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If x and y are positive, what is the value of x?

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If x and y are positive, what is the value of x? [#permalink]

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New post Updated on: 09 Mar 2012, 23:39
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If x and y are positive, what is the value of x?

(1) 200% of x equals to 400% of y.

(2) xy is the square of a positive integer.

Originally posted by pradeepparihar on 09 Mar 2012, 21:22.
Last edited by Bunuel on 09 Mar 2012, 23:39, edited 2 times in total.
Edited the question
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Re: if x and y are positive , what is the value of x?plz explain [#permalink]

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New post 09 Mar 2012, 23:17
(1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even

(2)
Xy = 1,4,9,16,…

Not Sufficient.

(1) + (2)

Suppose:

2y^2 = 16
Y = 2root(2)
X = 4root(2)
Or
2y^2 = 4
Y = root(2)
X = 2root(2)

Not Sufficient.

So Answer is E.
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Re: If x and y are positive, what is the value of x? [#permalink]

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New post 09 Mar 2012, 23:38
1
2
If x and y are positive, what is the value of x?

Notice that we are not told that \(x\) and \(y\) are integers only, we are just told that they are both positive.

(1) 200% of x equals to 400% of y --> \(\frac{200}{100}*x=\frac{400}{100}*y\) --> \(x=2y\). Not sufficient to get the single numerical value of \(x\).

(2) xy is the square of a positive integer --> \(xy=n^2\), for some positive integer \(n\). Not sufficient to get the single numerical value of \(x\).

(1)+(2) Since from (1) \(x=2y\) then from (2) \(x*\frac{x}{2}=n^2\) --> \(x^2=2n^2\) --> the value of \(x\) (x^2) is determined by the value of integer \(n\), so we still cannot get the single numerical value of \(x\). For example: if \(n=1\) then \(x=\sqrt{2}\) but if \(n=2\) then \(x=2\sqrt{2}\). Not sufficient.

Answer: E.

Hope it's clear.


subhashghosh wrote:
(1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even



Since we are not told that \(x\) and \(y\) are integers only, then from \(x=2y\) we cannot say whether \(x\) even:

\(x\) will be even if \(y=integer\);
\(x\) will be odd if \(y=\frac{odd}{2}\), for example if \(y=\frac{3}{2}\) then \(x=3=odd\);
\(x\) may not be an integer at all, for example if \(y=\frac{1}{3}\) then \(x=\frac{2}{3}\neq{integer}\).

In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.

Hope it's clear.
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Re: If x and y are positive, what is the value of x? [#permalink]

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New post 11 Mar 2012, 04:44
Bunuel wrote:
If x and y are positive, what is the value of x?

Notice that we are not told that \(x\) and \(y\) are integers only, we are just told that they are both positive.

(1) 200% of x equals to 400% of y --> \(\frac{200}{100}*x=\frac{400}{100}*y\) --> \(x=2y\). Not sufficient to get the single numerical value of \(x\).

(2) xy is the square of a positive integer --> \(xy=n^2\), for some positive integer \(n\). Not sufficient to get the single numerical value of \(x\).

(1)+(2) Since from (1) \(x=2y\) then from (2) \(x*\frac{x}{2}=n^2\) --> \(x^2=2n^2\) --> the value of \(x\) (x^2) is determined by the value of integer \(n\), so we still cannot get the single numerical value of \(x\). For example: if \(n=1\) then \(x=\sqrt{2}\) but if \(n=2\) then \(x=2\sqrt{2}\). Not sufficient.

Answer: E.

Hope it's clear.


subhashghosh wrote:
(1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even



Since we are not told that \(x\) and \(y\) are integers only, then from \(x=2y\) we cannot say whether \(x\) even:

\(x\) will be even if \(y=integer\);
\(x\) will be odd if \(y=\frac{odd}{2}\), for example if \(y=\frac{3}{2}\) then \(x=3=odd\);
\(x\) may not be an integer at all, for example if \(y=\frac{1}{3}\) then \(x=\frac{2}{3}\neq{integer}\).

In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.

Hope it's clear.


Hello Bunuel,

Thanks for this wonderful explanation!

However I'm still not able to figure out the meaning of the following statement

Quote:
In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.


Can you please provide more clarity and let know which particular number property you are using to deduce the above statement?
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Re: If x and y are positive, what is the value of x? [#permalink]

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New post 11 Mar 2012, 04:49
raul2011 wrote:
Bunuel wrote:
If x and y are positive, what is the value of x?

Notice that we are not told that \(x\) and \(y\) are integers only, we are just told that they are both positive.

(1) 200% of x equals to 400% of y --> \(\frac{200}{100}*x=\frac{400}{100}*y\) --> \(x=2y\). Not sufficient to get the single numerical value of \(x\).

(2) xy is the square of a positive integer --> \(xy=n^2\), for some positive integer \(n\). Not sufficient to get the single numerical value of \(x\).

(1)+(2) Since from (1) \(x=2y\) then from (2) \(x*\frac{x}{2}=n^2\) --> \(x^2=2n^2\) --> the value of \(x\) (x^2) is determined by the value of integer \(n\), so we still cannot get the single numerical value of \(x\). For example: if \(n=1\) then \(x=\sqrt{2}\) but if \(n=2\) then \(x=2\sqrt{2}\). Not sufficient.

Answer: E.

Hope it's clear.


subhashghosh wrote:
(1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even



Since we are not told that \(x\) and \(y\) are integers only, then from \(x=2y\) we cannot say whether \(x\) even:

\(x\) will be even if \(y=integer\);
\(x\) will be odd if \(y=\frac{odd}{2}\), for example if \(y=\frac{3}{2}\) then \(x=3=odd\);
\(x\) may not be an integer at all, for example if \(y=\frac{1}{3}\) then \(x=\frac{2}{3}\neq{integer}\).

