If p is prime number, which of the following statements must be true?

Question

I. (p + 3)*(p + 5)*(p + 9) must be divisible by 8 
II. (6p + 1)*(6p – 1) must be divisible by 6 
III. (p^2 – p)*(p + 1) must be divisible by 3

(A) I only
(B) III only
(C) I and II
(D) II and III
(E) I, II and III

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preetamsaha   minustark   shameekv1989   sauravleo123   prateek25   Sourav199201   debjit1990   razorhell  - Here's the second question of Day 5. All the best!

shameekv1989 · Answer

If p is prime number, which of the following statements must be true?

I. (p + 3)*(p + 5)*(p + 9) must be divisible by 8 
II. (6p + 1)*(6p – 1) must be divisible by 6 
III. (p2 – p)*(p + 1) must be divisible by 3

(A) I only
(B) III only
(C) I and II
(D) II and III
(E) I, II and III

I) (p + 3)*(p + 5)*(p + 9) => If p is even i.e. 2 then all terms will be odd and wouldn't be divisible by 8. Though if p is an odd prime number then expression would be divisible by 8 - NOT ALWAYS TRUE

II) (6p + 1)*(6p – 1)=  36p^2-1  when this expression is divided by 6 the first terms is divisible by 6 and thus the remainder will always be -1 => 5 
NEVER TRUE

III) (p^2-p)(p+1) => (p-1)*p*(p+1) => Multiplication of 3 consecutive terms. 
For p  \geq{ 2}  the expression above will always be divisible by 3 - MUST BE TRUE

Answer - B

prateek25 · Answer

1. Let p =2 implies (p+3)(p+5)(p+9) implies odd number and is NOT divisible by 8, reject 1. 
2. Let p = 3 implies (6p+1)(6p-1) = 19*17 NOT divisible by 6, reject 2.

Ans should be B since "none of the above" is not an option. No need to check for 3rd statement.

preetamsaha · Answer

If p is prime number, which of the following statements must be true?

I. (p + 3)*(p + 5)*(p + 9) must be divisible by 8
if p=2, not divisible by 8. not must be true.
II. (6p + 1)*(6p – 1) must be divisible by 6 
if p=2, not divisible by 6. not must be true.

III. (p2 – p)*(p + 1) must be divisible by 3 
=p(p-1)(p+1) 
= the product of three consecutive numbers. always divisible by 3. ( p ≥ 2) 
must be true.

correct answer is B

debjit1990 · Answer

Ans: B
p is prime number
I. (p + 3)*(p + 5)*(p + 9) must be divisible by 8 
putting p=2, 5*7*11..not divisible by 8...I is wrong

II. (6p + 1)*(6p – 1) must be divisible by 6 
putting p=2,13*11..not divisible by 6..II is wrong

III. (p2 – p)*(p + 1) must be divisible by 3
p(p-1)(p+1) or (p-1)p(p+1)
now all numbers are consecutive, so it must be divisible by 3....III is correct

GMATWhizTeam · Answer

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If p is prime number, which of the following statements must be true?

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GMAT Problem Solving (PS) Questions

If p is prime number, which of the following statements must be true?

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