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

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jamifahad
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X is a two-digit number. If the ratio between the units [#permalink] New post   18 May 2011, 02:00
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

88% (02:12) correct 13% (02:06) wrong based on 24 sessions
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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.

Show 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?




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D
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amit2k9
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Re: X is a two-digit number. If the ratio between the units [#permalink] New post   18 May 2011, 02:45
possibles combinations (2,1),(4,2),(6,3),(8,4)

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

D
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Re: X is a two-digit number. If the ratio between the units [#permalink] New post   18 May 2011, 05:02
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: X is a two-digit number. If the ratio between the units [#permalink] New post   18 May 2011, 06:33
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.

Show 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: X is a two-digit number. If the ratio between the units [#permalink] New post   18 May 2011, 10:40
both condition points to 63 ..
Hence D
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Re: X is a two-digit number. If the ratio between the units [#permalink] New post   17 Nov 2016, 07:24
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.

Show 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?


a/b = 1/2
b = 2a

1)

2a(2a+a) = 54
2a(3a) = 54
6a^2=54
a^2 = 9
a = 3 or -3
It would not make sense to have a negative number in this situation, so answer is 3

2)
(2a*a)/2 = 9
a^2 = 9
a = 3 or -3
It would not make sense to have a negative number in this situation, so answer is 3

Answer is D



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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Re: X is a two-digit number. If the ratio between the units [#permalink]
17 Nov 2016, 07:24
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