<p>Source: Barron’s 22nd</p>
<li>There are 12 men on a basketball team, and in a game 5 of them play at any one time. If the game is 1 hour long, and if each man plays exactly the same amount of time, how many minutes does each man play?</li>
</ol>
<p>(A) 10
(B) 12
(C) 24
(D) 25
(E) 30</p>
<p>I don’t understand the wording. By the way, the answer is (D).</p>
<p>Since game is 60 minutes and everyone MUST play the same amount of time, then a "shift" is 5 minutes for 5 players. (LCM of 5 and 12 is 60). Since one player plays 5 "shifts", 5*5= 25
Took me 2 minutes to figure that out..</p>
<p>Perhaps the best approach to this problem is this :</p>
<p>say each player played x minutes in the game. In total they played 12x minutes since there were 12 players. But we know that the team is made of 5 players so we divide the total no of minutes ( 12x ) by 5 and this gives us the endurance of the game. So : 12x/5 = 1h = 60 min x = 25 min</p>
<p>here's an easier way (to me):</p>
<p>if there will be 5 men on the floor at any given point and the game is 60 minutes long, then 300 man-minutes will be played in total. For those 300 minutes to be split evenly 12 ways, each man plays 25 minutes.</p>
<p>12x=5*60
The total amount of time is constant.</p>
<p>xitammarg's method is what I used</p>
<p>Thanks repliers, I appreciate.</p>
<p>I could hardly understand the situation posed by the question.</p>
<p>Another take (not an easier one; just for fun).
If there were 60 men on a team, 12 5's could play consecutively, each man getting 60min / 12 = 5min of the floor time.
Since there are 12 men on a team, which is 5 times less than 60, each player gets 5 times more play time: 5 x 5min = 25min.</p>
<p>Ooh, that's a nice way to solve the problem!</p>
<p>How did you guys know how to approach this problem? Would the SAT ever ask this or is it just because of Barrons?</p>
<p>xitammarg's way is the cleanest</p>
<p>Ahmed: I doubt it would be on the real SAT. </p>
<p>What do you think Mike?</p>
<p>xitammarg's way is the most efficient imo. I had a bit of difficulty understanding the question at first. So I decided to try the situation with 5 men first, then 10 men and was able to derive the formula.
5 men on the team and 5 men playing on the court at anytime for 60mins = obviously 60 mins for each man.
10 men with 5 on the court at anytime for 60mins = 30mins per man.</p>
<p>Eventually I found T(M/5)=60</p>
<p>M = men. T= mins per man</p>
<p>i'm really not sure if this could be on the SAT. i haven't seen a similar question on the SAT before, but it <em>does</em> only require you to know multiplication and division, which are things the SAT reserves the right to test you on. what do you guys think?</p>
<p>How did you guys know how to approach this problem?</p>
<p>Think about the problem in your own terms. The problem wants you to tool around with 12 guys in 5 positions, when really, just calculating the total time to be played is an incredibly simple way of doing it. I can't really articulate how I approached the problem any better than that.
If this is hard now, just keep doing problems like that that require a little out of the box thinking. Seeing paths to the solution just becomes second-nature.</p>
<p>xitammarg: I think the problem is too tricky for the SAT. Then again, I've seen some even more tricky once in a while. Maybe it might be put as one of the hardest on the test, otherwise it wouldn't be put on.</p>