Multiples

[joyseychow]

If n is a multiple of 5, n=p^2q, where p and q are prime numbers. Which of the following must be a multiple of 25?

A. p^2
B. q^2
C. pq
D. p^2q^2
E. p^3q


Easy one, but I didn't get right. Why B cannot be the answer?

[tohellandback]

answer is D
n=p^2q
either p or q can be 5
clearly P^2*q^2 must be divisible by 25.

B cannot be the answer because
if p is 5 then q can be any prime number. 3,7, etc.
in that case p^2 will not be divisible by 25

[ankitns]

answer is D
n=p^2q
either p or q can be 5
clearly P^2*q^2 must be divisible by 25.

B cannot be the answer because
if p is 5 then q can be any prime number. 3,7, etc.
in that case p^2 will not be divisible by 25

q cannot be 5...plug in the numbers...if p = 2 and q = 5...we get
n = 2^10 = 1024..not a multiple of 5....

n can only be a multiple of 5 only if p is 5...and if p is a multiple of 5 then p^2 must be a multiple of 25...

Hence the answer is A[spoiler][/spoiler]

[tohellandback]

answer is D
n=p^2q
either p or q can be 5
clearly P^2*q^2 must be divisible by 25.

B cannot be the answer because
if p is 5 then q can be any prime number. 3,7, etc.
in that case p^2 will not be divisible by 25

q cannot be 5...plug in the numbers...if p = 2 and q = 5...we get
n = 2^10 = 1024..not a multiple of 5....

n can only be a multiple of 5 only if p is 5...and if p is a multiple of 5 then p^2 must be a multiple of 25...

Hence the answer is A[spoiler][/spoiler]

with p=2, how r u getting n=2^10
it will be n=2^2*5
..or hey may be you think its n=P^(2q)

[ankitns]

yes..I was thinking n=p^(2q)...

joyseychow: Could you please clarify whether the question states

n=p^(2q)

or

n=(p^2) * q


Thanks.

answer is D
n=p^2q
either p or q can be 5
clearly P^2*q^2 must be divisible by 25.

B cannot be the answer because
if p is 5 then q can be any prime number. 3,7, etc.
in that case p^2 will not be divisible by 25

q cannot be 5...plug in the numbers...if p = 2 and q = 5...we get
n = 2^10 = 1024..not a multiple of 5....

n can only be a multiple of 5 only if p is 5...and if p is a multiple of 5 then p^2 must be a multiple of 25...

Hence the answer is A[spoiler][/spoiler]

with p=2, how r u getting n=2^10
it will be n=2^2*5
..or hey may be you think its n=P^(2q)

[joyseychow]

yes..I was thinking n=p^(2q)...

joyseychow: Could you please clarify whether the question states

n=p^(2q)

or

n=(p^2) * q


Thanks.

answer is D
n=p^2q
either p or q can be 5
clearly P^2*q^2 must be divisible by 25.

B cannot be the answer because
if p is 5 then q can be any prime number. 3,7, etc.
in that case p^2 will not be divisible by 25

q cannot be 5...plug in the numbers...if p = 2 and q = 5...we get
n = 2^10 = 1024..not a multiple of 5....

n can only be a multiple of 5 only if p is 5...and if p is a multiple of 5 then p^2 must be a multiple of 25...

Hence the answer is A[spoiler][/spoiler]

with p=2, how r u getting n=2^10
it will be n=2^2*5
..or hey may be you think its n=P^(2q)

Sorry. It's n=(p^2) * q.

[real2008]

yes..I was thinking n=p^(2q)...

joyseychow: Could you please clarify whether the question states

n=p^(2q)

or

n=(p^2) * q


Thanks.

answer is D
n=p^2q
either p or q can be 5
clearly P^2*q^2 must be divisible by 25.

B cannot be the answer because
if p is 5 then q can be any prime number. 3,7, etc.
in that case p^2 will not be divisible by 25

q cannot be 5...plug in the numbers...if p = 2 and q = 5...we get
n = 2^10 = 1024..not a multiple of 5....

n can only be a multiple of 5 only if p is 5...and if p is a multiple of 5 then p^2 must be a multiple of 25...

Hence the answer is A[spoiler][/spoiler]

with p=2, how r u getting n=2^10
it will be n=2^2*5
..or hey may be you think its n=P^(2q)

Sorry. It's n=(p^2) * q.

then answer is D