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

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

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New post 23 Nov 2018, 18:55
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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
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If the difference between a two digit positive integer and its reversa  [#permalink]

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New post 23 Nov 2018, 19:08
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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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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

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New post 23 Nov 2018, 20:12
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
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Re: If the difference between a two digit positive integer and its reversa  [#permalink]

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New post 23 Nov 2018, 20:42
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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

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New post 23 Nov 2018, 21:58
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
Capture.PNG [ 2.04 KiB | Viewed 331 times ]
We have 4 such possible values, Answer must be (D) 4
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Re: If the difference between a two digit positive integer and its reversa &nbs [#permalink] 23 Nov 2018, 21:58
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