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If a is a positive number less than 10, is c greater than the average

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If a is a positive number less than 10, is c greater than the average  [#permalink]

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New post 08 Jan 2018, 23:38
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If a is a positive number less than 10, is c greater than the average (arithmetic mean) of a and 10?

(1) c = 5a
(2) On the number line, a is closer to 10 than it is to 0.

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Re: If a is a positive number less than 10, is c greater than the average  [#permalink]

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New post 09 Jan 2018, 02:43
Bunuel wrote:
If a is a positive number less than 10, is c greater than the average (arithmetic mean) of a and 10?

(1) c = 5a
(2) On the number line, a is closer to 10 than it is to 0.


To help us understand the logic behind the quesion, we'll first write it out as equations.
This is a Precise approach.

We know that a<10 and are asked if c> (a+10)/2.
Simplifying, we are asked if 2c > a+10

(1) Substituing c = 5a instead of 2c gives 10a > a + 10 which is true when 9a > 10 so a > 10/9 > 1.
If a=1 then a>1 is false and if a=2 then a>1 is false, so (1) is insufficient to answer the question.

(2) This tells us that a > 5 and means that 2c > a+10 is true if 2c > 15 so c > 7.5.
Since we have no information on the value of c, this is insufficient.

Combined:
(1) told us that the statement is true if a > 1 and (2) tells us that a > 5.
Sufficient!

(C) is our answer.
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Re: If a is a positive number less than 10, is c greater than the average  [#permalink]

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New post 03 Mar 2018, 10:14
Bunuel wrote:
If a is a positive number less than 10, is c greater than the average (arithmetic mean) of a and 10?

(1) c = 5a
(2) On the number line, a is closer to 10 than it is to 0.


Given \(0<a<10\)
To Find is \(c>\frac{(a+10)}{2}\) OR \(2c>(a+10)\) ---- (1)

Stat 1 \(c=5a\)
=> substituting in (1) we have
=> is \(10a>a+10\)
=> is \(9a>10\)
=> OR is \(a>\frac{10}{9}\) - No information

The above deduction suggest that if

Case 1 \(a>\frac{10}{9}\) let say \(a=2\)
=> then \(c=10\) , \(2c=20\) and \(a+10=12\)
=> So \(2c>(a+10)\)

Case 2 \(a<\frac{10}{9}\) let say \(a=1\)
=> then \(c=5\) , \(2c=10\) and \(a+10=11\)
=> So \(2c<(a+10)\)
Thus depending on the value of 'a' the answer to the question can be 'Y' or 'N'.
So NOT SUFFICIENT

Stat 2 On the number line, a is closer to 10 than it is to 0
=> Gives a>5 and No information of c
=> NOT SUFFICIENT

BOTH
=> \(a>5\) from Stat 2
=> then from Stat 1 for all values of 'a' \(c>25\)
=> Since \(\frac{(a+10)}{2}< 10\) AND \(c > 10\) (both ALWAYS as per the given conditions)
=> Therefore \(c>\frac{(a+10)}{2}\) OR \(2c>(a+10)\)
SUFFICIENT

Option 'C'

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Dinesh
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Re: If a is a positive number less than 10, is c greater than the average &nbs [#permalink] 03 Mar 2018, 10:14
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