Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59561

In the addition problem ADD + ADD + ADD = SUMS, each of A, D, S, U, an
[#permalink]
Show Tags
09 Nov 2017, 23:13
Question Stats:
34% (02:40) correct 66% (02:45) wrong based on 238 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.




Retired Moderator
Joined: 25 Feb 2013
Posts: 1159
Location: India
GPA: 3.82

In the addition problem ADD + ADD + ADD = SUMS, each of A, D, S, U, an
[#permalink]
Show Tags
11 Nov 2017, 07:24
Bunuel wrote: 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 \(+ADD\) \(+ADD\) \(+ADD\)  \(SUMS\) so unit's digit of \(3D\) is \(S\) and \(M\) and given that every digit is distinct, this implies that \(D>=4\) to have a carry forward of \(1\) or \(2\) So starting with \(D=4\) we can calculate values of all variables and test the given conditions to arrive at the final answer Case 1: \(D=4\) > \(S=2\) > \(M=3\) > \(A=8\) > \(U=5\) (as \(A\) is even and addition \(3D\) in Ten’s digit will give only \(1\) as carry forward. Since \(S\), in the thousands place, has to be \(2\) so \(A\) has to be \(8\), the largest even digit possible to have a carry forward of \(2\)) So in Case 1, we got all our distinct variables. We can stop here or we can test for \(D=5,6,7,8,9\) and match the subsequent conditions. For any other value of \(D\), one or the other condition will not satisfy. Hence our answer \(U=5\) Option D




Current Student
Joined: 18 Aug 2016
Posts: 594
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38

Re: In the addition problem ADD + ADD + ADD = SUMS, each of A, D, S, U, an
[#permalink]
Show Tags
09 Nov 2017, 23:34
Bunuel wrote: 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 ADD + ADD + ADD = SUMS Addition of three 3digit numbers giving sum of 4digit number can yield S as only 1 or 2 multiplication of 3 * D = Last digit 1 ...D=7 multiplication of 3 * D = Last digit 2 ...D=4 CASE 1: S = 1 and D = 7 now A is even can take 2,4,6,8,0 we know multiplication of 3 * A + 2 = 1U 0 and 2 not possible (no carry over to form 4digit) (0*3 = 0, 2*3 = 6) Putting A= 8 gives U= 6 but S= 2 ..not possible Putting A= 6 gives U= 0 but S= 2 ..not possible Putting A= 4 gives U= 4 and S= 1 ..not possible (unique digits) CASE 2: S = 2 and D = 4 we know multiplication of 3 * A + 2 = 1U now A is even can take 2,4,6,8,0 A cannot take 2,4 (already takenunique digits) Putting A= 6 gives U= 9 but S= 1 ..not possible Putting A= 8 gives U= 5 and S= 2 ..possible Hence A = 8, D = 4, S = 2 and U = 5 D
_________________
We must try to achieve the best within us
Thanks Luckisnoexcuse



Intern
Joined: 19 Sep 2011
Posts: 26

Re: In the addition problem ADD + ADD + ADD = SUMS, each of A, D, S, U, an
[#permalink]
Show Tags
13 Nov 2017, 21:04
Ans D ) u =5
D cannot be 1 , 2, 3 or 5 because then m= s which is not possible as given in the question. 3D = S and 3D = M and all digits are different which implies that M = 3D+ Carry from 3D = S. Also from the question it can be deduced that since 3A = SU then S can at max be digit 2 if we take the max value of A which is A= 8.
Let say s= 2 then D = 4 m=3 and u =5 only. Plug in the answer and ADD = 844



Manager
Joined: 11 Aug 2017
Posts: 59

Re: In the addition problem ADD + ADD + ADD = SUMS, each of A, D, S, U, an
[#permalink]
Show Tags
13 Mar 2019, 22:55
Bunuel wrote: 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 very time consuming question. how to arrive to the conclusion fast?? I cant find other approach other than basic number sense for max. value of fourth digit. Rest was hit and trial



Manager
Joined: 29 Nov 2018
Posts: 149
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)

