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PRINCESTONE-HOUSING PROJECT

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PRINCESTONE-HOUSING PROJECT

by pradeepkaushal9518 » Sun Jul 04, 2010 4:39 am
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.



Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.



Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.



BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.



EACH statement ALONE is sufficient.



Statements (1) and (2) TOGETHER are NOT SUFFICIENT
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Source: — Data Sufficiency |
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by kvcpk » Sun Jul 04, 2010 6:53 am
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..

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by mj78ind » Sun Jul 04, 2010 7:07 am
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?
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by kvcpk » Sun Jul 04, 2010 7:14 am
@mj78ind - Good question.. I request experts to comment..
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by san2009 » Mon Jul 05, 2010 4:25 am
want to be included on expert's comments as well. thanks
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by GMATGuruNY » Tue Jul 06, 2010 4:16 am
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.
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by GMATGuruNY » Tue Jul 06, 2010 6:59 am
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!
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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

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