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If m and p are positive integers and m^2 + p^2 < 100, what is the
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15 Jun 2022, 07:09
15 Jun 2022, 07:09
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If m and p are positive integers and \(m^2 + p^2 < 100\), what is the greatest possible value of mp ?
A. 36
B. 42
C. 48
D. 49
E. 51
A. 36
B. 42
C. 48
D. 49
E. 51
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Re: If m and p are positive integers and m^2 + p^2 < 100, what is the
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15 Jun 2022, 07:15
15 Jun 2022, 07:15
1
Carcass wrote:
If m and p are positive integers and \(m^2 + p^2 < 100\), what is the greatest possible value of mp ?
A. 36
B. 42
C. 48
D. 49
E. 51
A. 36
B. 42
C. 48
D. 49
E. 51
Let's test some pairs of values.
Since m and p are POSITIVE INTEGERS, we won't have a ton of options
Try m = 9 and p = 4 (aside: if m = 9, then 4 is the biggest possible value of p)
In this case, mp = (9)(4) = 36
Try m = 8 and p = 5 (aside: if m = 8, then 5 is the biggest possible value of p)
In this case, mp = (8)(5) = 40
Try m = 7 and p = 7 (aside: if m = 7, then 7 is the biggest possible value of p)
In this case, mp = (7)(7) = 49
Try m = 6 and p = 7 (aside: if m = 6, then 7 is the biggest possible value of p)
In this case, mp = (6)(7) = 42
Try m = 5 and p = 8
At this point, we can see that, if we continue, we'll be duplicating the work we did earlier.
That is, this case (m = 5 and p = 8) is the SAME as the 2nd case we examined.
If we continue, the next case we test will be m = 4 and p = 9. which is the SAME as the 1st case we examined, etc.
Since we've now tested all possible (and relevant) cases, we can see that the maximum value of mp is 49
Answer: D
Re: If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
12 Oct 2022, 06:22
12 Oct 2022, 06:22
GreenlightTestPrep wrote:
Carcass wrote:
If m and p are positive integers and \(m^2 + p^2 < 100\), what is the greatest possible value of mp ?
A. 36
B. 42
C. 48
D. 49
E. 51
A. 36
B. 42
C. 48
D. 49
E. 51
Let's test some pairs of values.
Since m and p are POSITIVE INTEGERS, we won't have a ton of options
Try m = 9 and p = 4 (aside: if m = 9, then 4 is the biggest possible value of p)
In this case, mp = (9)(4) = 36
Try m = 8 and p = 5 (aside: if m = 8, then 5 is the biggest possible value of p)
In this case, mp = (8)(5) = 40
Try m = 7 and p = 7 (aside: if m = 7, then 7 is the biggest possible value of p)
In this case, mp = (7)(7) = 49
Try m = 6 and p = 7 (aside: if m = 6, then 7 is the biggest possible value of p)
In this case, mp = (6)(7) = 42
Try m = 5 and p = 8
At this point, we can see that, if we continue, we'll be duplicating the work we did earlier.
That is, this case (m = 5 and p = 8) is the SAME as the 2nd case we examined.
If we continue, the next case we test will be m = 4 and p = 9. which is the SAME as the 1st case we examined, etc.
Since we've now tested all possible (and relevant) cases, we can see that the maximum value of mp is 49
Answer: D
this resembles an equation of a circle with the origin as the center so m&p must be equal and less than 10.
