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# Given that m^2 - 2m -15 = 0 and n^2 - 3n - 10 = 0, where m ≠ n, what

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Math Expert
Joined: 02 Sep 2009
Posts: 44588
Given that m^2 - 2m -15 = 0 and n^2 - 3n - 10 = 0, where m ≠ n, what [#permalink]

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10 Apr 2018, 22:18
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Difficulty:

25% (medium)

Question Stats:

87% (00:50) correct 13% (01:46) wrong based on 30 sessions

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Given that $$m^2 - 2m -15 = 0$$ and $$n^2 - 3n - 10 = 0$$, where m ≠ n, what is the product of m and n?

(A) -15
(B) -10
(C) -6
(D) 6
(E) 15
[Reveal] Spoiler: OA

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Re: Given that m^2 - 2m -15 = 0 and n^2 - 3n - 10 = 0, where m ≠ n, what [#permalink]

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10 Apr 2018, 23:41
Bunuel wrote:
Given that $$m^2 - 2m -15 = 0$$ and $$n^2 - 3n - 10 = 0$$, where m ≠ n, what is the product of m and n?

(A) -15
(B) -10
(C) -6
(D) 6
(E) 15

Factorizing the two equations
$$m^2 - 2m -15 = 0$$ -> $$m^2 - 5m + 3n -15 = 0$$ -> $$(m-5)(m+3) = 0$$ -> $$m = 5 or -3$$
$$n^2 - 3n - 10 = 0$$ -> $$n^2 - 5n + 2n - 10 = 0$$ -> $$(n-5)(n+2) = 0$$ -> $$n = 5 or -2$$

Therefore, the product of m and n such that m≠n is (-3)(-2) = 6(Option D)
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Joined: 07 Jul 2017
Posts: 1
Re: Given that m^2 - 2m -15 = 0 and n^2 - 3n - 10 = 0, where m ≠ n, what [#permalink]

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11 Apr 2018, 02:13
Can answer be -10 and -15 also? the question stated that m ≠ n , doesn’t that means m = 5, n = -2 or m = -3, n = 5 also possible?
Re: Given that m^2 - 2m -15 = 0 and n^2 - 3n - 10 = 0, where m ≠ n, what   [#permalink] 11 Apr 2018, 02:13
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