Question

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Answer 1

Answer:   15

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Explanation:

For this problem, we can make a lattice multiplication diagram. Place the digits of 124 across the top of the lattice multiplication box. Then place the digits along the right hand side of the box. Refer to figure 1 in the diagram below. I've color-coded the alternating bands of diagonals to help be able to add the values we need.

In figure 2, I multiplied all of the outer header single-digit values to get two-digit results. For instance, in the bottom right corner we have 4*3 = 12. Note how the 1 and the 2 of "12" is broken up like you see in figure 2. It's important to separate out the digits like this.

This is because we'll be adding along the diagonal color bands. The 2 in the white triangle in the very bottom right corner is the last digit of the product. This matches with 64086e2 having 2 as the last digit.

Then we add along the diagonal pink color band getting 6+1+2 = 9. This is the digit e. So e = 9 (refer to figure 3). The number 64086e2 updates to 6408692

We could keep going with the lattice process, but I'll stop here and move onto the next section below.

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Let m = 6408692

We can do trial and error to determine what d must be equal to. The list of choices we have are {0,1,2,3,4,5,6,7,8,9}

So let's go through those possible values of d

• If d = 0, then 124*51083 = 6334292 but it is not equal to m.
• If d = 1, then 124*51183 = 6346692 but it is not equal to m.
• If d = 2, then 124*51283 = 6359092 but it is not equal to m.
• If d = 3, then 124*51383 = 6371492 but it is not equal to m.
• If d = 4, then 124*51483 = 6383892 but it is not equal to m.
• If d = 5, then 124*51583 = 6396292 but it is not equal to m.
• If d = 6, then 124*51683 = 6408692 which is equal to m.

Since d = 6 and e = 9, this means d+e = 6+9 = 15.