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Number & Arithmetic15
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177 problems, every one written from scratch, every wrong answer carrying the mistake that produces it. 708 explanations in all.

Level

1–2
3–4
5–6
7–8
9–10
11–12

Point value

3 pt
4 pt
5 pt

Strand

NUMNumber & Arithmetic
CNTCounting
GEOGeometry & Visualization
LOGLogic & Deduction
PATPatterns & Sequences
MODModeling & Word Problems
CFTContest Craft

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11 problemsClear all filters

KA-0011
4 points, difficulty 2 of 3Level 3–4not yet calibrated
The four-digit number 27_4 is divisible by 3. Which digit could go in the gap?
NUM-04Divisibility rules: 2, 3, 4, 5, 9, 10also NUM-02
KA-0024
4 points, difficulty 2 of 3Level 5–6not yet calibrated
Red and blue counters are in the ratio 3 to 5. There are 40 counters altogether. How many are red?
NUM-11Ratio as parts of a wholealso NUM-09
KA-0033
4 points, difficulty 2 of 3Level 5–6not yet calibrated
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?
NUM-15Means, and working backwards from a meanalso LOG-08
KA-0053
4 points, difficulty 2 of 3Level 5–6not yet calibrated
What is the remainder when 2 to the power 30 is divided by 7?
NUM-06Remainders and modular cyclesalso PAT-03, NUM-07
KA-0056
4 points, difficulty 2 of 3Level 3–4not yet calibrated
The two digits of a number are swapped and the number gets bigger by 36. Which of these could be the number?
NUM-01Place value and digit positionsalso NUM-02
KA-0058
4 points, difficulty 2 of 3Level 5–6not yet calibrated
What is 2 + 4 + 6 + ... + 100?
NUM-08Clever regrouping (pair to round numbers)also PAT-02
KA-0062
4 points, difficulty 2 of 3Level 5–6not yet calibrated
24 pencils and 36 erasers are shared into identical gift bags, using every item. What is the largest number of bags possible?
NUM-05Factors, multiples, LCM and GCD by listingalso NUM-04
KA-0063
4 points, difficulty 2 of 3Level 3–4not yet calibrated
Which of these numbers can be divided exactly by both 4 and 9?
NUM-04Divisibility rules: 2, 3, 4, 5, 9, 10also NUM-01
KA-0065
4 points, difficulty 2 of 3Level 5–6not yet calibrated
A price goes up by 20%, then down by 20%. Compared with the original price, the final price is:
NUM-10Percentages and simple discountsalso NUM-09
KA-0066
4 points, difficulty 2 of 3Level 5–6not yet calibrated
The mean of four numbers is 9. Three of them are 5, 8 and 12. What is the fourth?
NUM-15Means, and working backwards from a meanalso LOG-08
KA-0149
4 points, difficulty 2 of 3Level 5–6not yet calibrated
What is the units digit of 3 multiplied by itself 100 times, that is 3 to the power 100?
NUM-07Last-digit behavior of products and powersalso NUM-06, PAT-03

Browse the problems — Kangaroo Atlas