Whole Numbers · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Which number can be shown as a line (a straight row of dots) but NOT as a rectangle with more than one row?
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Answer: C) 7
7 is prime, so its dots can only be arranged in a single line (1 row of 7). 6 = 2x3, 8 = 2x4 and 9 = 3x3 can form rectangles.
2. Which number can be arranged as BOTH a rectangle (with more than one row) and is also a square number?
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Answer: B) 9
9 = 3 x 3 is a square (and a rectangle). 6, 10, 12 are rectangles but not squares.
3. Riya arranges marbles in growing triangles: 1 marble in the first, then 1 + 2 in the second, then 1 + 2 + 3 in the third, and so on.
How many marbles are in her 8th triangle?
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Answer: C) 36
The 8th triangular number = 1+2+...+8 = 28×9=36.
4. Observe:
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
What is 1234 x 9 + 5?
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Answer: B) 11111
The results have one more 1 each line: 11, 111, 1111, so next is 11111. Check: 1234 x 9 = 11106, + 5 = 11111.
5. Anya writes three-digit numbers whose three digits, read in order, are consecutive whole numbers increasing by 1, like 123, 234, 345 (so 8 and 9 cannot be followed since the next digit would exceed 9).
How many such three-digit numbers can she write?
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Answer: B) 7
The first digit can be 1,2,3,4,5,6,7 (it must be at least 1 and the third digit first+2 must be at most 9, so first <= 7). That gives 123, 234, 345, 456, 567, 678, 789 = 7 numbers.