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If x and y are integers, what is the least positive number of 24x+15y?

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If x and y are integers, what is the least positive number of 24x+15y? [#permalink]

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New post 08 Jun 2016, 16:03
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If x and y are integers, what is the least positive number of 24x+15y?
A. 1
B. 3
C. 6
D. 9
E. 12

*An answer will be posted in 2 days.
[Reveal] Spoiler: OA

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Re: If x and y are integers, what is the least positive number of 24x+15y? [#permalink]

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New post 08 Jun 2016, 22:07
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MathRevolution wrote:
If x and y are integers, what is the least positive number of 24x+15y?
A. 1
B. 3
C. 6
D. 9
E. 12

*An answer will be posted in 2 days.



24x+15y > 0

This means

(take out 3 common) 8x+5y> 0

if 8x = 16, 5y=-15, then we get value as 1.
if 8x = -24, 5y=25, then we get value as 1.

A is the answer.
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Re: If x and y are integers, what is the least positive number of 24x+15y? [#permalink]

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New post 09 Jun 2016, 08:03
adiagr wrote:
MathRevolution wrote:
If x and y are integers, what is the least positive number of 24x+15y?
A. 1
B. 3
C. 6
D. 9
E. 12

*An answer will be posted in 2 days.



24x+15y > 0

This means

(take out 3 common) 8x+5y> 0

if 8x = 16, 5y=-15, then we get value as 1.
if 8x = -24, 5y=25, then we get value as 1.

A is the answer.


By taking 3 common, you have just calculated the minimum positive value for 8x+5y. But the question asks us to calculate the minimum value of 24x+15y, which is 3(8x+5y) = 3*1= 3

So the answer will be B.
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Re: If x and y are integers, what is the least positive number of 24x+15y? [#permalink]

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New post 09 Jun 2016, 11:40
Anybody actually have a way of solving this w/o plugging in numbers?
Is there a rule or use of prime factors.
Expert Post
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Re: If x and y are integers, what is the least positive number of 24x+15y? [#permalink]

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New post 10 Jun 2016, 21:55
Since 24(2)-15(3)=3, B is the correct answer.
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Re: If x and y are integers, what is the least positive number of 24x+15y? [#permalink]

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New post 03 Feb 2018, 23:33
MathRevolution wrote:
If x and y are integers, what is the least positive number of 24x+15y?
A. 1
B. 3
C. 6
D. 9
E. 12

*An answer will be posted in 2 days.


Since 24X + 15Y = X , where X is an Integer with the least value.
So 8X + 5Y = X/3 , where X/3 is an integer

So the question is what is the least value from answers that is divided by 3

Hence, B is the correct answer
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Re: If x and y are integers, what is the least positive number of 24x+15y? [#permalink]

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New post 03 Feb 2018, 23:40
The equation can be written as 8x + 5y = a/3.. so a can be 3,6,9...
Minimum = 3

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Re: If x and y are integers, what is the least positive number of 24x+15y?   [#permalink] 03 Feb 2018, 23:40
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