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1. In the number 4073, what is the value of the digit 7?[3]
2. What is 1 + 2 + 3 + ... + 20?[3]
3. Each shape stands for a whole number. A triangle plus a triangle plus a triangle is 12, and a triangle plus a square is 9. What is the square?[3]
4. A bread recipe uses flour and sugar in the ratio 5 to 3. The two together weigh 320 grams. How much of that is flour?[3]
A 120 gB 160 gC 200 gD 192 gE 64 g5. The four-digit number 27_4 is divisible by 3. Which digit could go in the gap?[4]
6. The mean of five numbers is 12. One of the numbers is removed and the mean of the remaining four is 11. What number was removed?[4]
7. What is 2 + 4 + 6 + ... + 100?[4]
A 1275B 2450C 2500D 2550E 51008. Which of these numbers can be divided exactly by both 4 and 9?[4]
9. The mean of four numbers is 9. Three of them are 5, 8 and 12. What is the fourth?[4]
10. What is the units digit of 7 multiplied by itself 2026 times, that is 7 to the power 2026?[5]
A it cannot be found without a calculatorB 1C 3D 7E 9Kangaroo Atlas · https://kangaroo-atlas.vercel.app · seed 2 · CC BY-NC-SA 4.0 · Independent project, not affiliated with Math Kangaroo in USA, NFP.
1. 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 7.2. C — 210 KA-0057 Clever regrouping (pair to round numbers)
A I paired the numbers from the outside in but left the 20 out of every pair, so I added only up to 19.B I estimated the total as a round number instead of working it out.D I used eleven pairs of 20 instead of ten pairs of 21.E I multiplied 20 by 21 and forgot that pairing counts every number twice.3. C — 5 KA-0061 Operation puzzles and cryptarithms
A I solved for the triangle and gave that instead of the square.B I found the triangle is 4 and gave that number, without going on to the second equation.D I halved the 12 instead of dividing it by the three triangles.E I subtracted the wrong way round, taking 9 from a number instead of taking the triangle from 9.4. C — 200 g KA-0151 Ratio as parts of a whole
A I worked out the part size correctly and then answered for the sugar instead of the flour.B I split the 320 grams into two halves instead of into eight equal parts.D I took three fifths of 320 rather than five eighths, using the ratio numbers as a fraction of each other.E I divided 320 by the 5 in the ratio and stopped, treating 5 as the number of parts.5. B — 2 KA-0011 Divisibility rules: 2, 3, 4, 5, 9, 10
A I added the known digits to get 13 and then checked whether the missing digit itself was a multiple of 3.C I chose 3 because the question mentioned dividing by 3, without testing the digit sum at all.D I tested the last two digits, which is the rule for 4, not the rule for 3.E I added the digits but left out the 4 at the end, so my sum was four too small.6. D — 16 KA-0033 Means, and working backwards from a mean
A I subtracted the two means from each other and gave the difference as the removed number.B I assumed the removed number must be the new mean, since the mean dropped to 11.C I assumed removing a number equal to the old mean is what changes the mean.E I added the two totals instead of subtracting one from the other.7. 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.8. D — 144 KA-0063 Divisibility rules: 2, 3, 4, 5, 9, 10
A I checked that it divides by 4 and stopped without testing the 9.B I checked the digit sum for 9 and stopped without testing the 4.C I saw an even number with a digit sum of 6 and treated 6 as good enough for 9.E I tested 9 with the digit sum and assumed any odd multiple of 9 also divides by 4.9. C — 11 KA-0066 Means, and working backwards from a mean
A I assumed the missing number must be the mean itself.B I averaged the three known numbers instead of working from the total.D I repeated one of the numbers already given rather than computing the missing one.E I used a total of 37 instead of 36, adding the mean in once too often.10. E — 9 KA-0037 Last-digit behavior of products and powers
A I assumed a number this large has no reachable last digit and gave up on the cycle.B I found the cycle 7, 9, 3, 1 but used a remainder of 0 when the remainder is actually 2.C I found the cycle but counted its positions starting at zero, shifting my answer along by one.D I assumed the units digit of any power of 7 is always 7.