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

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Manager
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Joined: 09 Jan 2016
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Location: India
GMAT 1: 750 Q50 V41
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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, 23:00
2
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Difficulty:

5% (low)

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

Kudos [?]: 246 [0], given: 94

Optimus Prep Instructor
Joined: 06 Nov 2014
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Kudos [?]: 524 [1], given: 23

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

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23 May 2016, 00:02
1
KUDOS
Expert's post
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, 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

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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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