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

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Bunuel
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If the difference between a two digit positive integer and its reversa [#permalink] New post   11 Nov 2019, 01:20
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A
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Competition Mode Question



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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D
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Re: If the difference between a two digit positive integer and its reversa [#permalink] New post   11 Nov 2019, 02:22
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xy-yx=3(x+y)
10x+y-10y-x=3x+3y
x=2y

4digits(x={1,2,3,4};y={2,4,6,8}) satisfies above equation

OA:D
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Re: If the difference between a two digit positive integer and its reversa [#permalink] New post   11 Nov 2019, 02:33
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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

Let the two digits number be 10a + b
Reverse is 10b + a

Now, 10a + b - 10b - a = 3(a + b)
9a - 9b = 3a + 3b
6a = 12b
a = 2b

'a' can have only four values for which 'b' would have four values. The numbers are:
a = 1, b = 2
a = 2, b = 4
a = 3, b = 6
a = 4, b = 8

Hence only four numbers are possible.

IMO Answer D.
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Re: If the difference between a two digit positive integer and its reversa [#permalink] New post   11 Nov 2019, 03:15
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10a+b-10b-a=3(a+b)

3(a-b)=(a+b)
a=2b
possible pairs ( 1,2) ( 2,4) (3,6) (4,8)
IMO D ; 4


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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Re: If the difference between a two digit positive integer and its reversa [#permalink] New post   11 Nov 2019, 04:32
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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


10A+B-(10B+A)=3(A+B)
9(A-B)=3(A+B)
A=2B
0<A≤9
A={2,4,6,8}; B={1,2,4,3}
(A,B)={2,1;4,2;6,4;8,3}: 4 pairs

Ans (D)
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Re: If the difference between a two digit positive integer and its reversa [#permalink] New post   11 Nov 2019, 05:26
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Imo. D

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?
10a+b - (10b+a) = 3 (a+b)
9a-9b = 3a+3b
6a=12b
a/b=2/1
Let's check the respective numbers
21-12 = 3 *3
42-24 = 3 * 6
63-36 = 3 * 9
84-48 = 3 * 12

Sp, total 4 such pairs are possible.

Hence, D.
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Re: If the difference between a two digit positive integer and its reversa [#permalink] New post   11 Nov 2019, 09:38
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Let the two digit number be m = xy = 10x + y
And number obtained by reversing be n = yx = 10y + x

Difference = 10x + y - (10y + x) = 9x - 9y = 9(x - y)

Given, 9(x - y) = 3(x + y)
—> 3(x - y) = x + y
—> 2x = 4y
—> x = 2y
—> Possible values = 12, 24, 36, 48
—> Possible pairs of 2 digit number and its reversal = {(12,21). (24,42), (36,63), (48,84)}
—> 4 pairs

IMO Option D

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Re: If the difference between a two digit positive integer and its reversa [#permalink] New post   11 Nov 2019, 15:53
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10x+y-(10y+x)=3(x+y)→
x=2y
so 4 possible pairs are:
21&12
42&24
63&36
84&48
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Re: If the difference between a two digit positive integer and its reversa [#permalink] New post   11 Nov 2019, 21:43
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Let the two digit positive number =ab
then its reverse is ba
ab-ba=3(a+b)
but ab=10a+b and ba=10b+a
10a+b-(10b+a)=3a+3b
9a-9b=3a+3b
6a-12b=0
6(a-2b)=0
This implies a=2b
since when b=0 a=0, b cannot be 0
only four other possible values exist which yield unique value for a, since the largest unit digit that a can take is 8 based on the given condition of a=2b.
The set of possible values of b={1, 2, 3, 4}

The answer is, therefore, option D in my view.
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Re: If the difference between a two digit positive integer and its reversa [#permalink] New post   11 Nov 2019, 22:39
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Answer is D(4)

x=2 y=1
x=4 y=2
x=6 y=3
x=8 y=4
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Re: If the difference between a two digit positive integer and its reversa [#permalink] New post   19 Nov 2019, 19:27
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Bunuel wrote:

Competition Mode Question



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

Are You Up For the Challenge: 700 Level Questions


We can let a = tens digit and b = ones digit, and create the equation:

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

10a + b - 10b - a = 3a + 3b

6a = 12b

a = 2b

We see that a can be 2, 4, 6, or 8, so there are 4 such pairs.

Answer: D
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Re: If the difference between a two digit positive integer and its reversa [#permalink] New post   16 Mar 2021, 01:19
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Two-digit positive integer: 10x + y [Ten's digit is 'x' and unit digit is 'y']

Its reversal: 10y + x

=> 10x + y - 10y - x = 3(y + x)

=> 9x - 9y = 3y + 3x

=> 9x - 3x = 3y + 9y

=> 6x = 12y

=> x = 2y

Ten's digit should be double of unit digit: Possible pairs = (2,1), (4,2), (6,3), (8,4)

Four pairs.

Answer D
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Re: If the difference between a two digit positive integer and its reversa [#permalink] New post   25 May 2022, 12:00
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Let the two-digit integer be ‘pq’, which can also be represented as 10p + q.
Therefore, the integer formed by reversing the given integer would be ‘qp’, which can also be represented as 10q + p.

The difference between the two-digit integer and its reverse = 10p + q – (10q + p) = 9p – 9q.

9p – 9q = 3(p + q).

Therefore, 6p = 12q or p = 2q.

Since p and q are digits of a number, they can take values from 0 to 9.
Four ordered pairs of values satisfy the equation above, namely, (2,1), (4,2), (6,3) and (8,4) in that order for p and q.

The correct answer option is D.
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Re: If the difference between a two digit positive integer and its reversa [#permalink] New post   21 Oct 2023, 07:57
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Re: If the difference between a two digit positive integer and its reversa [#permalink]
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