GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2018, 22:50

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

Intern
Joined: 16 Jun 2010
Posts: 16
If x, y, p, and q are positive, is x>=y?  [#permalink]

Show Tags

Updated on: 16 Apr 2013, 03:36
00:00

Difficulty:

5% (low)

Question Stats:

84% (01:04) correct 16% (01:36) wrong based on 213 sessions

HideShow timer Statistics

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

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

Originally posted by chintzzz on 19 Jun 2010, 03:12.
Last edited by Bunuel on 16 Apr 2013, 03:36, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 49860

Show Tags

19 Jun 2010, 03:33
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).

_________________
Intern
Joined: 11 Feb 2013
Posts: 14

Show Tags

13 Apr 2013, 12:57
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 ...
VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1077
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Show Tags

13 Apr 2013, 13:08
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
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Manager
Status: Looking to improve
Joined: 15 Jan 2013
Posts: 156
GMAT 1: 530 Q43 V20
GMAT 2: 560 Q42 V25
GMAT 3: 650 Q48 V31
Re: If x, y, p, and q are positive, is x>=y?  [#permalink]

Show Tags

13 Apr 2013, 13:35
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
_________________

KUDOS is a way to say Thank You

Manager
Joined: 07 Apr 2012
Posts: 104
Location: United States
Concentration: Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 590 Q48 V23
GPA: 3.9
WE: Operations (Manufacturing)

Show Tags

07 Sep 2013, 10:02
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 ?
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 613

Show Tags

07 Sep 2013, 10:07
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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49860

Show Tags

07 Sep 2013, 10:08
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.
_________________
Manager
Joined: 07 Apr 2012
Posts: 104
Location: United States
Concentration: Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 590 Q48 V23
GPA: 3.9
WE: Operations (Manufacturing)

Show Tags

07 Sep 2013, 11:05
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?
Math Expert
Joined: 02 Sep 2009
Posts: 49860

Show Tags

07 Sep 2013, 11:08
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"?
_________________
Manager
Joined: 07 Apr 2012
Posts: 104
Location: United States
Concentration: Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 590 Q48 V23
GPA: 3.9
WE: Operations (Manufacturing)

Show Tags

07 Sep 2013, 12:14
I used to think in DS , we need to suffice to all conditions, so asked for AND conditiom
Math Expert
Joined: 02 Sep 2009
Posts: 49860

Show Tags

07 Sep 2013, 12:16
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?
_________________
Manager
Joined: 07 Apr 2012
Posts: 104
Location: United States
Concentration: Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 590 Q48 V23
GPA: 3.9
WE: Operations (Manufacturing)

Show Tags

07 Sep 2013, 22:20
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 $$\geq$$
Math Expert
Joined: 02 Sep 2009
Posts: 49860

Show Tags

08 Sep 2013, 06:02
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: $$x\geq{y}$$ --> $$2\geq{2}$$.
_________________
Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 384
Re: If x, y, p, and q are positive, is x>=y?  [#permalink]

Show Tags

17 Sep 2016, 06:33
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
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12650
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If x, y, p, and q are positive, is x>=y?  [#permalink]

Show Tags

27 Nov 2017, 12:42
1
Hi All,

We're told that X, Y, P and Q are POSITIVE. We're asked if X is >= to Y. This is a YES/NO question. We can solve it with a mix of arithmetic and TESTing VALUES.

1) (P)(X)/(Q)(Y) = P/Q

If we cross-multiply this fraction, we get...
(P)(X)(Q) = (P)(Q)(Y)

Since we know that all of the variables are POSITIVE, we can 'cancel out' the P and Q, which leaves us...
X = Y
Thus, the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) (X)(Y) = P

With this Fact, we have no idea how X and Y relate to one another. For example:
IF... X=1, Y=2, P=2 then the answer to the question is NO.
IF... X=1, Y=1, P=1 then the answer to the question is YES.
Fact 2 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Re: If x, y, p, and q are positive, is x>=y? &nbs [#permalink] 27 Nov 2017, 12:42
Display posts from previous: Sort by