GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 May 2019, 20:17

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
VP
Joined: 07 Dec 2014
Posts: 1192
A positive integer with three distinct digits, when added to its rever  [#permalink]

### Show Tags

Updated on: 11 Aug 2017, 21:31
1
00:00

Difficulty:

55% (hard)

Question Stats:

67% (00:29) correct 33% (02:15) wrong based on 9 sessions

### HideShow timer Statistics

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

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 re-post 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.

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.
Senior Manager
Joined: 17 Oct 2016
Posts: 260
Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38
GMAT 2: 680 Q48 V35
GPA: 3.05
WE: Pharmaceuticals (Health Care)
Re: A positive integer with three distinct digits, when added to its rever  [#permalink]

### Show Tags

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
_________________
_____________________
Chasing the dragon
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Re: A positive integer with three distinct digits, when added to its rever  [#permalink]

### Show Tags

11 Aug 2017, 21:04

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)}
_________________
You've got what it takes, but it will take everything you've got
Retired Moderator
Joined: 18 Dec 2014
Posts: 358
GMAT 1: 770 Q50 V45
GPA: 3.85
WE: Design (Energy and Utilities)
A positive integer with three distinct digits, when added to its rever  [#permalink]

### Show Tags

11 Aug 2017, 22:55
1
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

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
_________________
12345aBcDeFgHiJkLmNoPqRsTuVwXyZ67890
Manager
Joined: 27 Dec 2016
Posts: 232
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
A positive integer with three distinct digits, when added to its rever  [#permalink]

### Show Tags

12 Aug 2017, 00:26
pushpitkc wrote:

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
_________________
There's an app for that - Steve Jobs.
Senior Manager
Joined: 17 Oct 2016
Posts: 260
Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38
GMAT 2: 680 Q48 V35
GPA: 3.05
WE: Pharmaceuticals (Health Care)
Re: A positive integer with three distinct digits, when added to its rever  [#permalink]

### Show Tags

12 Aug 2017, 01:04
septwibowo wrote:
pushpitkc wrote:

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 re-post 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.

_________________
_____________________
Chasing the dragon
Re: A positive integer with three distinct digits, when added to its rever   [#permalink] 12 Aug 2017, 01:04
Display posts from previous: Sort by