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If x and y are positive integers such that y is a multiple of 5 and 3x

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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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New post 09 Feb 2018, 17:09
Can someone pls verify if this method will work for all similar question types? This is the way I approached as well

wvu wrote:
I approached this in a different style I think than the other posters - is this way correct as well?

First, 200 factors down to \(2^3 * 5^2\)

Looking at the information we know that from the equation \(3x + 4y\), where y is a multiple of 5, we have the factors of \(2^2\) (from the 4), 3, and 5. Given this, we can then determine that we need one more factor of both 2 and 5. E - 10 is the only answer choice that provides those two factors.
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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New post 10 Feb 2018, 01:37
mrdlee23 wrote:
Can someone pls verify if this method will work for all similar question types? This is the way I approached as well

wvu wrote:
I approached this in a different style I think than the other posters - is this way correct as well?

First, 200 factors down to \(2^3 * 5^2\)

Looking at the information we know that from the equation \(3x + 4y\), where y is a multiple of 5, we have the factors of \(2^2\) (from the 4), 3, and 5. Given this, we can then determine that we need one more factor of both 2 and 5. E - 10 is the only answer choice that provides those two factors.


We know that -
\(3x + 4y = 200, y = 5m\)
\(3x + 20m = 200\)
\(x = \frac{10(20 - m)}{3}\)

So, x has to be multiple of 10.
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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New post 12 Feb 2018, 04:38
mrdlee23 wrote:
Can someone pls verify if this method will work for all similar question types? This is the way I approached as well

wvu wrote:
I approached this in a different style I think than the other posters - is this way correct as well?

First, 200 factors down to \(2^3 * 5^2\)

Looking at the information we know that from the equation \(3x + 4y\), where y is a multiple of 5, we have the factors of \(2^2\) (from the 4), 3, and 5. Given this, we can then determine that we need one more factor of both 2 and 5. E - 10 is the only answer choice that provides those two factors.


Since y is a factor of 5, 4y will end in 0.
So get the sum of 200, 3x should end in 0 as well. So x should be a multiple of 10.
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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New post 16 Apr 2018, 00:59
Abhishek009 wrote:
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question


Plug in values and check -

Let y = 5 ; 3x + 4y = 200

So, 3x + 20 = 200

Or, x = 60 ( Options C & D rejected , Left with options A, B & E )


Let y = 20 ; 3x + 4y = 200

So, 3x + 80 = 200

Or, x = 40 ( Options A &B rejected , Left with option E )

Hence, answer will be optin (E)


Hey, Abhishek009! 40 is also a multiple of 8, option D. So we still have D and E remaining.
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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New post 16 Apr 2018, 01:19
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advait92 wrote:
Hey, Abhishek009! 40 is also a multiple of 8, option D. So we still have D and E remaining.


Hey advait92 ,

As Abhishek009 has explained, we have already rejected option D when we substituted y = 5 in the equation.

Remember for a "MUST" be true question, it should work for all the scenarios but we are not getting x a multiple of 8 whenever we have y = 5.

Hence, D cannot be the answer.

Does that make sense?
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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New post 16 Apr 2018, 02:00
abhimahna wrote:
advait92 wrote:
Hey, Abhishek009! 40 is also a multiple of 8, option D. So we still have D and E remaining.


Hey advait92 ,

As Abhishek009 has explained, we have already rejected option D when we substituted y = 5 in the equation.

Remember for a "MUST" be true question, it should work for all the scenarios but we are not getting x a multiple of 8 whenever we have y = 5.

Hence, D cannot be the answer.

Does that make sense?


Hey abhimahna! Thank you for bringing this to my notice.
Re: If x and y are positive integers such that y is a multiple of 5 and 3x   [#permalink] 16 Apr 2018, 02:00

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