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A positive integer with three distinct digits, when added to its rever
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Updated on: 11 Aug 2017, 21:31
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A positive integer with three distinct digits, when added to its reverse, sums to a number with three identical digits. How many such pairs of integers are there? A. 2 B. 3 C. 4 D.5 E. 6 source:self sorry about the error, edited it gracie == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
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Originally posted by gracie on 11 Aug 2017, 20:37.
Last edited by gracie on 11 Aug 2017, 21:31, edited 2 times in total.



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Re: A positive integer with three distinct digits, when added to its rever
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11 Aug 2017, 20:47
I think you mean how many pairs of 3digit inters are there which when added to their respective reverse digits, gives us an integer with 3 identical digits. The answer is 3 i.e C234 & 432 123 & 321 246 & 642
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Re: A positive integer with three distinct digits, when added to its rever
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11 Aug 2017, 21:04
gracie, Please correct the OA! Also the question needs change: A positive integer with three distinct digits, when added to its reverse, sums to a three digit number with identical digits. How many such pairs of integers are there? I think the answer should be 6 {(234,432),(123,321),(246,642),(147,741),(345,543),(135,531)}
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A positive integer with three distinct digits, when added to its rever
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11 Aug 2017, 22:55
gracie wrote: A positive integer with three distinct digits, when added to its reverse, sums to a number with three identical digits. How many such pairs of integers are there?
A. 2 B. 3 C. 4 D.5 E. 6
source:self
sorry about the error, edited it gracie Let the three digit no. be ABC. Now, when you add the reverse, i.e. CBA, the middle term B will get added twice. So, the middle term of the resulting three digit no. has to be EVEN. Now, the middle term of the resulting three digit no. when ABC and CBA are added can be 4, 6 or 8 only. Why? Coz 0 and 2 are not possible since A & C cannot add up to 0 or 2 (Note: A & C are different, so 1+1 is not valid; also neither A nor C can be 0, as reversing will give a two digit number). Now, for middle term to be Even, and 2*B to be 4 or 6 or 8, B = 2 or 3 or 4. For 2*B=4: (A,C) = (1,3) > One possibility. For 2*B=6: (A,C) = (1,5), (2,4) > 2 possibilities For 2*B=8: (A,C) = (1,7), (2,6), (3,5) > 3 possibilities. Hence, in total we have 1+2+3 = 6 possible combinations. Thus, the correct answer is E. Hope it's clear
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A positive integer with three distinct digits, when added to its rever
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12 Aug 2017, 00:26
pushpitkc wrote: gracie, Please correct the OA! Also the question needs change: A positive integer with three distinct digits, when added to its reverse, sums to a three digit number with identical digits. How many such pairs of integers are there? I think the answer should be 6 {(234,432),(123,321),(246,642),(147,741),(345,543),(135,531)} This question is slightly unclear. Can we count three other combinations? 1. 420 & 024 : 444 2. 630 & 036 : 666 3. 840 & 048 : 888 Now I am confused
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Re: A positive integer with three distinct digits, when added to its rever
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12 Aug 2017, 01:04
septwibowo wrote: pushpitkc wrote: gracie, Please correct the OA! Also the question needs change: A positive integer with three distinct digits, when added to its reverse, sums to a three digit number with identical digits. How many such pairs of integers are there? I think the answer should be 6 {(234,432),(123,321),(246,642),(147,741),(345,543),(135,531)} This question is slightly unclear. Can we count three other combinations? 1. 420 & 024 : 444 2. 630 & 036 : 666 3. 840 & 048 : 888 Now I am confused 024 is 24 lol. I dont think its a three digit integer . Mods can correct me! == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
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Re: A positive integer with three distinct digits, when added to its rever
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