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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
C is the answer
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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
GMAT Club Bot
Re: If a and b are two-digit numbers that share the same digits, but in re [#permalink]
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