pradeepkaushal9518 wrote:If the total cost of a housing project with f units is $1,750,000, what was the cost per unit for the housing project?
(1) If half as many units were built for the same total price, the cost per unit would be $250,000.
(2) If six more units had been built for the same total price, the cost per unit would be $3,750 less.

total for f units= $1,750,000

if f/2 houses were built, then cost per unit is $250,000
so $250,000 * f/2 = total cost = $1,750,000
so f/2 = 7
f=14
CPU can be found..

If six more units had been built for the same total price, the cost per unit would be $3,750 less.
f+6 then CPU is $3,750 less.
here there are 2 variables, f and CPU. and we have 2 equations
f*CPU = $1,750,000
(f+6)*(CPU-3750) = $1,750,000

Hence solvable..

Pick D

kvcpk wrote:

pradeepkaushal9518 wrote:If the total cost of a housing project with f units is $1,750,000, what was the cost per unit for the housing project?
(1) If half as many units were built for the same total price, the cost per unit would be $250,000.
(2) If six more units had been built for the same total price, the cost per unit would be $3,750 less.

total for f units= $1,750,000

if f/2 houses were built, then cost per unit is $250,000
so $250,000 * f/2 = total cost = $1,750,000
so f/2 = 7
f=14
CPU can be found..

If six more units had been built for the same total price, the cost per unit would be $3,750 less.
f+6 then CPU is $3,750 less.
here there are 2 variables, f and CPU. and we have 2 equations
f*CPU = $1,750,000
(f+6)*(CPU-3750) = $1,750,000

Hence solvable..

Pick D

@kvcpk

I know this might sound a bit nerdy, but I have this internal battle all the time. For stmt 2, we would get a quadratic equation in f, how do we know that both the values of f will not be positive, because if there are two positive values of f, then stmt 2 alone does not solve the question ...... so usually I end up solving the question, to roughly figuring out the roots .but that involves time? What is your take?

Any experts would like to chip in?

@mj78ind - Good question.. I request experts to comment..

want to be included on expert's comments as well. thanks

mj78ind wrote:

kvcpk wrote:

pradeepkaushal9518 wrote:If the total cost of a housing project with f units is $1,750,000, what was the cost per unit for the housing project?
(1) If half as many units were built for the same total price, the cost per unit would be $250,000.
(2) If six more units had been built for the same total price, the cost per unit would be $3,750 less.

total for f units= $1,750,000

if f/2 houses were built, then cost per unit is $250,000
so $250,000 * f/2 = total cost = $1,750,000
so f/2 = 7
f=14
CPU can be found..

If six more units had been built for the same total price, the cost per unit would be $3,750 less.
f+6 then CPU is $3,750 less.
here there are 2 variables, f and CPU. and we have 2 equations
f*CPU = $1,750,000
(f+6)*(CPU-3750) = $1,750,000

Hence solvable..

Pick D

@kvcpk

I know this might sound a bit nerdy, but I have this internal battle all the time. For stmt 2, we would get a quadratic equation in f, how do we know that both the values of f will not be positive, because if there are two positive values of f, then stmt 2 alone does not solve the question ...... so usually I end up solving the question, to roughly figuring out the roots .but that involves time? What is your take?

Any experts would like to chip in?

I understand your concern, but think about the situation in Statement 2. Fixed total cost of 1,750,000 for f units. If 6 more units are built, the cost per unit decreases by $3750. How could there be two positive values of f that would work? There can be only one positive value of f that, if increased by 6, would reduce the cost per unit by $3750.

So solving the quadratic would be a waste of your time.

In fact, no math at all is needed for statement 2. Since there could be only one positive value of f that, if increased by 6, would reduce the cost per unit by $3750, statement 2 is clearly sufficient. No need to set up any equations.

I think that we have to make a distinction between math problems that are about pure math and those that are about the real world.

If a DS question asks, "What is the value of x?", and statement 1 says that x^2 = 25, then x= 5 or x=-5. Insufficient.

If a DS question asks, "If a room contains x people, what is the value of x?", and statement 1 says that "If each person in the room were to bring his/her significant other, the room would contain 25 people", then x^2=25 and x=5, because the problem is restricted to positive integers. (We can't have -5 people in the room). Sufficient.

The GMAT writers expect you to understand how a math problem about the real world is restricted. You'll never see a math problem in which a pet store sells 2.7 cats, since most pet stores tend to sell the entire cat when making a sale. (If you know a pet store that would be willing to sell you 7/10 of a cat, please let me know so that I can avoid that pet store at all costs.)

Hope this helps!