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If m and n are two positive integers such that 5m + 7n = 46, then what

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

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New post 27 Nov 2016, 11:51
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E

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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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New post 27 Nov 2016, 18:46
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SajjadAhmad 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


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

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 \(n=3 \implies m=5 \implies mn=15\)

The answer is A
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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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New post 28 Nov 2016, 09:23
SajjadAhmad 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 \(7*5 = 35\)

Answer will be (E)

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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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New post 06 Dec 2016, 05:02
Abhishek009 wrote:
SajjadAhmad 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 \(7*5 = 35\)

Answer will be (E)


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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New post 06 Dec 2016, 07:12
SajjadAhmad wrote:
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 \(7*5 = 35\)

Answer will be (E)


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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New post 15 Dec 2019, 08:25
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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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