Last year you posted the answers to the Easter and Passover questions in time for the start of school again after the Easter and Passover vacation. We just got back and my teacher asked me to check to see if they're up. Are they coming?
Dear Henry B.,
Here they are!
(First, though, I think it might help if you print out the questions, which are contained in the Q&A directly preceding this one.)
1) With this kind of problem, look for any relationship you can find between the numbers.
24 minutes x 10 = 240 minutes...
Too big, but...
24 minutes x 5 = 120 minutes, which = the 2-hour period we are being asked about. So, 1/3 inch x 5 =
1/3 x 5 = 5/3
= 1 2/3 (choice D)
2) Here, try to spot numbers that are unnecessary. Since we're being asked about cases, it doesn't matter how many eggs (or pieces of matzoh) are in a box.
So, since each box contains 3 reds (or egg matzohs) and there are 64 boxes in each case, there are 64 x 3, or 192, in each case. So, in 10 cases there are 192 x 10, or 1920. (choice D)
3) If 60% of the people go, then 40% do not go.
Here they tell you that 12 people do not go.
So, 40% of the group = 12, which I would rewrite as 4/10 (G) = 12.
From there it is fairly straightforward algebra to work through to come up with the fact that G = 30. (choice C)
4) Here, think of each "deal" of 1-free-with-5-bought as a packaged lot, as in a group of objects sealed in a Ziploc bag. So here each packaged lot would contain 6 items.
So, 30 of these objects are in 5 lots, with 5 paid for in each lot.
5 paid-for x 5 bags = 25 paid for.
$75 for all means that each of the 25 paid-for items cost $3. (choice E)
5) There are 7 colors. Look for a pattern or simiilarity with something familiar to you. How about the days of the week? A calendar usually presents all 7 days in a week at the top of each month, listed horizontally. So if you look at a particular day, say a Wednesday, then 7 days from there (or one week from there) is another Wednesday. Likewise, 14 days, 21 days, or any multiple of 7, even 700 days, from Wednesday is going to be a Wednesday. This problem asks about the 83rd toy egg (or matzoh ball). Well, pick a multiple of 7 that's cloase tro 83. How about 77?
Next, count up to 83 from there. Ticking off each egg (or matzoh ball or day of the week) with your finger, when you get to the 83rd you will land on a purple target. (choice D).
6) Note the "twist": The ratio switches the set-up from:
(games played is simply games lost + games won), and the rest I think you can figure out from there. The answer is 25:33 (choice C).
7) Come up with a distance for the trip, and instead of concerning yourself with being realistic, or picking a realistic distance for their home to be from their church, etc., pick an imaginary distance that is divisible by 40 and divisible by 60. Why not 120? So they live 120 miles from their destination. So, at 40 mph, going one way takes 3 hours. Going at 60 mph, returning, the 120 miles takes 2 hours. So, they have a total driving time of 5 hours, and a total distance covered of 240 miles. 240 divided by 5 = 48. Their average speed for the round-trip in miles per hour is 48 (choice B)
8) Think of permutations for the 4 out of the 6 people who would be willing to sit anywhere. That gives the result of 24 (remember the formula for permutations -- here it would be 4 x 3 x 2 x 1 = 24). Then multiply that answer by 2, since there are two versions of each of the permutations, one with person A sitting on side A and person B sitting on side B, and the other with person B sitting on side A and person A sitting on side B. (choice C)
9) Here, try to think of a ratio as a clear package of things that won't come apart. Here, 3 of one type and 4 of another. Together that's 7.
So, since he collects only reds and blues, his collection must be a pile of these packages, each containing 7 in total. So, the total number in his collection must be a multiple of 7. Here, choice D is 77.
10) Guests are people, so they are not divisible beyond whole units (i.e., no 1/2 person). Look at the choices and try telling the story with each choice and see what happens. So, starting with the top choice, 2 people. 2/3 of those 2 people... NO GOOD.
Try 1/4 of 30 (choice B) and 1/4 of 45 (choice C), and 1/4 of 50 (choice D).
All no good.
You will have eliminated all choices but choice E, or 60. That's the correct choice! And you can check it by taking the number 60 and going through the story's problem and seeing that it works perfectly, and no one has to be chopped up!
I hope this helps!
Until next time,