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If b is a positive integer less than 8, is c less than the

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If b is a positive integer less than 8, is c less than the [#permalink] New post 19 Apr 2011, 04:26
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If b is a positive integer less than 8, is c less than the average (arithmetic mean) of b and 8?

1. On the number line, c is closer to 8 than it is to b.
2. c = 4b
[Reveal] Spoiler: OA

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Re: DS: Number line and mean [#permalink] New post 19 Apr 2011, 04:47
(1)

-------------------0-------b--------------------c-----8---------------

-------------------0-------b-------------------------8----c-----------

b = 2

|c - 8| < |c - b|

If c > 8 , then given that

c - 8 < c - b

=> b < 8 already given

If c < 8, then

8-c < c - b

(8+b)/2 < c

Sufficient.


(2) Is (b + 8)/2 > 4b

or b + 8 > 8b

or 8 > 7b

or b < 8/7

InSufficient, b is +ve so it can be 0 < b < 8/7

(b + 8)/2 < 4b

or b + 8 < 8b

or 8/7 < b, which is possible

So (2) is InSufficient

Answer - A
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Re: DS: Number line and mean [#permalink] New post 19 Apr 2011, 04:57
Your answer is correct. I've just posted a challenging Inequalities DS. You may want to solve that too :)

Here is the link: inequalities-ds-112497.html
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Re: DS: Number line and mean [#permalink] New post 19 Apr 2011, 05:36
It's done too, please check.
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Re: DS: Number line and mean [#permalink] New post 19 Apr 2011, 05:48
If b is a positive integer less than 8, is c less than the average (arithmetic mean) of b and 8?

1. On the number line, c is closer to 8 than it is to b.
Trying substituting some values for b.
e.g.: b=1 ; (8 + b) / 2 = 4.5;
c is closer to 8 i.e. c =5; so sufficient.

2. c = 4b
Again trying substituting some values for b.
e.g.: B=1 c= 4; (8 + b) / 2 = 4.5 => c < b
B=2 c = 8; (8 + b) / 2 = 5 => c > b
Insufficient
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Re: DS: Number line and mean   [#permalink] 19 Apr 2011, 05:48
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