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For all x, the expression x* is defined to be ax + a, where a is......

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For all x, the expression x* is defined to be ax + a, where a is...... [#permalink]

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New post 22 May 2016, 23:00
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Question Stats:

92% (00:54) correct 8% (00:37) wrong based on 207 sessions

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For all \(x\), the expression \(x^*\) is defined to be \(ax + a\), where \(a\) is a constant. What is the value of \(2^*\)?

(1) \(3^* = 2\)
(2) \(5^* = 3\)
[Reveal] Spoiler: OA

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Re: For all x, the expression x* is defined to be ax + a, where a is...... [#permalink]

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New post 23 May 2016, 00:02
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nalinnair wrote:
For all \(x\), the expression \(x^*\) is defined to be \(ax + a\), where \(a\) is a constant. What is the value of \(2^*\)?

(1) \(3^* = 2\)
(2) \(5^* = 3\)


x* = ax + a = a (x + 1)
2* = ?

Statement 1: 3* = 2
or 3a + a = 2
a = 1/2

Hence 2* = (1/2)*(2 + 1) = 3/2
SUFFICIENT

Statement 2: 5* = 3
Or 5a + a = 3
a = 1/2

Hence 2* = (1/2)*(2 + 1) = 3/2
SUFFICIENT

Correct Option: D
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Re: For all x, the expression x* is defined to be ax + a, where a is...... [#permalink]

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New post 24 May 2016, 04:54
Trying to solve these equations is unnecessary and in 90% of DS questions a waste of time

A) 3a + a = 2

Linear eqn with 1 variable, 1 solution. sufficient

2) 5 a + a = 6

Same reasoning as above

Answer : D
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Re: For all x, the expression x* is defined to be ax + a, where a is......   [#permalink] 24 May 2016, 04:54
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