If n is a multiple of 5 and n=q* P^2 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
thx,
OA: D
p^2
q^2
pq
P^2q^2
P^3q
thx,
OA: D
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Prime Numbers
Source: Beat The GMAT — Problem Solving |
As per given req, an of p q can be 5, so if we take square of each term, the multiple of 5 will be guaranteed.
Charged up again to beat the beast 
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Geva@EconomistGMAT
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In n is a multiple of 5, then either p, or q, or both must be a multiple of 5. Plug in a few numbers sets, and see which answer choice you can eliminate:gvosough wrote:If n is a multiple of 5 and n=q* P^2 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
thx,
OA: D
plug in p=2, q=5: A, C, and E are eliminated because the result for these plug ins is not divisible by 25. B and D cannot be eliminate yet.
Plug in p=5, q=2, and now B is eliminated because it is not a multiple of 25. D remains the last answer choice, and must be the right one by POE.
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ankur.agrawal
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If we put in p=5 , q=2, then A, E also are multiple of 25. How can we take set of two different values & eliminate different answer options. Shudn't we stick to one set of values ? Am i missing something.Geva@MasterGMAT wrote:In n is a multiple of 5, then either p, or q, or both must be a multiple of 5. Plug in a few numbers sets, and see which answer choice you can eliminate:gvosough wrote:If n is a multiple of 5 and n=q* P^2 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
thx,
OA: D
plug in p=2, q=5: A, C, and E are eliminated because the result for these plug ins is not divisible by 25. B and D cannot be eliminate yet.
Plug in p=5, q=2, and now B is eliminated because it is not a multiple of 25. D remains the last answer choice, and must be the right one by POE.
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Geva@EconomistGMAT
- GMAT Instructor
- Posts: 905
- Thanked: 378 times
- GMAT Score:760
The fact that A and E are multiples of 5 for a certain configuration of p and q only means that A and E CAN be multiples of 5 - not MUST be. For an answer to be right, it MUST be true for any value of p and q we choose (which satisfies the question stem, of course). D is such an answer - no matter which value of p and q you choose, as long as one of them is a multiple of 5 (required by the question stem), D will always be a multiple of 25. if you look at D closely, you can see the algebraic reasoning proving why it must be true. But you need some tool to make D stand out of the crowd to see this. Plugging in and eliminating is a way to thin out the herd of five answer choices, leaving only the right answer standing.ankur.agrawal wrote:If we put in p=5 , q=2, then A, E also are multiple of 25. How can we take set of two different values & eliminate different answer options. Shudn't we stick to one set of values ? Am i missing something.Geva@MasterGMAT wrote:In n is a multiple of 5, then either p, or q, or both must be a multiple of 5. Plug in a few numbers sets, and see which answer choice you can eliminate:gvosough wrote:If n is a multiple of 5 and n=q* P^2 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
thx,
OA: D
plug in p=2, q=5: A, C, and E are eliminated because the result for these plug ins is not divisible by 25. B and D cannot be eliminate yet.
Plug in p=5, q=2, and now B is eliminated because it is not a multiple of 25. D remains the last answer choice, and must be the right one by POE.
The fact is that there are four answer choices here that CAN be multiples of 25, but are not must. This opens the way to dealing with Must be true questions: don't try to find the one true answer, but rather focus on eliminating the four wrong answers by finding a counter example for each. If you can find a single example of p and q that satisfy the question stem, but for which C is not a multiple of 25, then C is not a "Must be true" and is eliminated.
The idea is to keep plugging in changing sets until you have found a single counter example for all four wrong answer choice. D remains as the only right answer by POE, and you needn't worry about why it is true: it's true because the other four are false, and one answer in five has to be correct. You are effectively using the multiple choice format against itself.
