Math Help: Test 10, Section 8, Question 16

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1

<p>Can anyone explain Test 10 Section 8 question 16 p.981 on the Blue Book for me please? Thank you!</p>

2

<p>This is quite difficult algebraically, so let’s pick some numbers. Suppose there are m = 10 coworkers, and the total cost is y = 60 dollars. So each coworker would be contributing $6. Now suppose p = 4 fail to contribute. Now only 6 are contributing, so they must pay $10 each. The additional amount is 10 - 6 = 4.</p>

<p>Now substitute m=10, y=60, and p=4 into each answer choice. We get the following:</p>

<p>(A) 6
(B) 10
(C) 40
(D) 36
(E) 4</p>

<p>Since (A), (B), (C), and (D) came out incorrect, the answer is choice (E).</p>

<p>Algebraic solution: I don’t recommend doing it this way, but for completeness here is an algebraic solution.</p>

<p>Originally, each coworker would be contributing y/m dollars. When p coworkers fail to contribute, each of the remaining m-p coworkers must contribute y/(m-p) dollars. The additional amount is y/(m-p) - y/m. The least common denominator is m(m-p). Multiply the numerator and denominator of the left fraction by m, and of the right fraction by m-p. We get (my - (m-p)y)/[m(m-p)]. The numerator of this fraction simplifies as my - my + py = py. So the answer is (E).</p>

3

<p>To follow the algebraic solution, here is a good source:</p>

<p>[PRACTICE</a> TEST 10 SECTION 8 QUESTION 16 MATH OFFICIAL SAT GUIDE - YouTube](<a href=“- YouTube”>- YouTube)</p>

4

<p>Thank you so much! I’ve always had some trouble with the math section.
By the way, could you see if this math plan works? </p>

<p>I took 2 diagnostic tests, then from there correct them. With what I’ve got, refer to the Gruber’s math workbook (or “Refresher sessions”). I plan to do the session tests (total of 8) each day for about 30-1hr.
I’m a rising junior: do you recommend lots of practice test every week-end or let it sink with the conceptual review? And do you think since my weakest is math, that working solely on the math section right now is ok? I mean it’s not like I super duper ace the other two sections…
Thanks!</p>

5

<p>You can see my philosophy in my article “The Correct Way to Prepare for SAT Math.” It’s posted on CC - just do a search.</p>