1.
A nurse must see 8 children. Each appointment takes 6 minutes, and she takes a 4-minute break between appointments. From the start of the first to the end of the last, how long does she take? Careful — count the breaks.
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Answer:
Did you know? A fever is not the germ heating you up. Your body turns the heat up on purpose, because many germs breed badly when warm.
2.
On a balance, 4 syringes exactly balance 1 tray. A tray and a syringe together weigh 45 grams. How much does one syringe weigh? How much does the tray weigh?
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Answer:
Did you know? Handwashing with plain soap works because soap pulls apart the greasy coat that many germs are wrapped in.
3.
A vaccination clinic opens at 8:50 am. It runs for 1 hour 35 minutes, pauses for 20 minutes, then runs for 45 minutes more. At what time does it finish?
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Answer:
Did you know? Doctors trace an outbreak backwards, person by person, to find the very first case. They call that one the index case.
4.
A row of 12 chairs is set out. Every 3rd chair is marked for a nurse. Every 4th chair is marked for a helper. How many chairs carry both marks? How many carry no mark at all?
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Answer:
Did you know? Quarantine gets its name from the Italian for forty days, the time ships once had to wait offshore before anyone could land.
1.
You have 9 vials. Eight weigh exactly the same; one is heavier. You have a balance scale — it only tells you which side is heavier, not by how much. What is the fewest number of weighings that is certain to find the heavy one? Explain how.
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Answer:
Did you know? Your lymph system has no pump of its own. It moves because your muscles squeeze it as you walk about.
2.
One nurse can vaccinate a whole class in 40 minutes. A second nurse can do the same class in 24 minutes. Working together at those speeds, how long does the class take? Hint: think about how much of the class each one finishes in a single minute.
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Answer:
Did you know? White blood cells can squeeze straight through the wall of a blood vessel to reach a wound, changing shape to get out.
3.
The code on a vaccine fridge is 3 digits long. Each digit is one of 1, 2, 3, 4, and no digit may repeat. How many different codes are possible?
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Answer:
Did you know? Vaccines are checked in stages on thousands of volunteers before anyone else is offered them. The stages are called trial phases.
4.
Five sample boxes are stacked. The blue box is directly above the red. The green is at the very bottom. The yellow is directly below the white. The red is directly above the green. List the stack from top to bottom.
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Answer:
Did you know? Some people carry a germ, feel perfectly well, and still pass it on. Tracing an outbreak has to allow for that.
3rd Grade
1. 76 minutes — 1 hour 16 minutes.
Appointments: 8 × 6 = 48 minutes. Breaks come between them, so there are only 7, not 8: 7 × 4 = 28. Total 48 + 28 = 76. Answering 80 means he put a break after the last child.
2. A syringe is 9 g; the tray is 36 g.
The tray weighs the same as 4 syringes, so a tray plus a syringe is really 5 syringes. 45 ÷ 5 = 9 g each, and the tray is 4 × 9 = 36 g. Check: 36 + 9 = 45. ✓
3. 11:30 am.
8:50 + 1 h 35 min = 10:25. Then + 20 min = 10:45. Then + 45 min = 11:30 am. Adding the three spans first (2 h 40 min) and then to 8:50 works too.
4. 1 chair has both marks; 6 chairs have none.
Nurse chairs: 3, 6, 9, 12 — that is 4. Helper chairs: 4, 8, 12 — that is 3. Chair 12 is on both lists, so only 1 carries both. Marked chairs altogether: 4 + 3 − 1 = 6, so 12 − 6 = 6 are bare.
4th Grade
1. Two weighings.
Split the 9 into three groups of 3. Weigh group A against group B. If one side sinks, the heavy vial is in that group; if they balance, it is in group C. That is one weighing to find the group of 3. Now take that group, weigh one vial against another: heavier side wins, and if they balance it is the third. That is two total. Answering 3 or 4 usually means he weighed one vial at a time.
2. 15 minutes.
In one minute the first nurse does 1/40 of the class and the second does 1/24. Together: 1/40 + 1/24. Sixtieths do not work here — use 120ths: 3/120 + 5/120 = 8/120, which is 1/15. One fifteenth of the class each minute means the whole class takes 15 minutes. Note it is faster than either nurse alone, which is the sanity check.
3. 24 codes.
First digit: 4 choices. Second: only 3 left. Third: 2 left. 4 × 3 × 2 = 24. Answering 64 means he allowed repeats (4 × 4 × 4).
4. White, yellow, blue, red, green.
Green is at the bottom. Red is directly above green, so red is second. Blue is directly above red, so blue is third. That leaves the top two slots for yellow and white, and white must be directly above yellow — so yellow is fourth and white is on top.