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

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Intern
Joined: 31 Jan 2018
Posts: 8
If a and b are two-digit numbers that share the same digits, but in re [#permalink]

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03 Feb 2018, 21:26
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Question Stats:

49% (01:42) correct 51% (01:23) wrong based on 71 sessions

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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
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Aug 2009
Posts: 5649
Re: If a and b are two-digit numbers that share the same digits, but in re [#permalink]

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03 Feb 2018, 21:56
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

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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BANGALORE/-

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Joined: 02 Sep 2009
Posts: 43792
Re: If a and b are two-digit numbers that share the same digits, but in re [#permalink]

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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

Similar question to practice: https://gmatclub.com/forum/if-a-and-b-a ... 94795.html
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Posts: 919
Location: India
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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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03 Feb 2018, 23:07
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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09 Feb 2018, 06:54
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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If a and b are two-digit numbers that share the same digits, but in re   [#permalink] 09 Feb 2018, 06:54
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