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# N and P are points on the number line below 20. Is P closer to 10 than

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Math Expert
Joined: 02 Sep 2009
Posts: 47157
N and P are points on the number line below 20. Is P closer to 10 than  [#permalink]

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29 Jul 2016, 10:33
1
4
00:00

Difficulty:

95% (hard)

Question Stats:

45% (01:45) correct 55% (01:38) wrong based on 91 sessions

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N and P are points on the number line below 20. Is P closer to 10 than N is?

(1) P is greater than the average of 10 and N.

(2) P/N = 3

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Re: N and P are points on the number line below 20. Is P closer to 10 than  [#permalink]

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29 Jul 2016, 10:52
Bunuel wrote:
N and P are points on the number line below 20. Is P closer to 10 than N is?

(1) P is greater than the average of 10 and N.

(2) P/N = 3

1) P is greater than average of 10 and N. Lets say N=1; Average = 5.5. Now P could be 10 , in that case it is closer to N and P could be 19, in that case N is closer to 10.

- Insufficient.

2) P/N=3 or P=3N.

Say N = 5, P is as close to 10 a N. for N=6, P=18,in this case N is closer to 10. -- Insufficient.

Combining 1 and 2, if N is 5. P=15, and P is also greater than 7.5(average) but P is as close to 10 as N.

if N is 6, P =18, and P>8(average), but here N is closer to 10 than P.-- Insufficient.

Hence, E is correct
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N and P are points on the number line below 20. Is P closer to 10 than  [#permalink]

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31 Jul 2016, 01:08
Bunuel wrote:
N and P are points on the number line below 20. Is P closer to 10 than N is?

(1) P is greater than the average of 10 and N.

(2) P/N = 3

Given P<20, N<20

(1) P>(10+N)/2
if N<10, we dont know whether P closer to 10 than N (e.g. N=8, P>9 => P=9,5; 10 or P=15...)
if N>10, we dont know whether P closer to 10 than N (e.g. N=12, P>11 => P=12 or P=15...)
if N=10, N closer to 10 than P (e.g. N=10, P>10 )
NOT SUFF

(2) P/N=3, P=3N
if N>0 P>N we dont know whether P closer to 10 than N (N=3, P=9 YES; N=6 P=18 NO)
if N<0 P<N N closer to 10 than P
if N=0 P=N the distance btw P=N and 10 the same
NOT SUFF

(1)&(2) P>(10+N)/2; P=3N => substitute 3N>(10+N)/2=>5N>10=> N>2=>P>6 => P>N
(N=3, P=9 YES; N=6 P=18 NO)
NOT SUFF

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Re: N and P are points on the number line below 20. Is P closer to 10 than  [#permalink]

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17 Oct 2017, 07:47
From Statement 1: we get $$P > (N+10)/2$$. This does not give us anything.
From Statement 2: we get $$P=3N$$, we don't get anything again.

Using 1 and 2, we get: $$N= P/3$$
and $$P > (P/3+10)/2$$
On solving above, this gives$$P > 6$$.

This gives nothing about the positioning of P with respect to 10. Hence both statements are insufficient. The answer is E.
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Re: N and P are points on the number line below 20. Is P closer to 10 than &nbs [#permalink] 17 Oct 2017, 07:47
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