July 30 2007: QOTW: Fifth Grade Maths
My brother received his marks for the Australasian Maths Competition today - a Distinction, which is admirable when viewed alone, but which pales in comparison next to the consistent High Distinctions I received for the same competitions at his age. Nevertheless. Let not the fact that I pwn him in every which way detract from his achievements.
In any case, he got four questions wrong in the exam - and analysing his results at home, he still couldn’t figure out how to reach the correct answer for one particular question. I figure it out instantly of course (brain that I am), though neither of my parents could understand it.
So today, I ask you the question, and provide you with several options for the answer. If you can figure it out (and provide a reasoning for how you came by your answer, not simply the answer itself), you get plugged in tomorrow’s entry. Bon chance!
Question of the Week: Twenty people were surveyed at a sports centre. Five people played both squash and tennis. Eight people did not play squash. Eleven people did not play tennis. How many people did not play either squash or tennis? (A:1, B:3, C:4, D: 7)
Hmm… I was always horrible at problems like that.
I’d say:
You have to take away the 5 people who play both from the 20 people - so that means you have 15 people who don’t play both, squash and tennis.
From those 15 people 8 don’t play S and 11 don’t play T. 11+8=19 meaning 4 people don’t play either Squash or Tennis.
Or 3… - the difference?? Or I’m totally wrong ;)
No idea - you gotta blog the results!
Tracy on July 30 2007 #
I am not even going to try, even if you were offering me chocolate. I suck -horribly- at maths questions and these type of scenarios. It goes wayyy over my brain.
Bobbi-lee on July 30 2007 #
Answer is C: 4.
Ok damn I hate reasoning…
Eight people did not play squash: 20 - S = 8
Eleven people did not play tennis: 20 - T = 11
S = 20 - 8 = 12
T = 20 - 11 = 9
People who play ONLY squash: 12 - 5 = 7
People who play ONLY tennis: 9 - 5 = 4
Therefore… Those who don’t play either: 20 (total) - 7 (squash) - 4 (tennis) - 5 (both) = 4
I miss Aussie Maths Competition! I quite liked problem solving back then provided that I’ll be able to work out the answer. If I can’t, the question sucks. :P
Rilla on July 30 2007 #
I don’t like this question. I like guessing C, though & so, my answer is C:4.
Crackpot Reasoning:
+ 8 people don’t play squash so (20-8) 12 people do.
+ 11 people don’t play tennis so (20-11) 9 people do.
+ 5 people said that they played both sports so (12-5) 7 people play just squash & (9-5) 4 people play just tennis.
+ (7+4) 11 people play just one sport.
+ (20-5-11) 4 people play neither.
You know, I like math but, I like it best when numbers aren’t involved. XD
Chantelle on July 30 2007 #
umm I suck at math! but I’m guessing C) 4 because if you add the 5 that played both, the 8 that didn’t play squash, and the 11 that didn’t play tennis that = 24, but there are only 20 people total…so 4 people must have overlapped in the “don’t play ____” area.
again I repeat: I suck at math…I’m too simple-minded :D
marilyn on July 30 2007 #
Well I suck at these things, but I’ll try my best.
First of all I detract 5 from 20, because these played both sports. So we now have 15 people.
From these 15:
- 8 didn’t play squash => 7 played squash
- 11 didn’t play tennis => 4 played tennis
7+4 = 11 these played either squash or tennis.
15 - 11 = 4 the people who didn’t play either.
So the correct answer would be C
Vera on July 30 2007 #
You know you shouldn’t listen to Marilyn when she says she’s too simple minded. That’s the girl whose Biology professor said she was amazingly awesome for getting 100% on all her exams. :P
I wonder if my Venn diagram counts as proper working out and stuff. You sound as pedantic as my math teacher, “You must show ALL working or you don’t get full marks!” ;)
Tracey on July 30 2007 #
I found one of your recent comments on melbournemaniac incredibly amusing and did some link hopping. Having nothing better to do..
A simple venn diagram could solve this? Sample is 20. We have 2 subsets: squash and tennis. The intersection of the two groups is 5.
8 do not play squash, therefore the total within the squash subset must be 20-8= 12. Of the 12 who play squash, we know 5 play tennis also. Therefore those who play squash only must be 12-5= 7.
11 do not play tennis, therefore the total within the tennis subset must be 20-11=9. Of the 9 who play tennis, we know 5 play tennis also. Therefore those who play tennis only must be 9-5=4.
Finally, the number of ppl who play neither tennis nor squash must be:
20-(7+4+5)=4
- answer is C
how entertaining. i procrastinate brilliantly. thank you for helping me
tam on July 30 2007 #
Math before 8:00 a.m. Will wonders never cease?
20 = squash players + tennis players + both + neither
20 = S + T + 5 + N
15 = S + T + N
15 = (15-8) + (15-11) + N
15 = 7 + 4 + N
N = 4
Julianne on July 30 2007 #
Umm, don’t you use the venn diagram to solve questions like these? It makes life a lot easier. :D
Skye on July 31 2007 #
Hah, I know the answer, but people’ve guessed already, so I’m late!
Skye, that’s exactly what people do, if they’re not super math geeks!
Ramsha on July 31 2007 #
On a totally unrelated note I would love to try squash!
(4)
Nan on July 31 2007 #
Well, 20 people total.
8 don’t play one 11 don’t play the other. So that’s 19. Meaning 1 person doesn’t play either.
However, I’m not sure because of the wording. They say OR and EITHER which infers that they mean either or. Meaning not both. Meaning how many only played one. 5 play both and 1 plays neither so 20-6=14 which isn’t an option.
Skye on July 31 2007 #
Well, first I subtracted 5 from 20, because we already know that they play both. Next, I subtracted 8 and 11 from 15, separately, to figure out how many people play just squash or tennis. I figured out that 7 people play just tennis and 4 people play just squash. So, I subtracted the sum of the three numbers, 16, from 20 and got 4.
So, the answer is C:4.
(Scrolling through the comments after solving it, I realised that I probably used the least efficient method of solving this. I suck at setting up equations for problems like this. =/)
Josh on July 31 2007 #
I absolutely suck at Maths.
Juice on July 31 2007 #