Brian Galvin is the Director of Academic Programs at Veritas Prep, where he oversees all of the company’s GMAT preparation courses.
Few businessmen have ever had the cache of Lee Iacocca, the famed Chrysler Corporation chairman who led the company back from the brink of bankruptcy to pioneer automotive market segments like the SUV and the minivan. On the merits of those successes, Iacocca was a household name in the 80s, appointed by President Reagan to lead a renovation of the Statue of Liberty, asked (but ultimately declining) to fill a vacant Pennsylvania Senate seat, and even appearing on an episode of Miami Vice.
Iacocca was known for an efficient, no-nonsense management style, exemplified by his famous line “If you can find a better car, buy it.” His matter-of-fact style also produced another famous quote that can help you as you approach GMAT problems that include algebra:
“Talk to people in their own language. If you do it well, they'll say, 'God, he said exactly what I was thinking.' And when they begin to respect you, they'll follow you to the death.”
A consummate salesman, Iacocca understood the need to relate to people in their own words and their own style. Few CEOs could sell employees on voluntary, across-the-board paycuts (as he did at Chrysler in the early 1980s), but his quote above demonstrates how it may be possible, and the GMAT will give you opportunities to demonstrate that you can identify and speak the language of those you need to convince.
Consider the question (about a car company, to speak Iacocca’s language):
A certain car company manufactured x cars at a cost of c dollars per car. If a certain number of cars were sold below cost at a sale price of s dollars per car, while the rest of the cars were sold for the normal retail price of n dollars per car, how many cars could the company afford to sell at the sale price in order to break even (no profit and no loss)?
(A) x(c – n)/(s – n)
(B) x(n – c)/(s – n)
(C) x(c – n)/(s – c)
(D) x(s – n)/(c – n)
(E) (x – n)(x – s)
If the GMAT seeks to determine whether you can, as Iacocca says, talk to people in their own language, those questions that involve algebraic statements in their answer choices are the questions that will do that best. Your job here is to first take the stimulus and turn it into a true statement, and then take that statement and put it in the question’s terms. Use the answer choices as your guide – once you’ve set up your initial equation, keep an eye on the answer choices for direction as to how to manipulate your statement to look more like theirs.
Here, we can set up an initial equation by nothing that, to break even, Revenues must equal Costs:
Revenue = Cost
Our calculations for either side will look like:
Cost = x cars * c dollars per car = xc
Revenue – there are two sales prices, n as the retail price and s as the sale price. There are x total cars, and we need to come up with a number of cars to sell at sale price s, so let’s call that y:
Revenue = y cars sold at price s * price s, and (x-y) (the remaining cars) sold at price n * price n
So, our equation is:
Revenue = Cost
ys + (x-y)n = xc
Now, we need to make that equation look like the answer choices. The question asks us to solve for the “the number sold at price s”, which we’ve termed “y”, so that’s one guide. Or, we can look at the answer choices to also note that y does not appear, and make our goal to isolate and eliminate y. Solving for y, we can take the following steps from our starting point:
ys + (x-y)n = xc
Multiply out the parentheses to get the y out:
ys + xn – yn = xc
Subtract the xn term from both sides to get the y terms alone:
ys – yn = xc – xn
We need to isolate y by factoring it on the left, and looking at the answer choices we should realize that x is factored out in most of them, so we can factor y from the left and x from the right to get closer to “the language of the answer choices”:
y(s-n) = x(c-n)
Divide both sides by (s-n) to get y on its own, and to look like the answer choices:
y = x(c – n)/(s – n)
This matches answer choice A, the correct answer.
Often times, algebraic-answer questions like this are tests of your ability to follow the logic step-by-step as you attempt to speak the same language as the answer choice. Whether the question involves auto sales or not, summon your Inner Iacocca to put your thoughts in the terms of the answer choices, a crucial business skill and an important way to succeed on the GMAT. (And, to paraphrase Iacocca, if you can find a better way to solve a problem, do it!)
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Dear Veretas Team,
I have a question regarding this problem. My question: How do you know that exactly (x-y) will be multiplied by n? Because if the logic is reversed the answers will be irrelevant. I mean instead of coming to “ys + (x-y)n = xc” equation you can end up with “(x-y)s + yn = xc”, then the anwers will be irrelevant even if the logic is right. Thanks!!!
Sincerely,
Azamat
Veretas Student