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GMAT Algebra (Data Sufficiency)
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Author:  questioner [ Wed Apr 17, 2013 7:54 am ]
Post subject:  GMAT Algebra (Data Sufficiency)

Cutting Edge Knife Company hired P salespeople, each of whom sold 200 knives. Each salesperson then hired P more salespeople, each of whom also sold 200 knives each. What is the value of P?

(1) The first P salespeople sold 1/9 of all the knives sold.
(2) 14,400 knives were sold in total.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(D) The first P people each sold 200 knives, so they sold 200P knives altogether. Each of the initial P people found P more people to sell knives, each of whom also sold 200 knives. That means there are P² people (that is, P people who also enlisted P people each) who also sold 200 knives each. The total number of knives sold can be written as: 200P + 200P² = T, where T is the total number of knives sold.

Statement (1) tells us that the first P people sold 1/9 of the total number of knives sold. Algebraically, we have:200P = (1/9)T. Now we have two equations with two variables. We can insert the second equation into the first:(1/9)T + (1/9)TP = T.So, (1/9)TP = (8/9)T, and (1/9)P = 8/9, since T cannot equal 0.(Remember, we cannot divide an equation by a variable unless we know that the variable does not equal zero. Here, if T = 0, the equation holds true for all values of P.)Multiply both sides of the equation by 9, and P = 8. Since Statement (1) gives us the value of P, it is sufficient.

Statement (2) tells us what the value of T is, so we can substitute that as well, yielding: 200P + 200P² = 14,400. By subtracting 14,400 from both sides of the equation and factoring out 200, we get: 200(P² + P – 72) = 0. This polynomial can be factored:200(P + 9)(P – 8) = 0.We can now solve for the values of P that will make one of the factors equal to zero (so the entire product is zero and the equation holds).When P = -9 or 8, one of the factors will be zero. Since P cannot be negative (there cannot be a negative number of salesmen), P = 8. Statement (2) is also sufficient.

Since each statement is sufficient alone, the correct answer is choice (D).For more information on type of questions, order the online prep course by clicking hereUse the feedback button below to send questions or comments.


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By subtracting 14,400 from both sides of the equation and factoring out 200, we get: 200(P² + P – 72) = 0. if you say that you factor out 200, then 200 should not be in 200(P² + P – 72) = 0, right?

Author:  Gennadiy [ Wed Apr 17, 2013 7:54 am ]
Post subject:  Re: GMAT Algebra (Data Sufficiency)

Factoring out does not mean that we divide by 200. It only means that we get the same expression, but where 200 is a factor.
200p² + 200p – 72 = 200(p² + p – 72).

Though when we have 200(p² + p – 72) = 0 , we can divide both sides of the equation by 200 as well in order to simplify it.

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