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08 Jan 2018, 23:38
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (02:11) correct
37%
(01:51)
wrong
based on 128
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.
(1) c = 5a
(2) On the number line, a is closer to 10 than it is to 0.
09 Jan 2018, 02:43
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Bunuel
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.
03 Mar 2018, 10:14
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Bunuel
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
