Math Counts Question 7

Since John entered exactly 1 digit incorrectly he must have left one of the factors unchanged. $3596$ is not divisible by $67$ , but by $3596 = 62 \cdot 58$ so the factors he actually multiplied must have been $62$ and $58$ , their sum is $62+58 = \boxed{120}$ .

67 * 58 = 3886
3886 - 3596 = 290
58 * 5 = 290
67 - 5 = 62
62 * 58 = 3596
62 + 58 = 120

It is mentioned that only one digit is entered incorrectly. So it has to be either a digit in 67 or 58.

The given product is 3596. It should either be divisible by 67 or 58( as only one digit is incorrect in either of the two)

We see that 3596 is divisible by 58 . 58x62=3596. Hence, the answer is 58+62=120.

I tried dividing $3596$ with both $67$ and $58$ , as only one number can be changed

Division by $67$ doesn't give a whole number, so I divided by $58$ instead

I then got the result of $62$

$\large 62 + 58 = \boxed{120}$

John only entered 1 digit incorrectly which means that one of the factors remains the same. To find this digit you need to divide one of factors to 3596 (Note: this factor will remain the same). Since 3596 can't be divided by 67, 67 is the number that won't remain the same. Hence, 3596 ÷ 58 = 62. Finally, 62 + 58 = 120

58*62=3596 58+62=120

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