If x, y, p, and q are positive, is x>=y? : GMAT Data Sufficiency (DS)
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# If x, y, p, and q are positive, is x>=y?

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If x, y, p, and q are positive, is x>=y? [#permalink]

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19 Jun 2010, 02:12
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If x, y, p, and q are positive, is x>=y?

(1) $$\frac{px}{qy}=\frac{p}{q}$$
(2) $$xy=p$$
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 Apr 2013, 02:36, edited 1 time in total.
Edited the question.
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19 Jun 2010, 02:13
sorry.. (1)px/qy=p/q
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19 Jun 2010, 02:33
chintzzz wrote:
If x,y,p, and q are positive, is x>=y?

(1) $$\frac{px}{qy}=\frac{p}{q}$$
(2) $$xy=p$$

First of all to format formulas mark and push [ m] button.

If x, y, p, and q are positive, is x>=y?

Question: is $$x$$ more than or equal to $$y$$ (is $$x\geq{y}$$)?

(1) $$\frac{px}{qy}=\frac{p}{q}$$ --> reduce by $$\frac{p}{q}$$ --> $$\frac{x}{y}=1$$ --> $$x=y$$, so we can answer yes to the question: $$x$$ is equal to $$y$$. Sufficient.

(2) $$xy=p$$ --> Clearly not sufficient (if $$x$$, $$y$$ and $$p$$ equal to 1, 2, and 2 respectively then the answer is NO but if they equal to 2, 1 and 2 then the answer is YES).

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13 Apr 2013, 11:57
Bunuel wrote:
chintzzz wrote:
If x,y,p, and q are positive, is x>=y?

(1) $$\frac{px}{qy}=\frac{p}{q}$$
(2) $$xy=p$$

First of all to format formulas mark and push [ m] button.

If x, y, p, and q are positive, is x>=y?

Question: is $$x$$ more than or equal to $$y$$ (is $$x\geq{y}$$)?

(1) $$\frac{px}{qy}=\frac{p}{q}$$ --> reduce by $$\frac{p}{q}$$ --> $$\frac{x}{y}=1$$ --> $$x=y$$, so we can answer yes to the question: $$x$$ is equal to $$y$$. Sufficient.

(2) $$xy=p$$ --> Clearly not sufficient (if $$x$$, $$y$$ and $$p$$ equal to 1, 2, and 2 respectively then the answer is NO but if they equal to 2, 1 and 2 then the answer is YES).

Hi,

the statement 1 is just telling us that x = y ...but its not giving ny info that if x>y...so its not sufficient
so how can v mark the answer as A ...
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13 Apr 2013, 12:08
Perhaps wrote:
Hi,

the statement 1 is just telling us that x = y ...but its not giving ny info that if x>y...so its not sufficient
so how can v mark the answer as A ...

The question asks is $$x\geq{y}$$? If we know that x=y then we can answer YES to the question, its very simple.
Let me know if it s clear
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Re: If x, y, p, and q are positive, is x>=y? [#permalink]

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13 Apr 2013, 12:35
when x >= y means x > y OR x = y and NOT x > y AND x = y (A impossible scenario)

//kudos, if the above explanation is good
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07 Sep 2013, 09:02
Bunuel wrote:
chintzzz wrote:
If x,y,p, and q are positive, is x>=y?

(1) $$\frac{px}{qy}=\frac{p}{q}$$
(2) $$xy=p$$

First of all to format formulas mark and push [ m] button.

If x, y, p, and q are positive, is x>=y?

Question: is $$x$$ more than or equal to $$y$$ (is $$x\geq{y}$$)?

(1) $$\frac{px}{qy}=\frac{p}{q}$$ --> reduce by $$\frac{p}{q}$$ --> $$\frac{x}{y}=1$$ --> $$x=y$$, so we can answer yes to the question: $$x$$ is equal to $$y$$. Sufficient.

(2) $$xy=p$$ --> Clearly not sufficient (if $$x$$, $$y$$ and $$p$$ equal to 1, 2, and 2 respectively then the answer is NO but if they equal to 2, 1 and 2 then the answer is YES).

from A we get x=y only , but what abut x > y ?
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07 Sep 2013, 09:07
ygdrasil24 wrote:

from A we get x=y only , but what abut x > y ?