In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.

Hope it's clear.


Hello Bunuel,

Thanks for this wonderful explanation!

However I'm still not able to figure out the meaning of the following statement

Quote:
In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.


Can you please provide more clarity and let know which particular number property you are using to deduce the above statement?


Which particular number property - I think Bunuel is saying that 0 is neither positive nor negative.
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Re: If x and y are positive, what is the value of x? [#permalink]

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New post 11 Mar 2012, 04:59
raul2011 wrote:
Hello Bunuel,

Thanks for this wonderful explanation!

However I'm still not able to figure out the meaning of the following statement

Quote:
In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.


Can you please provide more clarity and let know which particular number property you are using to deduce the above statement?


Sure. We know that \(n\) is a positive integer. Now, if \(x\) is an even integer, then \(x^2=2n^2\) should be true for some integers \(n\) and \(x\), but it's true only for one integer solution \(x=n=0\), which cannot be valid, since we are given that \(x\) is a positive number (0 is neither positive nor negative).

Hope it's clear.
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Re: If x and y are positive, what is the value of x? [#permalink]

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New post 11 Sep 2012, 05:45
Bunuel wrote:
If x and y are positive, what is the value of x?

Notice that we are not told that \(x\) and \(y\) are integers only, we are just told that they are both positive.

(1) 200% of x equals to 400% of y --> \(\frac{200}{100}*x=\frac{400}{100}*y\) --> \(x=2y\). Not sufficient to get the single numerical value of \(x\).

(2) xy is the square of a positive integer --> \(xy=n^2\), for some positive integer \(n\). Not sufficient to get the single numerical value of \(x\).

(1)+(2) Since from (1) \(x=2y\) then from (2) \(x*\frac{x}{2}=n^2\) --> \(x^2=2n^2\) --> the value of \(x\) (x^2) is determined by the value of integer \(n\), so we still cannot get the single numerical value of \(x\). For example: if \(n=1\) then \(x=\sqrt{2}\) but if \(n=2\) then \(x=2\sqrt{2}\). Not sufficient.

Answer: E.

Hope it's clear.


subhashghosh wrote:
(1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even



Since we are not told that \(x\) and \(y\) are integers only, then from \(x=2y\) we cannot say whether \(x\) even:

\(x\) will be even if \(y=integer\);
\(x\) will be odd if \(y=\frac{odd}{2}\), for example if \(y=\frac{3}{2}\) then \(x=3=odd\);
\(x\) may not be an integer at all, for example if \(y=\frac{1}{3}\) then \(x=\frac{2}{3}\neq{integer}\).

In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.

Hope it's clear.


Hi Bunuel,

Thanks for the nice explanation . I would like to modify the question a bit & would like to present a twist to the same question.

If the new statement reads "If x and y are positive integers, what is the value of x" rather than "If x and y are positive, what is the value of x"
Now what will be the answer.

As per me the answer should be C because i believe no such value will exist.

Kindly enlighten us all.
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Re: If x and y are positive, what is the value of x? [#permalink]

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New post 11 Sep 2012, 06:03
fameatop wrote:
Bunuel wrote:
If x and y are positive, what is the value of x?

Notice that we are not told that \(x\) and \(y\) are integers only, we are just told that they are both positive.

(1) 200% of x equals to 400% of y --> \(\frac{200}{100}*x=\frac{400}{100}*y\) --> \(x=2y\). Not sufficient to get the single numerical value of \(x\).

(2) xy is the square of a positive integer --> \(xy=n^2\), for some positive integer \(n\). Not sufficient to get the single numerical value of \(x\).

(1)+(2) Since from (1) \(x=2y\) then from (2) \(x*\frac{x}{2}=n^2\) --> \(x^2=2n^2\) --> the value of \(x\) (x^2) is determined by the value of integer \(n\), so we still cannot get the single numerical value of \(x\). For example: if \(n=1\) then \(x=\sqrt{2}\) but if \(n=2\) then \(x=2\sqrt{2}\). Not sufficient.

Answer: E.

Hope it's clear.


subhashghosh wrote:
(1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even



Since we are not told that \(x\) and \(y\) are integers only, then from \(x=2y\) we cannot say whether \(x\) even:

\(x\) will be even if \(y=integer\);
\(x\) will be odd if \(y=\frac{odd}{2}\), for example if \(y=\frac{3}{2}\) then \(x=3=odd\);
\(x\) may not be an integer at all, for example if \(y=\frac{1}{3}\) then \(x=\frac{2}{3}\neq{integer}\).

In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.

Hope it's clear.


Hi Bunuel,

Thanks for the nice explanation . I would like to modify the question a bit & would like to present a twist to the same question.

If the new statement reads "If x and y are positive integers, what is the value of x" rather than "If x and y are positive, what is the value of x"
Now what will be the answer.

As per me the answer should be C because i believe no such value will exist.

Kindly enlighten us all.


In this case, for (1)+(2) we would have the same equation: \(x=2n^2\), which has only one integer solution for \(x\) and \(n\): \(x=n=0\) but since we are told that \(x\) is a positive integer then this solution is no good.

But we won't see such question on the real test where no value can satisfy the statements. So, the question in this case would be flawed.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If x and y are positive, what is the value of x? [#permalink]

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Re: If x and y are positive, what is the value of x?   [#permalink] 16 Jan 2018, 06:45
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