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1. One bus leaves every 12 minutes and another every 18 minutes. They leave together at 9:00. When do they next leave together?[3]
A 9:06B 9:30C 9:36D 9:54E 12:362. In the number 4073, what is the value of the digit 7?[3]
3. Which of these fractions lies between one third and one half?[3]
4. The two digits of a number are swapped and the number gets bigger by 36. Which of these could be the number?[4]
5. What is 2 + 4 + 6 + ... + 100?[4]
A 1275B 2450C 2500D 2550E 5100Kangaroo Atlas · https://kangaroo-atlas.vercel.app · seed 1 · CC BY-NC-SA 4.0 · Independent project, not affiliated with Math Kangaroo in USA, NFP.
1. C — 9:36 KA-0041 Factors, multiples, LCM and GCD by listing
A I found the greatest common divisor of 12 and 18 instead of the least common multiple.B I added the two intervals together rather than looking for a time that is a multiple of both.D I found a common multiple but not the least one, landing on a later coincidence.E I multiplied the two intervals together instead of finding their least common multiple.2. C — 70 KA-0055 Place value and digit positions
A I gave the last digit of the number instead of looking at the 7 at all.B I gave the digit itself rather than what it is worth in the position it sits in.D I counted the positions from the left, so I read the 7 as being in the hundreds place.E I gave the value of the largest digit instead of the value of the 7.3. C — 2/5 KA-0141 Number lines and betweenness
A I compared the bottom numbers and assumed a bigger denominator means a bigger fraction.B I saw that 4 lies between 3 and 2 and assumed one quarter therefore lies between the two fractions.D I checked that it is bigger than one third but never checked it against one half.E I compared the top numbers only and ignored what the bottoms do to the size.4. B — 15 KA-0056 Place value and digit positions
A I checked that the digits differ and stopped, without working out how much the swap actually changes the number.C I saw a difference of 2 between the digits and expected that to give a change of 36.D I ignored the direction: swapping this number makes it smaller, not bigger.E I picked a number whose digits differ by 4 without noticing that the larger digit is already in front.5. D — 2550 KA-0058 Clever regrouping (pair to round numbers)
A I found the sum of 1 to 50 and forgot that every term here is twice as big.B I used 49 pairs instead of 25, losing one pair from the count.C I estimated the answer as a round number rather than pairing properly.E I paired the terms but forgot that pairing counts every number twice, so I never halved.