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A positive integer with three distinct digits, when added to its rever

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A positive integer with three distinct digits, when added to its rever [#permalink]

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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
[Reveal] Spoiler: OA

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 [#permalink]

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New post 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 C
234 & 432
123 & 321
246 & 642
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Re: A positive integer with three distinct digits, when added to its rever [#permalink]

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New post 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 [#permalink]

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New post 11 Aug 2017, 22:55
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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 [#permalink]

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New post 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 :lol: :lol: :lol:
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Re: A positive integer with three distinct digits, when added to its rever [#permalink]

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New post 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 :lol: :lol: :lol:


024 is 24 lol. I dont think its a three digit integer :-D . Mods can correct me!
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Kudos [?]: 33 [0], given: 17

Re: A positive integer with three distinct digits, when added to its rever   [#permalink] 12 Aug 2017, 01:04
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