Warehouse W

[pbandyop]

Warehouse W's revenue from the sale of sofas was what percentage greater this year than it was last year?
1) Warehouse W sold 10% more sofas this year than last.
2) Warehouse W's selling price per sofa was $30 greater this year than last.

(1) seems sufficient to me, but the correct answer is E. Any explanation would be much appreciated. Thanks in advance.

[RonPurewal]

Warehouse W's revenue from the sale of sofas was what percentage greater this year than it was last year?
1) Warehouse W sold 10% more sofas this year than last.
2) Warehouse W's selling price per sofa was $30 greater this year than last.

(1) seems sufficient to me

nope.

it appears you're assuming that the price of the sofas is constant - a completely unfounded assumption. if you were guaranteed that the sofas were selling at the same price for which they sold last year, then (1) would mean the revenue was 10% greater ... but you have no such guarantee.

since you know nothing about the price at which the sofas sold this year vis-a-vis last year, you know nothing about the percent increase in revenue.

--

(2) doesn't help, either, because we have no information about the # of sofas sold (which is clearly a relevant concern).

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together: still not good enough, because we don't have any value to which to compare $30. for instance, if the sofas were $50 last year and $80 this year, that's going to be a very large percent increase; if sofas were $1000 last year and $1030 this year, the percent increase will be very small.

[Guest]

Warehouse W's revenue from the sale of sofas was what percentage greater this year than it was last year?
1) Warehouse W sold 10% more sofas this year than last.
2) Warehouse W's selling price per sofa was $30 greater this year than last.

(1) seems sufficient to me

nope.

it appears you're assuming that the price of the sofas is constant - a completely unfounded assumption. if you were guaranteed that the sofas were selling at the same price for which they sold last year, then (1) would mean the revenue was 10% greater ... but you have no such guarantee.

since you know nothing about the price at which the sofas sold this year vis-a-vis last year, you know nothing about the percent increase in revenue.

--

(2) doesn't help, either, because we have no information about the # of sofas sold (which is clearly a relevant concern).

--

together: still not good enough, because we don't have any value to which to compare $30. for instance, if the sofas were $50 last year and $80 this year, that's going to be a very large percent increase; if sofas were $1000 last year and $1030 this year, the percent increase will be very small.

What if we consider the # of sofas sold and their price to be 100 for the last year? Won't we be getting the required % ?

[RonPurewal]

What if we consider the # of sofas sold and their price to be 100 for the last year? Won't we be getting the required % ?

you can only pick numbers when you don't lose any generality by doing so. in other words, if varying a quantity produces different answers to a question, then you absolutely cannot settle on one numerical value for that quantity.

in general, testing only 1 value for a quantity is almost always a HORRIBLE idea on data sufficiency problems. almost every data sufficiency problem relies on differences induced by changing the value of a quantity, and this one is no exception.

you should restrict single-number-picking to problem solving questions, on which the multiple choices guarantee that you aren't missing anything. on data sufficiency, you should try a variety of values and watch what happens to the quantities in the problem.

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analogy:
what % of his original weight has dexter lost so far in 2008?
(1) dexter has lost 30 pounds so far in 2008.

here it should be fairly clear that (1) is insufficient; the higher the original weight, the lower the %.
you can't just declare that dexter originally weighed 100lbs and that he has therefore lost 30% of his weight; that would be absurd.
same reasoning applies to this problem.

[rtrsaravanan]

Just out of curiosity..

if the second statement had instead given a 30% increase in the each sofa's rate.. instead of $30.. can we say C would be answer for this question..

[RonPurewal]

Just out of curiosity..

if the second statement had instead given a 30% increase in the each sofa's rate.. instead of $30.. can we say C would be answer for this question..

yes, that would be correct.

in that case, let's say that "p" was the original price, and "q" the original quantity.
then last year's revenue was (p)(q)
and this year's is (1.3p)(1.1q) = 1.43pq
so that's a 43% increase

[mba012012]

I thought answer is C.

Instead of taking multiple values, i have given only 100$ as the price. My bad ! Loosing answers by making silly mistakes ! :(

Thanks RP !

[RonPurewal]

I thought answer is C.

Instead of taking multiple values, i have given only 100$ as the price. My bad ! Loosing answers by making silly mistakes ! :(

Thanks RP !

yeah, that's a bad move for data sufficiency. when you plug numbers on data sufficiency, always VARY the things that are VARIABLES!
if a quantity is allowed to adopt a range of values and you leave it fixed, then you may well conclude that you have a lot more definite information than you actually do.

[dedhia.neirav]

Let the cost of sofa per piece last year be C1 and this year by C2.
Let the number of sofas sold be S1 and S2.

1. S1 = 1.1S2
2. C2 = C1+30

To find = (C2S2-C1S1)/(C1S1)*100

Cannot we solve this further and obtain the increase. I marked C for the same case.

[jlucero]

Let the cost of sofa per piece last year be C1 and this year by C2.
Let the number of sofas sold be S1 and S2.

1. S1 = 1.1S2
2. C2 = C1+30

To find = (C2S2-C1S1)/(C1S1)*100

Cannot we solve this further and obtain the increase. I marked C for the same case.

First, your equation #1 is backwards. They sold MORE sofas in year two, so the equation should be 1.1S1 = S2.

Second, there's no way to completely eliminate all of the variables here to get down to a single answer:

(C2S2-C1S1)/(C1S1)*100
([C1 + 30][1.1S1] - C1S1) / (C1S1) * 100
((1.1C1S1 + 33S1 - C1S1) / C1S1) * 100
((0.1C1S1 + 33S1) / C1S1) * 100

Notice right here that when we distribute the 1.1S1 to [C1 + 30], we're left with a C1S1 and a S1 in the numerator. This makes canceling out the S1 impossible.

The logical reasoning behind this comes down to the fact that we know the increase in the price of the sofas, but have no idea what the sofas originally cost. If the sofas originally cost $1 and now cost $31, the revenue is going to be much larger the second year. Meanwhile, if the sofas originally cost a thousand dollars, then $30 extra isn't going to mean as much to the increase in revenue.