If n is a multiple of both 5 and n = p^2q, where p and q are prime numbers, then p^2q is also a multiple of 5, or either p or q must be 5. Only choice is [spoiler](D) p^2q^2[/spoiler] that guarantees that it's a multiple of 25.GmatKiss wrote:If n is a multiple of 5 and n = p^2q, where p and q are prime numbers, which of the following must be a multiple of 25?
p^2
q^2
pq
p^2q^2
p^3q
Multiple of 5 and N
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If x is a multiple of 5 and x ± y is also a multiple of 5, then it means that y is also a multiple of 5. Do you agree till here?GmatKiss wrote:Not comprehensive. Could you please elaborate a bit. Thanks
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neelgandham
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If n is a multiple of 5 and n = p^2q, where p and q are prime numbers, which of the following must be a multiple of 25?
p,q are prime numbers(p!=q is my assumption).
n = p^2q and n is a multiple of 5. Implies, either p is equal to 5 or q is equal to 5. So let us check the options
A)p^2
If p=5, p^2 is a multiple of 25
If q=5, p^2 is definitely not a multiple of 25
So, option A is not the answer
B)q^2
If p=5, q^2 is definitely not a multiple of 25
If q=5, q^2 is a multiple of 25
So, option B is not the answer
C)pq
If p=5, pq is definitely not a multiple of 25
If q=5, Don't bother checking
So, option C is not the answer
D)p^2q^2
If p=5, p^2q^2 is a multiple of 25
If q=5, p^2q^2 is a multiple of 25
So, option D is the answer
E)p^3q
Don't bother checking
IMO D
p,q are prime numbers(p!=q is my assumption).
n = p^2q and n is a multiple of 5. Implies, either p is equal to 5 or q is equal to 5. So let us check the options
A)p^2
If p=5, p^2 is a multiple of 25
If q=5, p^2 is definitely not a multiple of 25
So, option A is not the answer
B)q^2
If p=5, q^2 is definitely not a multiple of 25
If q=5, q^2 is a multiple of 25
So, option B is not the answer
C)pq
If p=5, pq is definitely not a multiple of 25
If q=5, Don't bother checking
So, option C is not the answer
D)p^2q^2
If p=5, p^2q^2 is a multiple of 25
If q=5, p^2q^2 is a multiple of 25
So, option D is the answer
E)p^3q
Don't bother checking
IMO D
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If n is multiple of 5, and n = p²q where p and q are prime, then either p or q or both of them must be equal to 5. Let's analyze each of the cases. (Note that only one of the following can happen at a time)GmatKiss wrote:If n is a multiple of 5 and n = p^2q, where p and q are prime numbers, which of the following must be a multiple of 25?
p^2
q^2
pq
p^2q^2
p^3q
1. p = 5, p² is multiple of 25, q² not
2. q = 5, q² is multiple of 25, p² not
3. p = q = 5, p² = q² = multiple of 25
We have to find a generalized expression containing p and q such that it becomes multiple of 25. From above analysis we know p² or q² is not that expression as they may or may not be a multiple of 25. But in p²q² both of them are present and simultaneously all the three cases are merged into one! For any of the above cases p²q² will be always a multiple of 25.
The correct answer is D.
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D it is!GmatKiss wrote:If n is a multiple of 5 and n = p^2q, where p and q are prime numbers, which of the following must be a multiple of 25?
p^2
q^2
pq
p^2q^2
p^3q
If OA is A, IMO B
If OA is B, IMO C
If OA is C, IMO D
If OA is D, IMO E
If OA is E, IMO A
FML!! :/
If OA is B, IMO C
If OA is C, IMO D
If OA is D, IMO E
If OA is E, IMO A
FML!! :/