No, the OA is correct . $$x\geq{y}$$ means x=y OR x>y. Any value of x satisfying EITHER of these 2 conditions works.
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07 Sep 2013, 09:08
ygdrasil24 wrote:
Bunuel wrote:
chintzzz wrote:
If x,y,p, and q are positive, is x>=y?

(1) $$\frac{px}{qy}=\frac{p}{q}$$
(2) $$xy=p$$

First of all to format formulas mark and push [ m] button.

If x, y, p, and q are positive, is x>=y?

Question: is $$x$$ more than or equal to $$y$$ (is $$x\geq{y}$$)?

(1) $$\frac{px}{qy}=\frac{p}{q}$$ --> reduce by $$\frac{p}{q}$$ --> $$\frac{x}{y}=1$$ --> $$x=y$$, so we can answer yes to the question: $$x$$ is equal to $$y$$. Sufficient.

(2) $$xy=p$$ --> Clearly not sufficient (if $$x$$, $$y$$ and $$p$$ equal to 1, 2, and 2 respectively then the answer is NO but if they equal to 2, 1 and 2 then the answer is YES).

from A we get x=y only , but what abut x > y ?

The answer is A, not E.

The question asks: is x greater than or equal to y. (1) says that x IS equal to y, so we have an YES answer to the question.
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07 Sep 2013, 10:05
First of all to format formulas mark and push [ m] button.

If x, y, p, and q are positive, is x>=y?

The question asks: is x greater than or equal to y. (1) says that x IS equal to y, so we have an YES answer to the question.[/quote][/quote]
OK , so does it mean its an OR condition and not AND ? Is that a general rule when >eq or <eq occurs?
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07 Sep 2013, 10:08
ygdrasil24 wrote:
OK , so does it mean its an OR condition and not AND ? Is that a general rule when >eq or <eq occurs?

$$x\geq{y}$$ translates to is x greater than or equal to y. How can it be "and"?
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07 Sep 2013, 11:14
I used to think in DS , we need to suffice to all conditions, so asked for AND conditiom
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07 Sep 2013, 11:16
ygdrasil24 wrote:
I used to think in DS , we need to suffice to all conditions, so asked for AND conditiom

Actually it has nothing to do with DS. $$\geq$$ sign in mathematics translates to greater than or equal to.

Also, how can x be greater than AND equal to y?
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07 Sep 2013, 21:20
Bunuel wrote:
ygdrasil24 wrote:
I used to think in DS , we need to suffice to all conditions, so asked for AND conditiom

Actually it has nothing to do with DS. $$\geq$$ sign in mathematics translates to greater than or equal to.

Also, how can x be greater than AND equal to y?

You have a point but if x $$\geq$$ y, and we have a solution x = y, it obviously does not mean x has to be gretaer than y, or if x is $$\geq$$ y , it does not mean x = y, I was of the view that x should fit in the equality i.e $$\geq$$
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08 Sep 2013, 05:02
ygdrasil24 wrote:
Bunuel wrote:
ygdrasil24 wrote:
I used to think in DS , we need to suffice to all conditions, so asked for AND conditiom

Actually it has nothing to do with DS. $$\geq$$ sign in mathematics translates to greater than or equal to.

Also, how can x be greater than AND equal to y?

You have a point but if x $$\geq$$ y, and we have a solution x = y, it obviously does not mean x has to be gretaer than y, or if x is $$\geq$$ y , it does not mean x = y, I was of the view that x should fit in the equality i.e $$\geq$$

You are missing a point. If x=y, it's OK to write: $$x\geq{y}$$ --> $$2\geq{2}$$.
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Re: If x, y, p, and q are positive, is x>=y? [#permalink]

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17 Sep 2016, 05:33
A is correct. Here's why:

(1) (px)/(qy) = (p/q)
[q/p][(px)/(qy)] = [(p/q)][q/p] --> x=y (relationship has been established)

SUFFICIENT

(2) xy = p

NOT SUFFICIENT - we don't know anything about the relationship between x and y
Re: If x, y, p, and q are positive, is x>=y?   [#permalink] 17 Sep 2016, 05:33
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