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X is a two-digit number. If the ratio between the units

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X is a two-digit number. If the ratio between the units [#permalink] New post 18 May 2011, 01:00
00:00
A
B
C
D
E

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Question Stats:

92% (01:26) correct 8% (03:24) wrong based on 12 sessions
X is a two-digit number. If the ratio between the units digit and the tens digit is 1 to 2, what is the value of X?
(1) The sum of the digits multiplied by the tens digit is 54.
(2) The product of the digits divided by 2 is 9.

[Reveal] Spoiler:
I think OA should be E.
Given: x(tens digit) y(units digit) y/x =1/2
Stmt1: The sum of the digits multiplied by the tens digit is 54.
(x+y)x=54
x^2+xy=54
x^2+x^2/3 =54
3x^2/2=54
x^2=36
x=6 or x=-6
y=3 or y=-3
Number 10x+y=63 or -63

Stmt2:The product of the digits divided by 2 is 9.
xy/2=9
x^2/4=9
x=6 or x=-6
Number 10x+y=63 or -63

Any thoughts?
[Reveal] Spoiler: OA

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Re: Digits [#permalink] New post 18 May 2011, 01:45
possibles combinations (2,1),(4,2),(6,3),(8,4)

a 6*9 = 54
b 18/2 = 9

D
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Re: Digits [#permalink] New post 18 May 2011, 04:02
X = AB

(1)

B/A = 1/2

(A+B) * A = 54

54 = 6 * 3 * 3

Only X = 63 satisfies this

Sufficient

(2)

B/A = 1/2

AB/2 = 9

=> B = 3, A = 6

Sufficient

Answer - D
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Re: Digits [#permalink] New post 18 May 2011, 05:33
jamifahad wrote:
X is a two-digit number. If the ratio between the units digit and the tens digit is 1 to 2, what is the value of X?
(1) The sum of the digits multiplied by the tens digit is 54.
(2) The product of the digits divided by 2 is 9.

[Reveal] Spoiler:
I think OA should be E.
Given: x(tens digit) y(units digit) y/x =1/2
Stmt1: The sum of the digits multiplied by the tens digit is 54.
(x+y)x=54
x^2+xy=54
x^2+x^2/3 =54
3x^2/2=54
x^2=36
x=6 or x=-6
y=3 or y=-3
Number 10x+y=63 or -63

Stmt2:The product of the digits divided by 2 is 9.
xy/2=9
x^2/4=9
x=6 or x=-6
Number 10x+y=63 or -63

Any thoughts?


I see your point:

Qualified as digit: 0,1,2,3,4,5,6,7,8,9

Thus, a digit can never be -ve.

However, the number itself may be negative. From each of these two statements, we know what the digits are going to be. But, we may not know what the number may be. +ve or -ve.

"X is a two-digit number" -- If this means two-digit positive number, then D is the answer. Otherwise, "E" would be the answer.
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Re: Digits [#permalink] New post 18 May 2011, 09:40
both condition points to 63 ..
Hence D
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Re: Digits   [#permalink] 18 May 2011, 09:40
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