Problem 9 · 2022 Math Kangaroo
Medium
Number Theory
factor-pairs
In the multiplication grid displayed, each white cell should show the product of the numbers in the grey cells that are in the same row and column respectively. One number is already entered. The integer x is bigger than the positive integer y. What is the value of y?
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Answer: A — 6
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Hint 1 of 2
The bottom-right white cell equals (y+1) times (x+1).
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Hint 2 of 2
Factor 77 and use that x and y are positive integers with x > y.
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Approach: factor the product in the corner cell
- The 77 cell is the product of its grey row label (y+1) and column label (x+1): (y+1)(x+1) = 77.
- 77 = 7 * 11, and since x > y we take x+1 = 11, y+1 = 7.
- Then y = 6.
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