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# If a and b are two-digit numbers that share the same digits, but in re

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Re: If a and b are two-digit numbers that share the same digits, but in re [#permalink]
ggpapas wrote:
If a and b are two-digit numbers that share the same digits, but in reverse order, the what is the value of a?

(1) a-b = 45
(2) The number a is a multiple of 9

Let $$a=10x+y$$ and $$b=10y+x$$, where $$x$$ & $$y$$ are digits of the two digit number $$a$$ & $$b$$. To know the value of $$a$$ we need the value of $$x$$ & $$y$$

Statement 1: $$a-b=10x+y-10y-x=45$$

$$=>9(x-y)=45=>x-y=5$$. Two variable one equation. Insufficient

Statement 2: $$a$$ is multiple of $$9$$, hence sum of digits must be multiple of $$9$$

$$=> x+y=9$$ or $$x+y=18$$. Again two variable, one equation. Insufficient

Combining 1 & 2: $$x-y=5$$ & $$x+y=9$$, solving we get $$x=7$$ & $$y=2$$

for $$x+y=18$$, we will not get $$x$$ as integer, hence $$x+y=18$$ is not possible.

Therefore $$a=72$$. Sufficient

Option C
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If a and b are two-digit numbers that share the same digits, but in re [#permalink]
ggpapas wrote:
If a and b are two-digit numbers that share the same digits, but in reverse order, the what is the value of a?

(1) a-b = 45
(2) The number a is a multiple of 9

Let a = xy, b = yx

Statement I:

$$a - b = 45,$$
$$x - y = 5$$. The values of $$(x,y) = (6,1) (7,2) (8,3) (9,4)$$.. Insufficient.

Statement II:

Not sufficient as the numbers can be $$18, 27, 36,45, 54, 63....$$

Combine I & II:

$$(x,y) = (7,2)$$... Sufficient.
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Re: If a and b are two-digit numbers that share the same digits, but in re [#permalink]
Was it mentioned that both numbers should be positive?
why cant a be -27?
a=-27 and b=-72
a-b=45
a is a multiple of 9

i chose E thinking on this line.
what am i doing wrong?
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Re: If a and b are two-digit numbers that share the same digits, but in re [#permalink]
1
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ggpapas wrote:
If a and b are two-digit numbers that share the same digits, but in reverse order, the what is the value of a?

(1) a-b = 45
(2) The number a is a multiple of 9

1) 10x+y -10y -x = 45
or, 9x -9y = 45
or, x -y = 5
The difference between the two digits of x and y is 5. Since a > b, a can be 94,83,72,61. Not sufficient
2) Because of the divisibility rule of 9, any multiples of 9 has another reverse digit pair, such as 81 and 18, 45 and 54, 27 and 72, 36 and 63. not sufficient.
Together, 72 and 27 satisfies both condition and a >b. suffcient
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Re: If a and b are two-digit numbers that share the same digits, but in re [#permalink]
let
a= 10x+y
b=10y+x

a-b = 9x-9y = 9(x-y) = 45
x-y=5
y=x-5

10x+y = 9m
11x-5=9m

holds good only when x=7
therefore C
Re: If a and b are two-digit numbers that share the same digits, but in re [#permalink]
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