If p is a positive integer, is p 4 ?

Question

If p is a positive integer, is p > 4 ?

(1) p^4 > 256
(2) (p^2 -1)(p - 4) > 0

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Bunuel · Answer

Similar question to practice: https://gmatclub.com/forum/if-p-is-a-po ... 27163.html

chetan2u · Answer

Very important -- p is a positive integer . (1) p^4 > 256 Since 4^4=256.....p^4>4^4.....p>4 (2) ( p^2 -1)(p - 4) > 0 (p-1)(p+1)(p-4)>0 Now p+1 is always >0, so p-1 and p-4 will have same sign as (p-1)(p-4)>0 Two cases - a) both positive.. p-1>0 and p-4>0....p>1 and p>4... so p>4 b) both negative. p-1<0 and p-4<0, so p<1, but that is not possible as p\geq{1} Thus both p-1 and p-4 are positive and p>4. D

gvij2017 · Answer

Can you elaborate how p>4 for statement 1. 
When P= 4, how can I say p>4.

Would you please explain, Chetan2U Sir!

GMATWhizTeam · Answer

Solution Step 1: Analyse Question Stem • p is a positive integer. • We need to find out if p > 4 Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE Statement 1: p^4 > 256 • p^4 – 4^4 > 0 ⟹ (p^2 + 4^2)(p^2 – 4^2) > 0 ⟹ (p^2 + 4^2) ( p- 4)(p+ 4) > 0 https://www.dropbox.com/s/t880tz8liuudzy2/Number_20_1.PNG?dl=1 • Thus, either p > 4 \space or \space p < -4 . o Since p is a positive integer. So p is always greater than 4. Hence, statement 1 is sufficient and we can eliminate answer Options B, C and E. Statement 2: (p^2 – 1)(p-4) > 0 • (p – 1)( p+1)(p – 4) > 0 https://www.dropbox.com/s/7kcge7b20yss18s/Number_20_2.PNG?dl=1 • So, -1 < p < 1 or p > 4 o Since, there is no positive integer, between – 1 to 1 , both excluded, p cannot lie in this region.  Thus, p > 4 Hence, statement 2 is also sufficient and the correct answer is Option D.

chetan2u · Answer

Now  p^4>256  or  p^4>4^4 , hence  p>4

Papist · Answer

S1: In other words, p^4 is greater than 4^4. Since we know p is positive, it must be greater than 4. SUFFICIENT.

S2: The first part of the equation is a difference of squares. This can be rewritten as (p+1)(p-1)(p-4)>0. Since p>4 is a solution and the other two don't contradict it, the original equation must be true. SUFFICIENT.

ANSWER: D

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If p is a positive integer, is p > 4 ?

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