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

 It is currently 15 Oct 2019, 15:10

### 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

# If the difference between a two digit positive integer and its reversa

Author Message
TAGS:

### Hide Tags

VP
Joined: 07 Dec 2014
Posts: 1222
If the difference between a two digit positive integer and its reversa  [#permalink]

### Show Tags

23 Nov 2018, 19:55
5
00:00

Difficulty:

65% (hard)

Question Stats:

53% (02:07) correct 47% (02:21) wrong based on 52 sessions

### HideShow timer Statistics

If the difference between a two digit positive integer and its reversal is three times the sum of its digits, how many such pairs are there?

A. 1
B. 2
C. 3
D. 4
E. 5
Math Expert
Joined: 02 Aug 2009
Posts: 7957
If the difference between a two digit positive integer and its reversa  [#permalink]

### Show Tags

23 Nov 2018, 20:08
1
1
gracie wrote:
If the difference between a two digit positive integer and its reversal is three times the sum of its digits, how many such pairs are there?

A. 1
B. 2
C. 3
D. 4
E. 5

Let the number be ab, so 10a+b..
Reverse is 10b+a..
Therefore 10b+a-10a-b=3(a+b).....9(b-a)=3(a+b)....3b-3a=a+b.....b=2a

So possible numbers are ..
12, 24, 36, 48...

Since we are looking for pairs..
12&21
24&42
36&63
48&84

Thus total 4

D

Note.. if question asked you numbers possible then it would be 8.
_________________
VP
Joined: 07 Dec 2014
Posts: 1222
If the difference between a two digit positive integer and its reversa  [#permalink]

### Show Tags

23 Nov 2018, 21:12
chetan2u wrote:
gracie wrote:
If the difference between a two digit positive integer and its reversal is three times the sum of its digits, how many such pairs are there?

A. 1
B. 2
C. 3
D. 4
E. 5

Let the number be ab, so 10a+b..
Reverse is 10b+a..
Therefore 10b+a-10a-b=3(a+b).....9(b-a)=3(a+b)....3b-3a=a+b.....b=2a

So possible numbers are ..
12, 24, 36, 48...
But the question doesn't specify which is greater reversed number or original
So other 4 combinations will be 21, 42, 63, 84

Thus total 8..

Note.. question requires to specify which is greater to get one choice as an answer

hi chetan2u,
the question is asking for the number of pairs of reversed two digit integers, i.e., 12&21, 24&42, 36&63, 48&84.
I hope this helps,
gracie
Math Expert
Joined: 02 Aug 2009
Posts: 7957
Re: If the difference between a two digit positive integer and its reversa  [#permalink]

### Show Tags

23 Nov 2018, 21:42
gracie wrote:
chetan2u wrote:
gracie wrote:
If the difference between a two digit positive integer and its reversal is three times the sum of its digits, how many such pairs are there?

A. 1
B. 2
C. 3
D. 4
E. 5

Let the number be ab, so 10a+b..
Reverse is 10b+a..
Therefore 10b+a-10a-b=3(a+b).....9(b-a)=3(a+b)....3b-3a=a+b.....b=2a

So possible numbers are ..
12, 24, 36, 48...
But the question doesn't specify which is greater reversed number or original
So other 4 combinations will be 21, 42, 63, 84

Thus total 8..

Note.. question requires to specify which is greater to get one choice as an answer

hi chetan2u,
the question is asking for the number of pairs of reversed two digit integers, i.e., 12&21, 24&42, 36&63, 48&84.
I hope this helps,
gracie

Yeah, correct..
Did not read the last statement..
Thanks
_________________
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4778
Location: India
GPA: 3.5
Re: If the difference between a two digit positive integer and its reversa  [#permalink]

### Show Tags

23 Nov 2018, 22:58
gracie wrote:
If the difference between a two digit positive integer and its reversal is three times the sum of its digits, how many such pairs are there?

A. 1
B. 2
C. 3
D. 4
E. 5

$$( 10a + b ) - (10b + a ) = 3( a + b)$$

Or, $$9a - 9b = 3a + 3b$$

Or, $$6a = 12b$$

Or, $$a = 2b$$

Now, plug in all values of b such that 2b is a single digit integer...
Attachment:

Capture.PNG [ 2.04 KiB | Viewed 591 times ]
We have 4 such possible values, Answer must be (D) 4
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Re: If the difference between a two digit positive integer and its reversa   [#permalink] 23 Nov 2018, 22:58
Display posts from previous: Sort by