For all x, the expression x* is defined to be ax + a, where a is...... : GMAT Data Sufficiency (DS)
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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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22 May 2016, 22:00
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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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22 May 2016, 23:02
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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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24 May 2016, 03:54
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

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Re: For all x, the expression x* is defined to be ax + a, where a is......   [#permalink] 24 May 2016, 03:54
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