = $2100 in sales the next week. That would result in her making $60 more in the higher sales week. So she could have made $500 in sales the first week and $2100 in sales the other week. Or she could have made $800 in sales in one week and $2100 in sales the other week. Either way, for the lower sales week should would get paid $360, and for the higher sales week she would get $360 + $60.

We could also look at scenarios in which she would earn over $900 both weeks, but it's not necessary to do that as we already have multiple sales scenarios that create the same pay result.

So Statement 1 is insufficient.

Statement 2 tells us only that her sales for each week were both over $900. Any numbers over $900 would work.

So Statement 2 is insufficient.

Using the statements combined we know from Statement 2 that her sales were over $900 both weeks. In that case, for her commission to go up by $60, as per Statement 1, her sales had to go up exactly $1200.

So combined the statements are sufficient to answer the question.

Choose C.
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by nikhilgmat31 » Mon May 25, 2015 8:53 pm
Option A seems very tempting, I also thought of 1200 at first place & marked it wrongly :(
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by GMATGuruNY » Tue May 26, 2015 2:24 am
Architj wrote:In a certain mattress store, each week fiona earns a salary of $360 plus 5 percent of the amount of her sales which exceeds $900 for that week. what is the difference in the amounts of sales of fiona in week W1 and week W2?

I. the difference of fiona's earnings in W1 and W2 was $60.
II. in W1 as well as in W2, the amount of fiona's sales exceeded $900.
Let W� = total Week 1 sales, W₂ = total Week 2 sales, and x = the sales amount in Week 2 that exceeds $900.

Statement 1:
Test one case that also satisfies statement 2.
Case 1: W� = 1000.
Amount that exceeds $900 = 1000-900 = $100.
Commission in W� = 5% of 100 = 5.
Since $60 more is earned in Wâ‚‚, the commission in Wâ‚‚ = 5+60 = 65.
Since $65 is equal to a 5% commission on the amount that exceeds $900, we get:
65 = (5/100)x
x = 6500/5 = $1300.
Thus, Wâ‚‚ = x + 900 = 1300+900 = 2200.
Resulting difference:
W₂ - W� = 2200-1000 = 1200.

Test one case that DOESN'T also satisfy statement 2.
Case 2: W� = 0, implying that no commission is earned in Week 1.
Since $60 more is earned in Wâ‚‚, the commission in Wâ‚‚ = 60.
Since $60 is equal to a 5% commission on the amount that exceeds $900, we get:
60 = (5/100)x
x = 6000/5 = $1200.
Thus, Wâ‚‚ = x + 900 = 1200+900 = 2100.
Resulting difference:
W₂ - W� = 2100-0 = 2100.

Since W₂ - W� can be different values, INSUFFICIENT.

Statement 2 is clearly insufficient on its own.

Statements combined:
As Case 1 illustrates, when both statements are satisfied, W₂ - W� = 1200.
SUFFICIENT.

The correct answer is C.

An important take-away:
Always consider how the two statements might AFFECT EACH OTHER -- especially when one of the statements is clearly insufficient on its own.
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