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If x and y are greater than 0, is x = 1 ?

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If x and y are greater than 0, is x = 1 ? [#permalink]

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If x and y are greater than 0, is x = 1 ?

(1) x/y = 1
(2) xy = 1

[Reveal] Spoiler:
I don't understand why it's C.

Shouldn't statement (2) be sufficient?

If xy=1 wouldn't that mean x and y are both "1" b/c given "x and y >0"?

What am I missing?
[Reveal] Spoiler: OA

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Re: If x and y are greater than 0, is x = 1 ? [#permalink]

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New post 13 Aug 2011, 17:41
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Why 2 isn't sufficient is that X or Y can also be fractions.

X = 1/2, Y = 2

XY = 1

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Re: If x and y are greater than 0, is x = 1 ? [#permalink]

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New post 13 Aug 2011, 17:41
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Fairly straightforward:

Statement 1:

Both of these are valid: \(\frac{x}{y}=\frac{7}{7}=1\) and \(\frac{x}{y}=\frac{100}{100}=1\) - Insufficient

Statement 2:

Both of these are valid: \(x*y=1*1=1\) and \(x*y=0.2*5=1\) - Insufficient

However, combining both statements, the only valid solution is: \(\frac{x}{y}=\frac{1}{1}=1=x*y=1*1\) where \(x=1\) and \(y=1\).

Don't forget those pesky real numbers! Nowhere does the stem insist that these be integers.
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Re: If x and y are greater than 0, is x = 1 ? [#permalink]

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cellydan wrote:
Why 2 isn't sufficient is that X or Y can also be fractions.

X = 1/2, Y = 2

XY = 1

You are not wrong, but check there are multiple values that x can take ?
As per GMAC - All numbers are real numbers if not mentioned.


If X and Y are greater than 0, is x=1?
Question gives :
If X and Y are greater than 0.
Question asks : Is X = 1? --> Yes/No

(1) x/y = 1
Since y > 0 as per question stem, so x=y
x > 0 , so x can take any value - 1,2,3,etc
So 1 is not sufficient

(2) xy = 1
If x is equal to 1, then y is equal to 1
If x is equal to 2, then y is equal to 1/2
If x is equal to 3, then y is equal to 1/3
All are valid, but there is no unique value of x.
So (2) is not sufficient


Combining 1 and 2 - xy=1 and x=y
\(XY = 1\)
=> \(x^2 = 1\)
=> \(x = +1 or -1\)
But question tells x is greater than 1
So\(x = 1\)is the only value x can take.

OA is C

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If x and y are greater than 0, is x = 1 ? [#permalink]

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If x and y are greater than 0, is x = 1 ?

(1) x/y = 1
(2) xy = 1

Last edited by Bunuel on 28 Sep 2014, 11:29, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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Re: If x and y are greater than 0, is x = 1 ? [#permalink]

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DeeptiM wrote:
If x and y are greater than 0, is x=1?

1) x/y=1
2) xy=1


ST 1
x/y=1 and this means x=y so x and y can be 1 , 2, 3 , 4 , .......
EX : 5/5=1 4/4=1 1000/1000=1
NOT sufficient

ST2
xy=1 and means x=1/y so x can be 1/5 so y = 5
EX" 1/5 * 5 = 1
also not sufficient

ST1 & ST2
x=y and xy=1
you can simply find that xx=1 this means x^2 = 1 so x= +1 or x= -1
and because y and x must be larger than 0 so x must be +1
sufficient


the answer is C
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Re: If x and y are greater than 0, is x = 1 ? [#permalink]

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New post 23 Jul 2017, 09:46
gokoli wrote:
If x and y are greater than 0, is x = 1 ?

(1) x/y = 1
(2) xy = 1

[Reveal] Spoiler:
I don't understand why it's C.

Shouldn't statement (2) be sufficient?

If xy=1 wouldn't that mean x and y are both "1" b/c given "x and y >0"?

What am I missing?


Nice question. I used to fall in this trap a lot.

S1: x/y = 1
hence x = y .

Not sufficient

S2: xy =1
No more info hence not sufficient

Now combining both

X^2 =1
or x = +1,-1

Here is the trap where i used to miss the question statement all together . Since x is positive. It cannot take the negative value.

Hence x = 1. Sufficient

Answer is D

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Re: If x and y are greater than 0, is x = 1 ?   [#permalink] 23 Jul 2017, 09:46
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