BTGmoderatorDC wrote: ↑

Wed Oct 05, 2022 5:12 pm

In the addition problem ADD + ADD + ADD = SUMS, each of A, D, S, U, and M represents a different digit, and A is even. What is the value of the digit U?

A. 2
B. 3
C. 4
D. 5
E. 6


OA D

Source: Veritas Prep

Given: In the addition problem \(ADD + ADD + ADD = SUMS\), each of \(A, D, S, U,\) and \(M\) represents a different digit, and \(A\) is even.

Asked: What is the value of the digit \(U\)?

Let us take \(D = 1; \, S = 3\, \& \,M = 3\); Since \(S\, \& \,M\) are different digits \(D =1\) is not possible
Let us take \(D = 2;\, S = 6\, \& \,M = 6\); Since \(S\, \& \,M\) are different digits \(D =2\) is not possible
Let us take \(D = 3; \,S = 9\, \& \,M = 9\); Since \(S\, \& \,M\) are different digits \(D =3\) is not possible

Let us take \(D = 4; \,S = 2 \& \,M = 3\); Since \(S \& M\) are different digits \(D =4\) is possible
\(A44+A44+A44=2U32\)

There is a carry over of \(1\) for hundredth digit.
Since \(A\) is even; \(A = \{2,4,6,8\}\); \(3A = \{6,12,18,24\}\); \(3A+1 = \{7,13,19,25\}\)
Since \(3A+1 = 2U\); only \(A = 8\) is possible
\(844+844+844 = 2532\)
\(U = 5\)

Therefore, D