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1. Ana adds up the first seven odd numbers: 1 + 3 + 5 + 7 + 9 + 11 + 13. Is her total odd or even, and what is it?[3]
A odd, 47B odd, 49C even, 48D even, 49E odd, 452. In the number 4073, what is the value of the digit 7?[3]
3. What is 1 + 2 + 3 + ... + 20?[3]
4. 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]
5. The four-digit number 27_4 is divisible by 3. Which digit could go in the gap?[4]
6. The two digits of a number are swapped and the number gets bigger by 36. Which of these could be the number?[4]
7. Which of these numbers can be divided exactly by both 4 and 9?[4]
8. How many two-digit numbers have both of their digits odd?[5]
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1. B — odd, 49 KA-0002 Parity of numbers (odd/even behavior)
A I decided that adding odd numbers always keeps the total odd, and made an arithmetic slip as well.C I paired the numbers up and forgot that with seven numbers one is left over, so I expected an even total.D I added correctly but then labelled 49 as even because I had already decided the pairs would make it even.E I added only the first six numbers and stopped before including the thirteen.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 — 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.4. 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 9.5. 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. 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.7. 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 4.8. C — 25 KA-0135 Digit-constraint puzzles
A I counted the odd numbers in one row of ten and treated that as the whole answer.B I used four odd digits instead of five, forgetting that 9 is odd.D I counted every two-digit number that is itself odd, which only fixes the last digit.E I let the first digit be any of ten values rather than only the five odd ones.