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Math Expert V
Joined: 02 Sep 2009
Posts: 58320
In the above correctly worked addition sum, A,B,C and D represent diff  [#permalink]

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Difficulty:   15% (low)

Question Stats: 81% (02:11) correct 19% (02:22) wrong based on 75 sessions

HideShow timer Statistics In the above correctly worked addition sum, A,B,C and D represent different digits, and all the digits in the sum are different. What is the sum of A,B,C and D?

A. 23
B. 22
C. 18
D. 16
E. 14

Attachment: p003-8.gif [ 321 Bytes | Viewed 5011 times ]

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Math Expert V
Joined: 02 Aug 2009
Posts: 7953
Re: In the above correctly worked addition sum, A,B,C and D represent diff  [#permalink]

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1
Bunuel wrote: In the above correctly worked addition sum, A,B,C and D represent different digits, and all the digits in the sum are different. What is the sum of A,B,C and D?

A. 23
B. 22
C. 18
D. 16
E. 14

Attachment:
p003-8.gif

The first thing that we can say for sure is that D =1.. as B+5 or B+5+1 = 10*D + 4... and B is a digit....

Now A + C = 13, as None of A or C can be 1 as D =1.. so there are no combinations of A and C that can equal just 3..

Now from tens digit 5+B+1 = 14.... so B = 14-6=8....

so $$A+B+C+D= A+C+B+D = 13+8+1=22..$$
B
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Re: In the above correctly worked addition sum, A,B,C and D represent diff  [#permalink]

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2
'B' should be the answer.

Sum of two digits is giving three digits as the answer.

D must be 1

Now there could be two possibilities:-

Case 1:- A+C= 3

In this case 'B' would be 9. Hence sum off all digits will be 3+9+1= 13 (But this is not in the option)

Case 2:- A+C= 13

In this case 'B' would be 8. Hence sum of all digits would be 13+8+1= 22
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Math Expert V
Joined: 02 Aug 2009
Posts: 7953
Re: In the above correctly worked addition sum, A,B,C and D represent diff  [#permalink]

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'B' should be the answer.

Sum of two digits is giving three digits as the answer.

D must be 1

Now there could be two possibilities:-

Case 1:- A+C= 3

In this case 'B' would be 9. Hence sum off all digits will be 3+9+1= 13 (But this is not in the option)

Case 2:- A+C= 13

In this case 'B' would be 8. Hence sum of all digits would be 13+8+1= 22

Hi,

the high lighted portion cannot be a possiblity.....
Quote:
and all the digits in the sum are different
..
this means NOT ONLY A,B,C and D are different BUT ALSO they are different from existing digits 5,4 and 3
since you have correctly found D as 1, and A + C = 3, with both A and C as different digits..
so if A+C = 3..
two possiblities are
1) A and C are 0 and 3 but we already have 3 as one of the digits..
2) A and C are 1 and 2, but again D is already 1..

so NOT a possiblity..
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Re: In the above correctly worked addition sum, A,B,C and D represent diff  [#permalink]

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Bunuel wrote: In the above correctly worked addition sum, A,B,C and D represent different digits, and all the digits in the sum are different. What is the sum of A,B,C and D?

A. 23
B. 22
C. 18
D. 16
E. 14

Attachment:
The attachment p003-8.gif is no longer available

Ans B
file attached
Attachments 2016-05-19 22.26.27.jpg [ 303.84 KiB | Viewed 4185 times ]

Current Student Joined: 18 Oct 2014
Posts: 807
Location: United States
GMAT 1: 660 Q49 V31 GPA: 3.98
Re: In the above correctly worked addition sum, A,B,C and D represent diff  [#permalink]

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chetan2u wrote:
'B' should be the answer.

Sum of two digits is giving three digits as the answer.

D must be 1

Now there could be two possibilities:-

Case 1:- A+C= 3

In this case 'B' would be 9. Hence sum off all digits will be 3+9+1= 13 (But this is not in the option)

Case 2:- A+C= 13

In this case 'B' would be 8. Hence sum of all digits would be 13+8+1= 22

Hi,

the high lighted portion cannot be a possiblity.....
Quote:
and all the digits in the sum are different
..
this means NOT ONLY A,B,C and D are different BUT ALSO they are different from existing digits 5,4 and 3
since you have correctly found D as 1, and A + C = 3, with both A and C as different digits..
so if A+C = 3..
two possiblities are
1) A and C are 0 and 3 but we already have 3 as one of the digits..
2) A and C are 1 and 2, but again D is already 1..

so NOT a possiblity..

Thanks for pointing out chetan2u. Overlooked the possibility that A,B,C and D are different from existing digits.
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Re: In the above correctly worked addition sum, A,B,C and D represent diff  [#permalink]

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D has to be 1 because we are adding two numbers that are lower than 100, so the total has to be lower than 200.

Because D = 1, we know that A + C can't be 3, because either A or C would also need to be 1 and that is not allowed, so the only other possibility is 13.

Now, (5+1) + B = 14, thus B = 8.

13 + 8 + 1 = 22.
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In the above correctly worked addition sum, A,B,C and D represent diff  [#permalink]

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Bunuel wrote: In the above correctly worked addition sum, A,B,C and D represent different digits, and all the digits in the sum are different. What is the sum of A,B,C and D?

A. 23
B. 22
C. 18
D. 16
E. 14

Attachment:
p003-8.gif

Can we not have Zero has one of the value. It says different digits . So why not zero.

I mean can we take A =3 and C = 0 ,D=1, and B =9. Total comes to 13 ( I know its not in option) but I want to understand if ever we can consider Zero in such cases.

Thanks in advance for helping me understand. In the above correctly worked addition sum, A,B,C and D represent diff   [#permalink] 08 Sep 2019, 01:56
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