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# If a is a positive whole number, is b also a positive whole

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Director
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If a is a positive whole number, is b also a positive whole [#permalink]

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06 Aug 2013, 03:13
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25% (medium)

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76% (02:01) correct 24% (01:07) wrong based on 49 sessions

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If a is a positive whole number, is b also a positive whole number?

(1) The average (arithmetic mean) of a, b + 2, and a - 5 is a.

(2) The average (arithmetic mean) of a and b is NOT a positive whole number.

[Reveal] Spoiler:
Shouldn't it be D? Can someone provide detailed analysis with examples. Thanks in advance!
[Reveal] Spoiler: OA

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Director
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Re: If a is a positive whole number, is b also a positive whole [#permalink]

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06 Aug 2013, 03:23
fozzzy wrote:
If a is a positive whole number, is b also a positive whole number?

(1) The average (arithmetic mean) of a, (b + 2), and (a - 5) is a.

(2) The average (arithmetic mean) of a and b is NOT a positive whole number.

[Reveal] Spoiler:
Shouldn't it be D? Can someone provide detailed analysis with examples. Thanks in advance!

whole numbers: 0 1 2 3.....

(1) The average (arithmetic mean) of a, (b + 2), and (a - 5) is a.

$$(a+b+2+a-5)/3 = a$$

on solving $$b= a + 3$$
clearly b will be positive integer hence a whole number(as a is whole number)
HENCE SUFFICIENT

(2) The average (arithmetic mean) of a and b is NOT a positive whole number.
$$(a+b)/2$$ = this can be -ve / 0 / +ve fraction
when negative then it means that b is negative hence not a whole number
when 0 then b = -a so it can be whole number (when a=0) and not a whole number when a is positive
when fraction then b is either fraction or positive integer example : let a= 2 b = 3 avg = 2.5

hence insufficient

hence ans A
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Last edited by blueseas on 06 Aug 2013, 04:02, edited 1 time in total.
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Re: If a is a positive whole number, is b also a positive whole [#permalink]

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06 Aug 2013, 03:44
Expert's post
blueseas wrote:
(1) The average (arithmetic mean) of a, b + 2, and a - 5 is a.

(a+b+2-5)/4 = a

on solving b= 3a + 3

clearly b will be positive integer hence a whole number(as a is whole number)

Can u just edit this part.

Thanks.
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Re: If a is a positive whole number, is b also a positive whole [#permalink]

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06 Aug 2013, 05:22
If a is a positive whole number, is b also a positive whole number?

(1) The average (arithmetic mean) of a, b + 2, and a - 5 is a.
$$\frac{a+b+2+a-5}{3}=a$$ so $$2a+b-3=3a$$ so $$b=a+3=integer+integer=integer$$ and will be positive.
Sufficient.

(2) The average (arithmetic mean) of a and b is NOT a positive whole number.
$$\frac{a+b}{2}=\frac{4+5}{2}=4.5$$ and b is a whole number.
$$\frac{a+b}{2}=\frac{4+4.5}{2}=4.25$$ and b is NOT a whole number.
Not sufficient
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Re: If a is a positive whole number, is b also a positive whole [#permalink]

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06 Aug 2013, 13:11
fozzzy wrote:
If a is a positive whole number, is b also a positive whole number?

(1) The average (arithmetic mean) of a, b + 2, and a - 5 is a.

(2) The average (arithmetic mean) of a and b is NOT a positive whole number.

[Reveal] Spoiler:
Shouldn't it be D? Can someone provide detailed analysis with examples. Thanks in advance!

from st(1), b = a+3 , a is positive integer , so b+3 is also positive integer. st(1) alone sufficient.

from st(2), we can have that a+b/2 can be a positive fraction or negative whole number or negative fraction etc. for these patterns of values, b can be anything. so its a double case here. st(2) insufficient.

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Re: If a is a positive whole number, is b also a positive whole   [#permalink] 06 Aug 2013, 13:11
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