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Current Student B
Status: Persevere
Joined: 09 Jan 2016
Posts: 114
Location: Hong Kong
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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9 00:00

Difficulty:   5% (low)

Question Stats: 92% (01:02) correct 8% (01:15) wrong based on 816 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) $$5^* = 3$$
SVP  B
Joined: 06 Nov 2014
Posts: 1868
Re: For all x, the expression x* is defined to be ax + a, where a is......  [#permalink]

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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
Manager  Joined: 03 May 2015
Posts: 169
Location: South Africa
GPA: 3.49
WE: Web Development (Insurance)
Re: For all x, the expression x* is defined to be ax + a, where a is......  [#permalink]

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2
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

Intern  B
Joined: 27 Apr 2015
Posts: 39
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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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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Joined: 22 Aug 2013
Posts: 1398
Location: India
Re: For all x, the expression x* is defined to be ax + a, where a is......  [#permalink]

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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  B
Joined: 27 Apr 2015
Posts: 39
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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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'
Director  G
Joined: 09 Mar 2018
Posts: 990
Location: India
Re: For all x, the expression x* is defined to be ax + a, where a is......  [#permalink]

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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) $$5^* = 3$$

So basically

2^* will be 2a + a => 3a

Now if i can get value of a, i will be good

(1) $$3^* = 2$$
3a + a = 2
a = 1/2

We are good

(2) $$5^* = 3$$

6a = 3
a = 1/2

We are good

Both statements are Sufficient

D

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Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: For all x, the expression x* is defined to be ax + a, where a is......   [#permalink] 29 Jan 2019, 23:17
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