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

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Joined: 09 Jan 2016
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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
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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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Joined: 06 Nov 2014
Posts: 1889
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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Kudos if I helped

Intern
Joined: 27 Apr 2015
Posts: 40
GMAT 1: 370 Q29 V13
For all x, the expression x* is defined to be ax + a, where a is...... [#permalink]

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Updated on: 19 Dec 2017, 11:31
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) $$5^* = 3$$

Given
=>x*=ax+a
=>x*=a(x+1)
Therefore
=>2*=a(2+1)
=>2*=3a ----(1)
so if we can find the value of 'a' we can hav the value of 2*

Now
Statement 1 says 3*=2
3*=4a from (1)
=> 4a=2
=> a=2/4=1/2
sufficient

Statement 2 says 5*=3
5*=6a from (1)
=> 6a=3
=> a=3/6=1/2
sufficient

Therefore option 'D'

Thanks

Originally posted by dineshril on 19 Dec 2017, 07:47.
Last edited by dineshril on 19 Dec 2017, 11:31, edited 1 time in total.
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Posts: 1031
Location: India
Re: For all x, the expression x* is defined to be ax + a, where a is...... [#permalink]

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19 Dec 2017, 08:50
1
KUDOS
dineshril wrote:
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) $$5^* = 3$$

Given
=>x*=ax+a
=>x*=a(x+1)
Therefore
=>2*=a(2+1)
=>2*=3a ----(1)
so if we can find the value of 'a' we can hav the value of 2*

Now
Statement 1 says 3*=2
3*=4a from (1)
=> 4a=2
=> a=2/4=1/2
sufficient

Statement 2 says 5*=3
5*=6a from (1)
=> 6a=3
=> a=3/6=1/2
sufficient

Therefore option 'E'

Thanks

Hi

Correct solution. But when each statement alone is sufficient to answer a question, the answer is D

I guess that was a typo
Intern
Joined: 27 Apr 2015
Posts: 40
GMAT 1: 370 Q29 V13
Re: For all x, the expression x* is defined to be ax + a, where a is...... [#permalink]

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19 Dec 2017, 11:30
amanvermagmat wrote:
dineshril wrote:
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) $$5^* = 3$$

Given
=>x*=ax+a
=>x*=a(x+1)
Therefore
=>2*=a(2+1)
=>2*=3a ----(1)
so if we can find the value of 'a' we can hav the value of 2*

Now
Statement 1 says 3*=2
3*=4a from (1)
=> 4a=2
=> a=2/4=1/2
sufficient

Statement 2 says 5*=3
5*=6a from (1)
=> 6a=3
=> a=3/6=1/2
sufficient

Therefore option 'E'

Thanks

Hi

Correct solution. But when each statement alone is sufficient to answer a question, the answer is D

I guess that was a typo

Hi Aman

Thanks for the correction. Its 'D'
Re: For all x, the expression x* is defined to be ax + a, where a is......   [#permalink] 19 Dec 2017, 11:30
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