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 Author: questioner [ Mon Jun 07, 2010 2:41 pm ] Post subject: GMAT Algebra (Data Sufficiency) For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r) > (s – n)?(1) 250 > r + s(2) m + r + s= 375A. 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) Statement (1) tells us that 250 > r + s. Since the question statement tells us that m + n = 250, we can determine that m + n > r + s.Now, let us manipulate this inequality to see whether it is equivalent to the inequality in the question:(m + n) > (r + s)m > (r + s) – n(m – r) > (s – n)This is exactly what we were looking for. We can answer the question using Statement (1), hence it is sufficient.Statement (2) tells us that m + r + s = 375.Because we know that m + n = 250 and m > n, m must be greater than 125. Subtracting 125 from 375 yields 250, so if m is greater than 125, then r + s must be smaller than 250. We are now left with the same inequality that we were given in Statement (1), which can be manipulated to show that (m – r) > (s – n). So Statement (2) is also sufficient.Since both statements are sufficient alone, the correct answer is choice (D).-------------The two statements should never contradict themselves:1) 250 > r + s2) We know m > 125If I substitute 126 for m in the stament (2) then r + s = 249I thought r + s were greater than 250.

 Author: Gennadiy [ Mon Jun 07, 2010 2:47 pm ] Post subject: Re: GMAT Algebra (Data Sufficiency) There is no contradiction in this question.Statement (1) tells us that (r + s) is smaller than 250. When you plug in m = 126 into statement (2) and get r + s = 249, it doesn't contradict with statement (1) since 249 is smaller then 250.Furthermore, it is shown in the explanation that statement (2) actually implies statement (1).

 Author: questioner [ Mon Dec 06, 2010 11:36 am ] Post subject: Re: GMAT Algebra (Data Sufficiency) You should add that the integers are positive. The way it is worded leaves open the possibility of negative numbers and zero as well.

 Author: Gennadiy [ Mon Dec 06, 2010 11:54 am ] Post subject: Re: GMAT Algebra (Data Sufficiency) There is NO necessity in defining the integers to be positive.In fact, any of the integers r, s or n can be zero or negative. However, the statement implies that m is greater than 125, so it CAN NOT be zero or negative.Furthermore, let's take a look on the explanation "backwards". Let us analyse the desired inequality first:m – r > s – nwe easily transform it into:m + n > s + rThe question statement defines m + n = 250. Lets plug it in. So the original inequality is equivalent to:250 > s + rThat is exactly the first statement. Therefore the first statement is sufficient by itself.If we use the second statement by itself, then we can plug s + r = 375 – m into the inequality:250 > 375 – mm > 125That is true, because from the basic statement we know that m > n, som + m > n + m = 250.2m > 250m > 125Therefore each statement by itself is sufficient.As you see, we never required any of the numbers to be positive (except of m, which follows from the basic statement).

 Author: questioner [ Fri Jun 24, 2011 12:31 pm ] Post subject: Re: GMAT Algebra (Data Sufficiency) To evaluate statement (2) you are using the information provided in statement (1), otherwise you wouldn't get that m must be > 125 ... therefore the answer would be A ... unless you have another way to solve ...

 Author: Gennadiy [ Fri Jun 24, 2011 1:01 pm ] Post subject: Re: GMAT Algebra (Data Sufficiency)

 Author: Sara Salehi [ Sun Feb 17, 2013 12:49 pm ] Post subject: Re: GMAT Algebra (Data Sufficiency) I was thrown off by the parentheses around (m-r) and (s-n) and it lead me to believe that I couldn't manipulate the inequality by adding and subtracting the variables...I thought I had to keep (m-r) together since it was referring to the resulting value of m-r. Is that the reason they put parentheses, just to possibly trick you or do they actually mean anything?

 Author: Gennadiy [ Mon Feb 18, 2013 4:29 pm ] Post subject: Re: GMAT Algebra (Data Sufficiency) Parentheses are used to group items. They do not apply any restrictions on regrouping those items.They are used to ease visual comprehension here. This question statement with or without the parentheses remains the same.

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