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If x,y,z are positive integers then what is the ratio x : y: z ?

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If x,y,z are positive integers then what is the ratio x : y: z ?  [#permalink]

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New post Updated on: 14 Aug 2016, 13:24
3
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (01:56) correct 36% (01:56) wrong based on 114 sessions

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Originally posted by stonecold on 14 Aug 2016, 03:37.
Last edited by stonecold on 14 Aug 2016, 13:24, edited 1 time in total.
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Re: If x,y,z are positive integers then what is the ratio x : y: z ?  [#permalink]

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New post 14 Aug 2016, 09:31
1
stonecold wrote:
If x,y,z are positive integers then what is the ratio x : y: z ?

(1) x + y = 2 z
(2) 2x + 3y = z


Statement 1 : Three variables, one equation. we cannot deduce the ratio. Insufficient.

Statement 2 : Three variables, one equation. we cannot deduce the ratio. Insufficient.

Combining :

x + y = 2 z

or x + y = 2( 2x + 3y )

or 3x = -5y

or x/y = -5/3

Similarly, on substituting the values in any of the equations, we will get

y/z = -3/1

Hence, x:y:z = 5:3:1 -- Sufficient. Answer is C
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Re: If x,y,z are positive integers then what is the ratio x : y: z ?  [#permalink]

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New post 14 Aug 2016, 13:22
I think there is something wrong with this question. The stem says x, y, and z are positive integers. I got y/z = -3 which is not possible.
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Re: If x,y,z are positive integers then what is the ratio x : y: z ?  [#permalink]

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New post 14 Aug 2016, 14:26
Donnie84 wrote:
I think there is something wrong with this question. The stem says x, y, and z are positive integers. I got y/z = -3 which is not possible.


The stem may have been edited. However, it now says xyz is positive. Either all three are positive or two are negative.

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Re: If x,y,z are positive integers then what is the ratio x : y: z ?  [#permalink]

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New post 14 Aug 2016, 17:15
MarkusKarl wrote:
Donnie84 wrote:
I think there is something wrong with this question. The stem says x, y, and z are positive integers. I got y/z = -3 which is not possible.


The stem may have been edited. However, it now says xyz is positive. Either all three are positive or two are negative.

Posted from my mobile device


Thanks for the clarification.

So we have xyz > 0. This implies either 2 are negative integers or all 3 are positive integers.

Let's look at the statements.

1. x + y = 2z

This means that z is the average of x and y.
x, z, and y can take any values. Examples -> -10, -2, 6 or 1, 1, 1 or 5, 6, 7 and so on.
St1 is insufficient.

2. 2x + 3y = z

There can be many solutions to this equation. Example ->x = 1, y = 1, z = 5 or x = 2, y = 1, z = 7 and so on.
St2 is insufficient.

St1 and St2:

x + y = 2z
2x + 3y = z

Multiply 1st equation by 2 -> 2x + 2y = 4z
Now, subtract the 2nd equation from the 1st -> -y = 3z or y = -3z or y/z = -3.
Take y = -3z and plug it in the 1st equation -> x - 3z = 2z or x = 5z or x/z = 5.

y/z = -3
x/z = 5

x:y:z = 5:3:1

Answer (C.)

This next bit is not needed to answer this question but may help in other questions.

y/z = -3
x/z = 5
Either y is negative or z is negative. As per stem, 2 integers can be negative.
Either both x and z are negative or both x and z are positive. As per stem, 2 integers can be negative or all 3 can be positive.

If y is negative, then z must be positive, and then x must be positive. This would violate the stem conditions. Rejected.
So y must be positive which would make both z and x negative. This would not violate the stem conditions. Accepted.

Experts,

I think I have the right answer but I don't think this is a good question. Though ratios are not dependent on +/-, I haven't come across an official question where ratios involve a combination positive and negative numbers. In that context, what purpose does xyz > 0 serve?
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Re: If x,y,z are positive integers then what is the ratio x : y: z ?  [#permalink]

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New post 14 Aug 2016, 21:49
Donnie84 wrote:
MarkusKarl wrote:
Donnie84 wrote:
I think there is something wrong with this question. The stem says x, y, and z are positive integers. I got y/z = -3 which is not possible.


The stem may have been edited. However, it now says xyz is positive. Either all three are positive or two are negative.

Posted from my mobile device


Thanks for the clarification.

So we have xyz > 0. This implies either 2 are negative integers or all 3 are positive integers.

Let's look at the statements.

1. x + y = 2z

This means that z is the average of x and y.
x, z, and y can take any values. Examples -> -10, -2, 6 or 1, 1, 1 or 5, 6, 7 and so on.
St1 is insufficient.

2. 2x + 3y = z

There can be many solutions to this equation. Example ->x = 1, y = 1, z = 5 or x = 2, y = 1, z = 7 and so on.
St2 is insufficient.

St1 and St2:

x + y = 2z
2x + 3y = z

Multiply 1st equation by 2 -> 2x + 2y = 4z
Now, subtract the 2nd equation from the 1st -> -y = 3z or y = -3z or y/z = -3.
Take y = -3z and plug it in the 1st equation -> x - 3z = 2z or x = 5z or x/z = 5.

y/z = -3
x/z = 5

x:y:z = 5:3:1

Answer (C.)

This next bit is not needed to answer this question but may help in other questions.

y/z = -3
x/z = 5
Either y is negative or z is negative. As per stem, 2 integers can be negative.
Either both x and z are negative or both x and z are positive. As per stem, 2 integers can be negative or all 3 can be positive.

If y is negative, then z must be positive, and then x must be positive. This would violate the stem conditions. Rejected.
So y must be positive which would make both z and x negative. This would not violate the stem conditions. Accepted.

Experts,

I think I have the right answer but I don't think this is a good question. Though ratios are not dependent on +/-, I haven't come across an official question where ratios involve a combination positive and negative numbers. In that context, what purpose does xyz > 0 serve?


Its not a good question at all
But it is present in the MGMAT guide for fractions and decimals
I had the same confusion as you had

Regards
Stone cold
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Re: If x,y,z are positive integers then what is the ratio x : y: z ?  [#permalink]

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