Adding ABCD

[HaydnC736]

Hi, I am wondering where the supporting material is for this problem in the 6th Edition GMAT Prep books or in the Advanced Quant book. It is labelled as Extra Problem types.

ABC
+ BCB
----------
CDD

In the addition shown above, A, B, C, and D represent the nonzero digits of three 3-digit numbers. What is the largest possible value of the product of A and B ?

a. 8

b. 10

c. 12

d. 14

e. 18

Explanation: First, note that A, B, C, and D have to be digits between 1 and 9 (and the problem does not prevent some letters from having the same value).

The two rightmost columns both contain C + B = D. From that information, you can deduce that B + C < 9. (If B + C were 10 or more, then the rightmost column would “carry over” into the next column, making the tens digit into D + 1 rather than D.)

Next, A + B = C. A larger value of C, then, will reduce B (because B + C < 9) and therefore increase A (because A + B = C).

Since the questions asks to maximize the product for A and B, consider only the cases in which B + C = 9. Further, since A + B = C, you also know that B must be less than C. (Not sure why? Test a couple of real numbers to figure it out.) That leaves only a few cases, so write them out:

If B = 1 and C = 8, then A = 7. In this case, the product of A and B is 7.
If B = 2 and C = 7, then A = 5. In this case, the product of A and B is 10.
If B = 3 and C = 6, then A = 3. In this case, the product of A and B is 9.
If B = 4 and C = 5, then A = 1. In this case, the product of A and B is 4.

That’s all of the possible cases. The largest possible product is 10.

The correct answer is B

I am asking about the location in the books because I think this is an area of the test I can master, but need more practice.

Thank you,

Haydn

[Sage Pearce-Higgins]

This topic - digit problems - makes a brief appearance in chapter 9 of the FDP guide. There are also several problems in the Official Guide and perhaps the Official Quant Review of this type. However, it's not a big topic, and probably not worth investing a lot of study time in.