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If the difference between a two digit positive integer and its reversa
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11 Nov 2019, 01:20
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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 Are You Up For the Challenge: 700 Level Questions
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Re: If the difference between a two digit positive integer and its reversa
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11 Nov 2019, 02:22
xyyx=3(x+y) 10x+y10yx=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
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11 Nov 2019, 02:33
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
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11 Nov 2019, 03:15
10a+b10ba=3(a+b)
3(ab)=(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
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11 Nov 2019, 04:32
Quote: 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(AB)=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
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11 Nov 2019, 05:26
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) 9a9b = 3a+3b 6a=12b a/b=2/1 Let's check the respective numbers 2112 = 3 *3 4224 = 3 * 6 6336 = 3 * 9 8448 = 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
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11 Nov 2019, 09:38
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
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11 Nov 2019, 15:53
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
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11 Nov 2019, 21:43
Let the two digit positive number =ab then its reverse is ba abba=3(a+b) but ab=10a+b and ba=10b+a 10a+b(10b+a)=3a+3b 9a9b=3a+3b 6a12b=0 6(a2b)=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
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11 Nov 2019, 22:39
Answer is D(4)
x=2 y=1 x=4 y=2 x=6 y=3 x=8 y=4




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