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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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Difficulty: 555-605 Levelx   Algebrax   Divisibility/Multiples/Factorsx                        
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] New post   12 May 2021, 00:51
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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

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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] New post   21 May 2021, 06:36
Logical Route:
Since y is a multiple of 5 and its multiplied with 4, the unit digit will always be 0
When subtracting 4y (which will have unit digit as 0) with 200 we will get a number with unit digit 0
so 3x will also be a number with unit digit 0, that condition makes 10 as the must multiple
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] New post   06 Jun 2021, 23:31
y=5k

3x+4y=200
3x+4(5k)=200
3x = 200-20k
x= [20(10-k)]/3

it is possible that (10-k) is a multiple of 3. so x may or may not be a multiple of 3. But x is definitely a multiple of 20. But we do not option 20 from answer choices. So 10 which is a factor of 20 must be a multiple of x.
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] New post   24 Nov 2021, 22:07
Either write y in terms of x: y = (200-3x)/(20) then we see that denominator is a multiple of BOTH 2 and 5 = so only (E)10 will fit here,

Or, work backwards and try different numbers and see if the end result is divisible by 5.

Example: if x=6, then we have 2y=91 which will not be divisible by 5...
Eventually, only x=10 will work. Option (E) again
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] New post   14 Dec 2021, 09:31
EducationAisle is the following process correct?

3x = 200 - 4y
3x = 4(50-y)/3

So we can infer:
1. 50-y is a multiple of 3
2. 50-y is a multiple of 5
hence from 1. and 2. 50-y is a multiple of 15

So x = 4 x Multiple of 15. This means that x will be composed of at least a 3, 4, and 5. So x will be a multiple of 10 (E)
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] New post   14 Dec 2021, 10:26
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Hoozan wrote:
2. 50-y is a multiple of 5

How did you get this?
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] New post   14 Dec 2021, 11:51
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EducationAisle wrote:
Hoozan wrote:
2. 50-y is a multiple of 5

How did you get this?


50 is a multiply of 5. Y is a multiple of 5. So Multiple of 5 (50) - another multiple of 5 (y) = some multiple of 5
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] New post   15 Dec 2021, 04:52
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Since y is a multiple of 5 then 4y is also a multiple of 5 and an even multiple of 5 as it has a 4 in it. Thus the unit digit of 4y is 0.

3x = 200-4x

=>3x = 20(0) - ...(0) [Representing the unit digit under the brackets]

=......(0)

=> x is a multiple of 10 as 3 itself is not.

E is the only answer possible.
(option e)

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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] New post   26 Feb 2022, 17:05
Why cannot x be a multiple of 3?
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] New post   26 Feb 2022, 23:04
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x could be multiple of 3 too.

but ques is asking MUST be true.

x must be multiple of 20 and hence 10.

Akshay004 wrote:
Why cannot x be a multiple of 3?
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] New post   18 May 2022, 23:25
my doubt is that y can be 0 also.... as 0 is multiple of very number .......in this case no option is correct... please help where iM wrong
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] New post   18 May 2022, 23:57
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kakakakaak wrote:
my doubt is that y can be 0 also.... as 0 is multiple of very number .......in this case no option is correct... please help where iM wrong

The question mentions that x and y are positive integers.
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] New post   25 May 2022, 19:30
I've always found the plug and chug method to work best for me with similar problems.

In this case, we know that y can be 5, 10, 15... all the way to 50. I'll then just work through the equation as follows with the numbers in the parenthesis representing my "y":

3x + 4(5) = 200 --- x = 60
3x + 4(10) = 200 --- x is not an integer
3x + 4(15) = 200 --- x is not an integer
3x + 4(20) = 200 --- x = 40

Looking at 40 and 60, each are not individually divisible by 3, 6, 7, and 8. However, they are each individually divisible by 10. Answer choice E.
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] New post   28 Jul 2022, 14:46
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Video solution from Quant Reasoning:
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] New post   29 Jul 2023, 06:27
For 3x+4y=200 given that y is already a multiple of 5, 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]
29 Jul 2023, 06:27
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