1.
A lab counts a batch of white blood cell samples. 7 are removed as spoiled. Then 12 more arrive from the clinic. The batch is then split equally between two microscopes, and one microscope receives 14 samples. How many samples were in the batch to start with?
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Answer:
Did you know? A white blood cell can squeeze itself out through the wall of a blood vessel to reach a wound — it changes shape to get there.
2.
A tray holds 30 samples. 17 of them show antibodies. 14 of them show a fever marker. 8 samples show both. How many samples show neither?
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Answer:
Did you know? Your skin is your largest immune organ. Most germs never get past it at all.
3.
A patient's antibody level rises 3 units during each day, then falls back 2 units each night. It starts at 0 and needs to reach 10. On which day does it first reach 10? Think it through. This one is not the calculation it looks like.
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Answer:
Did you know? After an infection, some antibody-making cells become memory cells and simply wait — sometimes for the rest of your life.
4.
A tray holds vials of 3 different vaccines, all mixed together and all looking identical. Without looking, what is the fewest vials you must pick to be certain you have two of the same kind?
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Answer:
Did you know? Vaccines are usually kept cold because the harmless germ pieces inside them fall apart when they get warm.
1.
Three researchers — Idris, Hafsa, and Zakariya — each study a different cell (T-cell, B-cell, macrophage) in a different lab (North, South, Central). Who studies what, and where?
1. The researcher in the Central lab studies the macrophage. 2. Idris does not study the B-cell. 3. Hafsa studies the T-cell. 4. Zakariya is not in the North lab.
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Answer:
Did you know? A macrophage's name means "big eater" — it swallows germs whole and digests them.
2.
You need to measure exactly 4 mL of a solution. You have only a 5 mL syringe, a 3 mL syringe, and a large bottle of the solution. Neither syringe has any markings on it. How do you do it?
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Answer:
Did you know? Doses for children are worked out by body weight, not age — which is why the same medicine comes in different amounts.
3.
A sample was contaminated.
Anas says: "It was Bilal." Bilal says: "It wasn't me." Ruqayya says: "It was Anas."
Exactly one of the three is lying. Who contaminated the sample?
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Answer:
Did you know? Labs work in sterile cabinets with the air always flowing outward, so nothing from the room can drift onto a sample.
4.
A 42 cm length of tubing must be cut into 6 cm pieces. Each cut takes 3 minutes. How long does the whole job take?
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Answer:
Did you know? Blood for a transfusion is passed through a filter fine enough to catch tiny clots but not the blood cells themselves.
3rd Grade
1. 23 samples.
Work backwards, flipping every step. One microscope got 14 after an equal split → 28 before it. Undo the 12 arriving → 16. Undo the 7 removed → 23. Check forwards: 23 − 7 = 16, + 12 = 28, half of 28 = 14. ✓
2. 7 samples.
The 8 both-samples got counted twice, so samples with at least one = 17 + 14 − 8 = 22. Then 30 − 22 = 7. Draw two overlapping circles and it goes obvious.
3. Day 8.
It gains 1 unit a day overall, so 10 days looks right — and it is wrong. Track it: end of day 1 it is at 3, then 1 overnight. Day 2 → 4, then 2. By the end of day 7 it is at 9, dropping to 7. On day 8 it climbs 7 → 10 and it has arrived — the night-time fall never happens. The last climb is the one that escapes.
4. 4 vials.
Think about the unluckiest possible run. You could pick 3 and get one of every kind — still no pair. But there are only 3 kinds, so the 4th vial has to match one you already hold. 4. The answer is not 2, because "certain" means even on your worst day.
4th Grade
1. Idris — macrophage — Central · Hafsa — T-cell — North · Zakariya — B-cell — South.
Clue 3 gives Hafsa the T-cell. Clue 2 then leaves Idris only the macrophage, and clue 1 puts the macrophage in Central. Zakariya takes the B-cell. Clue 4 keeps him out of the North → Zakariya, South, so Hafsa has the North.
2. Fill 5, pour off 3, keep the 2, then top the 5 up and pour 1 more into the 3.
1. Fill the 5 mL. 2. Pour from it into the 3 mL until the 3 is full — that leaves exactly 2 mL in the 5. 3. Empty the 3 mL. 4. Tip the 2 mL into the 3 mL syringe. 5. Refill the 5 mL. 6. Pour from the 5 into the 3 — it only has room for 1 more mL, so exactly 4 mL is left behind in the 5. That is your 4.
3. Anas contaminated it.
Test each one and count the lies. If Anas did it: Anas lies, Bilal tells the truth, Ruqayya tells the truth — exactly one lie. ✓ If Bilal did it: Anas true, Bilal lies, Ruqayya lies — two. ✗ If Ruqayya did it: Anas lies, Bilal true, Ruqayya lies — two. ✗ Only Anas fits. Note it is one lie here, not one truth — read that line twice.
4. 18 minutes.
42 ÷ 6 = 7 pieces — but that is not the number of cuts. Lay it out: the last piece falls free on the cut before it, so 7 pieces need only 6 cuts. Then 6 × 3 = 18 minutes. Answering 21 means counting a cut that never happens.