April 9, 2010 SAT is Puzzle-Lite for RocketCat!
By judiethcarol&rocketcatapril2010c http://www.coolrocketschool.org/
Look below for the visual quick solution. Remember: Rocketcat is a white deaf cat with one blue eye and one green eye. He sees the solution with one of his copyright strategies: RACECAR,CONNECT THE DOTS,PUZZLEPIECES, UPSIDEDOWN—and others. Today: PICTURE PUZZLEPIECES
Mathematics: Standard Multiple Choice
Read the following SAT test question, then click on a button to select your answer.
Each of 5 men played a game of chess with each of 5 women, and then each woman played a game of chess with each of the other women. How many games of chess were played?
A.20
B.25
C.35
D.45
E. 50
Speeding this up a bit, Rocketcat noticed that A. & B. were eliminated right away because A. Is too low and B. Is too low because this is the number of the games the men played without adding ANY from the women playing each other.
SECRET AT THIS POINT FROM ROCKETCAT: E. is obviously TOO BIG. It is double the 25 from 5 men playing all of the women. The number of the games of the women playing each other will be fewer.
VISUALLY (does anyone remember that Rocketcat is deaf?), 45 is too big also, as the first part of the number sequence with the women’s games is 4.
VISUALLY, Rocketcat solved this problem without using the official way –SEE BELOW—He made a sketch and eliminated all the incorrect answers within seconds of figuring that the first figure is 25 games.
Notice the part about the women playing each other. Don’t count any of the games twice! Draw a little sketch!! Knock out the number of games with men and women. Each man plays 1 game with each woman. That’s 25 games)
Women playing every other woman is going to be a lower total because some of the ‘pairs’ will be duplicates. Picture one woman playing all the others = 4 games. The second female has already played the first, so she plays the other 3=3 games.
The third female has already played the first, second, and third, so she plays two more games. And the next to the last female plays the last female for one more game. The pattern here is actually 4+3+2+1=10. Add those ten games of the women playing each other to the 25 games of the total played by all five men with the women, and you have 35. The answer is C—35.
BELOW IS THE OFFICIAL EXPLANATION. NOTICING THE PATTERN HERE WILL HELP WITH OTHER QUESTIONS OF THIS TYPE. THERE WILL BE QUESTIONS LIKE THIS ON THE SAT AND/OR OTHER STANDARDIZED TESTS. THIS TYPE OF QUESTION MEASURES ABILITY TO NOTICE PATTERNS.
Each man will play game of chess with each of the women. Therefore, each man will play 5 games. Since there are 5 men, a total of 25 games will be played between the men and the women. Each woman will play game of chess with each of other women. In counting the number of games played, it is important to avoid counting any game more than once. The first woman will play 4 games. The second woman has already played the first woman, so she will play additional games with the 3 other women. Similarly, there are 2 more games played by the third woman, and 1 more game played by the fourth woman. All the games played by the fifth woman have already been counted. So the women play a total of 10, or games with each other. Thus, a total of games of chess have been played.
Explanation and strategies preceding test question explanation in last paragraph are by judiethcarolcooper&judiethcarol&rocketcatApril2010c www.coolrocketschool.org
