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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]

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18 May 2011, 02:00
00:00

Difficulty:

25% (medium)

Question Stats:

87% (01:24) correct 13% (01:15) wrong based on 38 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.

[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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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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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

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Kudos [?]: 592 [0], given: 36

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1964

Kudos [?]: 2051 [0], given: 376

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18 May 2011, 06:33
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?

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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Manager
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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]

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17 Nov 2016, 07:24
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?

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

Kudos [?]: 9 [0], given: 55

Re: X is a two-digit number. If the ratio between the units   [#permalink] 17 Nov 2016, 07:24
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