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

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Joined: 07 Dec 2014
Posts: 1224
If the difference between a two digit positive integer and its reversa  [#permalink]

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23 Nov 2018, 19:55
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Difficulty:

65% (hard)

Question Stats:

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

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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: 7998
If the difference between a two digit positive integer and its reversa  [#permalink]

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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.
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If the difference between a two digit positive integer and its reversa  [#permalink]

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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: 7998
Re: If the difference between a two digit positive integer and its reversa  [#permalink]

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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
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Re: If the difference between a two digit positive integer and its reversa  [#permalink]

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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 596 times ]
We have 4 such possible values, Answer must be (D) 4
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Abhishek....

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Re: If the difference between a two digit positive integer and its reversa   [#permalink] 23 Nov 2018, 22:58
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# If the difference between a two digit positive integer and its reversa

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