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Senior RC Moderator V
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If m and n are two positive integers such that 5m + 7n = 46, then what  [#permalink]

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Question Stats: 91% (01:19) correct 9% (01:46) wrong based on 65 sessions

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If m and n are two positive integers such that 5m + 7n = 46, then what is the value of mn ?
(A) 15
(B) 21
(C) 24
(D) 27
(E) 35

Source: Nova GMAT
Difficulty Level: 500

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Re: If m and n are two positive integers such that 5m + 7n = 46, then what  [#permalink]

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If m and n are two positive integers such that 5m + 7n = 46, then what is the value of mn ?
(A) 15
(B) 21
(C) 24
(D) 27
(E) 35

$$5m+7n=46 \implies m=\frac{46-7n}{5}$$

Since $$m>0 \implies 7n<46 \implies n \leq 6$$ (1)
Since $$m$$ is an integer so $$46-7n$$ is divisible by 5.

$$\implies 46-7n \equiv 0 \pmod{5} \iff -7n \equiv -1 \pmod{5} \iff 3n \equiv 9 \pmod{5} \iff n \equiv 3 \pmod{5}$$ (2)

From (1) and (2) we have $$n=3 \implies m=5 \implies mn=15$$

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Re: If m and n are two positive integers such that 5m + 7n = 46, then what  [#permalink]

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If m and n are two positive integers such that 5m + 7n = 46, then what is the value of mn ?
(A) 15
(B) 21
(C) 24
(D) 27
(E) 35

46 - 7n must be a multiple of 5m

Further we know , all multiples of 5 must have units digit as 0 or 5

Now, $$46 - 7n$$ will have units digit as 5 when $$n = 3$$

So, we have $$46 - 7*3 = 5*5$$

Hence, we have $$m = 5$$ & $$n = 3$$

$$mn$$ will be $$7*5 = 35$$

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Senior RC Moderator V
Joined: 02 Nov 2016
Posts: 4827
GPA: 3.39
Re: If m and n are two positive integers such that 5m + 7n = 46, then what  [#permalink]

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Abhishek009 wrote:
If m and n are two positive integers such that 5m + 7n = 46, then what is the value of mn ?
(A) 15
(B) 21
(C) 24
(D) 27
(E) 35

46 - 7n must be a multiple of 5m

Further we know , all multiples of 5 must have units digit as 0 or 5

Now, $$46 - 7n$$ will have units digit as 5 when $$n = 3$$

So, we have $$46 - 7*3 = 5*5$$

Hence, we have $$m = 5$$ & $$n = 3$$

$$mn$$ will be $$7*5 = 35$$

Abhishek009

I have a doubt in your explanation ... because official answer is A

Bunuel (math legend)

plz explain this question
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Re: If m and n are two positive integers such that 5m + 7n = 46, then what  [#permalink]

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Abhishek009 wrote:

46 - 7n must be a multiple of 5m

Further we know , all multiples of 5 must have units digit as 0 or 5

Now, $$46 - 7n$$ will have units digit as 5 when $$n = 3$$

So, we have $$46 - 7*3 = 5*5$$

Hence, we have $$m = 5$$ & $$n = 3$$

$$mn$$ will be $$7*5 = 35$$

Abhishek009

I have a doubt in your explanation ... because official answer is A

Bunuel (math legend)

plz explain this question

Probably this was a typo. Nothing is confused here.
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Re: If m and n are two positive integers such that 5m + 7n = 46, then what  [#permalink]

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_________________ Re: If m and n are two positive integers such that 5m + 7n = 46, then what   [#permalink] 15 Dec 2019, 08:25
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