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

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Math Expert
Joined: 02 Sep 2009
Posts: 58435
If a is a positive number less than 10, is c greater than the average  [#permalink]

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08 Jan 2018, 23:38
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Difficulty:

65% (hard)

Question Stats:

53% (02:19) correct 47% (01:31) wrong based on 59 sessions

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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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Joined: 07 Dec 2017
Posts: 1153
Re: If a is a positive number less than 10, is c greater than the average  [#permalink]

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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!

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Joined: 27 Apr 2015
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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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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'

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