In the addition problem ADD + ADD + ADD = SUMS, each of A, D, S, U, an
[#permalink]
Show Tags
18 Jun 2019, 20:41
Official explanation: When the GMAT asks abstract calculation problems, your job is to make that abstraction more concrete using two methods:
1) Limit the number of options by adhering to and proving rules about the situation provided.
2) Test numbers via trialanderror to eliminate options and to learn more about the situation.
For example here, you can start by limiting the options for A: since A must be even and it cannot be 0 (if it were, then the number ADD would just be DD), you only have four options for A: 2, 4, 6, and 8.
But if you quickly try 2, you'll see that even with the greatest possible D, you won't have large enough numbers to produce a thousands digit S in the sum. 299 + 299 + 299 is 897, and you need a number that's 1000 or greater. So you can limit your options for A to 4, 6, or 8.
Next, consider the sum SUMS. Since you're adding three threedigit numbers to produce SUMS, the S has a limit to it also. Even if you added the three greatest threedigit numbers possible, 999 + 999 + 999, you'd end up with a number less than 3000. So S can only be 1 or 2.
Also consider that in SUMS M and S must be different digits, meaning that adding three Ds must sum to something greater than 10 so that the operation forces you to carry a tens digit and make M different from S. (For example, 411 + 411 + 411 would give you 1233 with the same M and S. You need D to be large enough that you don't have repeat digits in the tens and units places in the sum).
So from quick trial and error and some application of the rules provided, you know three things:
A can only be 4, 6, or 8 S can only be 1 or 2 D must be greater than 3
From here you can use some units digit rules along with trialanderror to arrive at SUMS. In the units place, 3D (the sum of D + D + D) can only be 1 or 2. In order for it to be 1, D would have to be 7. So you might try:
477 + 477 + 477 = 1431
But note that in this situation U and D are each 4, which violates the situation that they must be different values. So this cannot work. The next possible value ending in 77 would be 677, but at that point the sum would begin with a 2 (677 + 677 + 677 = 2031, or you could just know that 667 is 1/3 of 2000 and so three 677s would be greater than that). And that doesn't work because the S values in SUMS would be different.
So S cannot be 1, meaning that it must be 2. In order for that to be the case, you'd need D to be 4 (since 4x3 = 12). Here you can try again: if A cannot be 4 (that would be a repeat value), then you could try 6, but recognize again that you'd need something greater than 666 to reach a thousands digit of 2, since 2000 divided by 3 is 666.67. So your only choice is 844 + 844 + 844 = 2532. This then means that the correct answer is 5.



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8619
Location: United States (CA)

Re: In the addition problem ADD + ADD + ADD = SUMS, each of A, D, S, U, an
[#permalink]
Show Tags
21 Jun 2019, 11:36
Bunuel wrote: 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 First of all, we can simplify the expression as 3(ADD) = SUMS. Therefore, instead of looking it as a sum, let’s look at it as a product. Since A is even and it can’t be 0, let’s say A is 2. However, when we multiply a number in the 200’s by 3, the product can’t be a 4digit number (since the product will be less than 900). We see that A can’t be 2. So let’s say A is 4. The product of a number in the 400’s and 3 is a 4digit number. In that case, S, the thousands digit of the product, must be 1. Since S is also the units digit of the product, we see the D must be 7. So let’s see if it works: 3(477) = 1431 However, this doesn’t work since we would have U = 4, but A is already 4. We see that A can’t be 4. So let’s say A = 6. The product of a number in the 600’s and 3 is a 4digit number. In that case, S is either 1 or 2. If S = 1, then D has to be 7 also. If S = 2, then D has to be 4. Let’s see which one works: 3(677) = 2031 (This doesn’t work; we see that the units digit is 1, but the thousands digit is not.) 3(644) = 1932 (This doesn’t work, either; we see that the units digit is 2, but the thousands digit is not.) Now we are left to try A = 8. If that is the case, then S must be 2 and D must be 4. Let’s see if it works: 3(844) = 2532 We see that this works indeed!. So U = 5. Answer: D
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 08 Jun 2019
Posts: 4

Re: In the addition problem ADD + ADD + ADD = SUMS, each of A, D, S, U, an
[#permalink]
Show Tags
04 Sep 2019, 02:51
Why cant ADD be 477, A is even, SUMS=1431, U=4



Intern
Joined: 25 Jan 2013
Posts: 29
Location: United States
Concentration: General Management, Entrepreneurship

Re: In the addition problem ADD + ADD + ADD = SUMS, each of A, D, S, U, an
[#permalink]
Show Tags
07 Sep 2019, 10:01
KritiG wrote: Why cant ADD be 477, A is even, SUMS=1431, U=4 U is 4 and A is already 4. Needs to be different digits.



SVP
Joined: 03 Jun 2019
Posts: 1875
Location: India

In the addition problem ADD + ADD + ADD = SUMS, each of A, D, S, U, an
[#permalink]
Show Tags
08 Sep 2019, 05:17
Bunuel wrote: 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 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 IMO D




In the addition problem ADD + ADD + ADD = SUMS, each of A, D, S, U, an
[#permalink]
08 Sep 2019, 05:17






