Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 17 Jul 2019, 10:03 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If a is a positive number less than 10, is c greater than the average

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56275
If a is a positive number less than 10, is c greater than the average  [#permalink]

### Show Tags 00:00

Difficulty:   65% (hard)

Question Stats: 53% (02:08) correct 47% (01:49) wrong based on 60 sessions

### HideShow timer Statistics If a is a positive number less than 10, is c greater than the average (arithmetic mean) of a and 10?

(1) On the number line, c is closer to 10 than it is to a.
(2) 2c – 10 is greater than a.

_________________
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1197
Location: India
GPA: 3.82
If a is a positive number less than 10, is c greater than the average  [#permalink]

### Show Tags

Bunuel wrote:
If a is a positive number less than 10, is c greater than the average (arithmetic mean) of a and 10?

(1) On the number line, c is closer to 10 than it is to a.
(2) 2c – 10 is greater than a.

Given $$a<10$$ and to find is $$c>$$mid point of $$a$$ & $$10$$ i.e. $$c>\frac{a+10}{2}=>2c>a+10$$

Statement 1: This implies $$c$$ is more than the mid-point of $$a$$ & $$10$$ because mid-point will be equidistant from both $$a$$ & $$10$$ and given $$c$$ is closer to $$10$$ than $$a$$. Sufficient

Statement 2: implies $$2c-10>a=>2c>a+10$$. Sufficient

Option D
Intern  B
Joined: 27 Apr 2015
Posts: 40
GMAT 1: 370 Q29 V13 Re: If a is a positive number less than 10, is c greater than the average  [#permalink]

### Show Tags

Bunuel wrote:
If a is a positive number less than 10, is c greater than the average (arithmetic mean) of a and 10?

(1) On the number line, c is closer to 10 than it is to a.
(2) 2c – 10 is greater than a.

Given $$0<a<10$$
To find :- is $$c>\frac{(a+10)}{2}$$

Stat 1 On the number line, c is closer to 10 than it is to a. Thus following 2 cases

Case 1 $$c>10$$, so 'c' will ALWAYS be closer to 10 than 'a' on the number line
=> Since $$a<10$$. Therefore avg of (a, 10) i.e $$\frac{(a+10)}{2}<10$$
=> thus $$c>10>\frac{(a+10)}{2}$$
=> $$c>\frac{(a+10)}{2}$$

Case 2 $$c<10$$
=> Since 'c' NEEDS to be closer to 10 than to 'a' it has to be > than the midpoint .i.e (avg) of (a, 10) on the number line.(If 'c' is < than the midpoint of (a, 10) it will be closer to 'a' than 10)
=> Therefore $$\frac{(a+10)}{2}<c<10$$
=> OR $$c>\frac{(a+10)}{2}$$
Thus SUFFICIENT in both cases

Stat 2 2c – 10 is greater than a
=> OR (2c – 10)>a
=> OR 2c>10+a
=> OR $$c>\frac{(a+10)}{2}$$
SUFFICIENT

Option 'D'

Regards
Dinesh
Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: If a is a positive number less than 10, is c greater than the average  [#permalink]

### Show Tags

Bunuel wrote:
If a is a positive number less than 10, is c greater than the average (arithmetic mean) of a and 10?

(1) On the number line, c is closer to 10 than it is to a.
(2) 2c – 10 is greater than a.

a>10, is $$c>\frac{a+10}{2}$$

(1) On the number line, c is closer to 10 than it is to a.
since c is closer to 10 than a, MEANS c is more towards 10 than the midpoint or average of a and 10
suff

(2) 2c – 10 is greater than a.
2c-10>a...
you can simplify in two ways..
a) $$2c>a+10......c>\frac{a+10}{2}$$
exactly what we are looking for
b) $$2c>a+10....2c-a>10.......c-a>10-c$$..
this again tells us that c is closer to 10 than it is closer to a (same as statement I)
suff
_________________ Re: If a is a positive number less than 10, is c greater than the average   [#permalink] 04 Mar 2018, 08:41
Display posts from previous: Sort by

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