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grandh01: Master | Next Rank: 500 Posts; Posts: 265; Joined: Tue Jul 03, 2012 11:04 pm; Followed by:6 members

manufacturing

by grandh01 » Sat Aug 18, 2012 3:50 pm

The cost C of manufacturing a certain
product can be estimated by the
formula C = 0.03rst2, where r and s
are the amounts, in pounds, of the two
major ingredients and t is the
production time in hours. If r is
increased by 50 percent, s is increased
by 20 percent, and t is decreased by
30 percent, by approximately what
percent will the estimated cost of
manufacturing the product change?
(A) 40% increase
(B) 12% increase
(C) 4% increase
(D) 12% decrease
(E) 24% decrease

Quote

Source: Beat The GMAT — Problem Solving | Sat Aug 18, 2012 3:50 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Sat Aug 18, 2012 4:48 pm

Hi!

Like many GMAT questions, this one looks much more difficult than it actually is.

First, we can simplify by recognizing that the numbers on the right side are wholly irrelevant. The question would have an identical solution if the original equation were:

C = rst

Since that equation is easier to use, let's use it!

Next, let's let r, s and t all be equal to 1 to start. So, our original value for C is 1 as well.

Now we apply the changes:

C(new) = (1.5)(1.2)(.7) = (1.5)(.84) = a bit more than 1.2 (.8*1.5=1.2), giving us an increase of slightly more than 20%... well heck, that's not an answer!

However, with a bit of reverse engineering, I'm guessing that the original equation should have been:

C = 0.03(r)(s)(t^2)

in which case our calculation is:

(1.5)(1.2)(.7)^2 = (1.5)(1.2)(.49) = 1.5(approx .6) = .9... and since we rounded .49 up to .5, the answer is a bit less than .9 - so I'm guessing that the official answer is D, 12% decrease.

grandh01 wrote:The cost C of manufacturing a certain
product can be estimated by the
formula C = 0.03rst2, where r and s
are the amounts, in pounds, of the two
major ingredients and t is the
production time in hours. If r is
increased by 50 percent, s is increased
by 20 percent, and t is decreased by
30 percent, by approximately what
percent will the estimated cost of
manufacturing the product change?
(A) 40% increase
(B) 12% increase
(C) 4% increase
(D) 12% decrease
(E) 24% decrease