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

##### This topic has expert replies
Moderator
Posts: 7109
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

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

by BTGmoderatorDC » Wed Oct 05, 2022 5:12 pm

00:00

A

B

C

D

E

## Global Stats

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

Legendary Member
Posts: 2104
Joined: Sun Oct 29, 2017 2:04 pm
Followed by:6 members

### Re: In the addition problem ADD + ADD + ADD = SUMS, each of A, D, S, U, and M represents a different digit, and A is eve

by swerve » Sun Oct 09, 2022 8:32 am
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

• Page 1 of 1