ab + cd = efg

Question

ab + cd = efg, where 
a and b are the digits of the two digit number ab, 
c and d are the digits of the two digit number cd,
e, f and g are the digits of the three digit number efg.

Is f = c ?

1. a + 1 = 10
2. b + d = 10 + g

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Bunuel · Answer

Anyone want to try?

Harley1980 · Answer

1) from this statement we know that  a = 9  
Insufficient because we know nothing about  b ,  d  and  c

2) from this statement we know that  b + d  is a number between  10  and  19  so when we will be add  ab  and  cd  we will receive additional  1  in  a + c   (in expression  ab + cd , not by itself) 
But we know nothing about  a 
Insufficient

1+2) we know that  a = 9  and that  b + d  gives additional  1  to  a + c 
So we can infer that  a + c  will be equal  9 + 1 + c = 10 + c 
So  c = f

Sufficient 
Answer is C

pacifist85 · Answer

I did it, but it really took me a lot of time.

says that A=9, which is not sufficient.
  says that B+D are more than 10, which is not sufficient.

are sufficient, which is easier to see on paper:

9.....B
C.....D
.........
0.....0 *

*So here, we know that B+D > 10. 
Let's say they are equal to 10. So, we will add them up to 0, with 1 left over.
Lets also give C the minimum possible value, 0.
We add the 1 left over to 9, and we end up with 10. So, we will write 0 and I will be left over. So, in this case, C=F=0.

You can try other numbers and you will see that C and F will again be the same number.

However, I would NEVER be able to do this on time and I don't really think we should be expecting this type of questions. Has there ever been a similar one? Seeing such a question would seem as a bit of a waste to me... And sort of like someone just wants to joke around!

Harley1980 · Answer

Hello pacifist85 This is your decision about such tasks to do them or not. But this tasks are definitely not a somebody's joke For example here is 3 task from official guide: each-of-the-letters-in-the-table-above-represents-one-of-the-numbers-59650.html if-x-0-rstu-where-r-s-t-and-u-each-represent-a-nonzero-109735.html is-the-positive-two-digit-integer-n-less-than-143505.html (it was a quick search but there is much more such tasks in gmat prep and gmat cats) These task not so common, but this type of tasks is like mixtures and probabilities tasks. They are rarely but if you exlude a lot of such types of tasks you can be in difficult situation on the exam. If you will change your decision about such tasks here is really cool articles about alphametic from Kharisma: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2015/04 ... -the-gmat/ https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2015/04 ... -the-gmat/

Harley1980 · Answer

Another alphametic tasks for practice:
if-the-units-digit-of-the-three-digit-positive-integer-k-is-nonzero-85443.html
in-the-correctly-worked-addition-problem-above-m-n-r-s-t-and-v-197408.html
if-in-the-addition-problem-above-a-b-c-d-e-f-x-y-a-97479.html
in-the-table-above-is-z-20q-104122.html
the-symbols-represent-non-zero-digits-if-148803.html
both-a-b-and-c-are-3-digits-integers-where-a-b-c-is-the-126570.html

You can find more of them by tag 'arithmetic':
search.php?search_id=tag&tag_id=30

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ab + cd = efg

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ab + cd = efg

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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