Data Sufficiency

Question #17 (incorrect)

Rent in an office building is directly proportional to the product of the square footage of the office and the number of years on the lease. What is the rent for a 3 -year lease on an 8400 square foot office?

A) 5-year lease for an 8000 square foot office is 150000 more than a 5-year lease for a 7000 square foot office.
B) Rent for a 12000 square foot office for a lease of n years is 720000 , and rent for an 18000 square foot office for the same number of years is 1080000.


A is definitely Sufficient
B => once you solve the equation, you will get constant*n = 60.

Is B sufficient or not?

Thanks

voodoo_child wrote:Question #17 (incorrect)

Rent in an office building is directly proportional to the product of the square footage of the office and the number of years on the lease. What is the rent for a 3 -year lease on an 8400 square foot office?

A) 5-year lease for an 8000 square foot office is 150000 more than a 5-year lease for a 7000 square foot office.
B) Rent for a 12000 square foot office for a lease of n years is 720000 , and rent for an 18000 square foot office for the same number of years is 1080000.


A is definitely Sufficient
B => once you solve the equation, you will get constant*n = 60.

Is B sufficient or not?

Thanks

B is not sufficient. Since we need to know the value of constant which is not possible to find if we go by the condition in B.

Agreed. B just tells you that multiplying the square feet by 1.5 also multiplies the rent by 1.5. This is essentially the definition of things being directly proportional. If this were sufficient, we could solve it without any statements at all, which of course is never the case on the GMAT

I have a different opinion. Using B), one can calculate (no of years) * (Constant) = 60. I think that this equation is sufficient to answer the question.

For instance, # of sq. feet = 1400; and number of years = 5; If I need to calculate total rent,

Total rent = (1400) * (5) * (Constant);

Now, I know that (5 * constant) = 60.

Hence, Constant = 12.

There Total rent could be calculated....Isn't it?

No. Remember that n refers to some specific number of years relating to the scenarios in Statement 2. When you use statement 2 to calculate k*n=60, the constant k=60/n. But that is for that specific value of n, whatever that is, not just any number of years you want to plug in. If we knew what it was we could get k, but we don't, so we can't.

What's more, if you solve the equation that comes from statement 1, k=30. So that's what the constant is in every case. It doesn't change with different values, or else it wouldn't be a constant. That conflicts with your example. I know we're not supposed to be using Statement 1, but it does show a problem with your reasoning, because the two statements are not supposed to conflict.

voodoo_child wrote:Question #17 (incorrect)

Rent in an office building is directly proportional to the product of the square footage of the office and the number of years on the lease. What is the rent for a 3 -year lease on an 8400 square foot office?

A) 5-year lease for an 8000 square foot office is 150000 more than a 5-year lease for a 7000 square foot office.
B) Rent for a 12000 square foot office for a lease of n years is 720000 , and rent for an 18000 square foot office for the same number of years is 1080000.


A is definitely Sufficient
B => once you solve the equation, you will get constant*n = 60.

Is B sufficient or not?

Thanks

B is cyclical logic, and doesn't tell you anything you don't already know: if you multiply the number of square feet times 1.5 (from 12000 to 18000), the rent will also increase times 1.5 (from 72 Hundred Thousand to 108 HT). This is the definition of a direct proportion, but doesn't actually tell you anything new. You can use the info in B to find the rent for a n-year lease on a 8400 sq. foot office, but you can't find n from this, which is what you need in order to extrapolate a 3 year lease on an 8400.