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

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

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New post 03 Feb 2018, 22:26
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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
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Posts: 6519
Re: If a and b are two-digit numbers that share the same digits, but in re  [#permalink]

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New post 03 Feb 2018, 22:56
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

Can some please help explain how the answer?



Let a be xy that is 10x+y and b will be 10y+x..
1) a-b=10x+y-10y-x=9(x-y)=45..... x-y=5..
Number a could be 61,72,83 or 94
Insuff
2) a is MULTIPLE of 9
Number could be 81,72,54 etc
Insufficient

Combined ..
Only 72 fits in both cases..
Sufficient

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

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New post 03 Feb 2018, 23:56
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


Similar question to practice: https://gmatclub.com/forum/if-a-and-b-a ... 94795.html
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Re: If a and b are two-digit numbers that share the same digits, but in re  [#permalink]

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New post 04 Feb 2018, 00:07
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]

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New post 09 Feb 2018, 07:54
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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