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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

(1) x < y and xy = 100. Since both \(x\) and \(y\) are positive AND \(x < y\), then in order \(xy=100\) to hold true, one multiple must be less than 10 and another greater than 10, thus \(x < 10 < y\). Sufficient.

(2) x^2 < 100 < y^2. Take the square root from all three parts: \(|x|<10<|y|\). Again, since both \(x\) and \(y\) are positive, then it transforms to \(x < 10 < y\). Sufficient.

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

(1) If \(x=y\) and \(xy=100\), then \(x=y=10\). So, if the two positive numbers \(x\) and \(y\) are not equal, one must be smaller than \(10\) and the other one must be greater than \(10\). It is given that \(x<y\), so necessarily \(x<10<y\). Sufficient.

(2) Since we are given that \(x\) and \(y\) are positive, we can take the square root of all the sides in the given inequality and obtain \(x<10<y\). Sufficient.

Answer D.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

(1) x < y and xy = 100. Since both \(x\) and \(y\) are positive AND \(x < y\), then in order \(xy=100\) to hold true, one multiple must be less than 10 and another greater than 10, thus \(x < 10 < y\). Sufficient.

(2) x^2 < 100 < y^2. Take the square root from all three parts: \(|x|<10<|y|\). Again, since both \(x\) and \(y\) are positive, then it transforms to \(x < 10 < y\). Sufficient.

Answer: D.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
_________________

Re: If x and y are positive, is x < 10 < y? [#permalink]

Show Tags

29 Jan 2013, 07:53

Option 2 is very clear.

Option 1 just drew a number line.

xy=100 Any combination of numbers say 5 X 20 or 4 X 25 etc can give me an 'x' greater than 10 as x should be less than y.

Probably this would be insufficient if x<y would not be given

Attachments

Problem_DS.jpg [ 9.17 KiB | Viewed 11017 times ]

_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

Re: If x and y are positive, is x < 10 < y? [#permalink]

Show Tags

24 Nov 2013, 22:49

Bunuel wrote:

SOLUTION

If x and y are positive, is x < 10 < y?

(1) x < y and xy = 100. Since both \(x\) and \(y\) are positive AND \(x < y\), then in order \(xy=100\) to hold true, one multiple must be less than 10 and another greater than 10, thus \(x < 10 < y\). Sufficient.

(2) x^2 < 100 < y^2. Take the square root from all three parts: \(|x|<10<|y|\). Again, since both \(x\) and \(y\) are positive, then it transforms to \(x < 10 < y\). Sufficient.

Answer: D.

What If GMAT twist it by not giving that x and y are +ves?
_________________

Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

(1) x < y and xy = 100. Since both \(x\) and \(y\) are positive AND \(x < y\), then in order \(xy=100\) to hold true, one multiple must be less than 10 and another greater than 10, thus \(x < 10 < y\). Sufficient.

(2) x^2 < 100 < y^2. Take the square root from all three parts: \(|x|<10<|y|\). Again, since both \(x\) and \(y\) are positive, then it transforms to \(x < 10 < y\). Sufficient.

Answer: D.

What If GMAT twist it by not giving that x and y are +ves?

In this case the answer would be C.
_________________

Re: If x and y are positive, is x < 10 < y? [#permalink]

Show Tags

13 Apr 2014, 10:27

Bunuel wrote:

honchos wrote:

Bunuel wrote:

SOLUTION

If x and y are positive, is x < 10 < y?

(1) x < y and xy = 100. Since both \(x\) and \(y\) are positive AND \(x < y\), then in order \(xy=100\) to hold true, one multiple must be less than 10 and another greater than 10, thus \(x < 10 < y\). Sufficient.

(2) x^2 < 100 < y^2. Take the square root from all three parts: \(|x|<10<|y|\). Again, since both \(x\) and \(y\) are positive, then it transforms to \(x < 10 < y\). Sufficient.

Answer: D.

What If GMAT twist it by not giving that x and y are +ves?

In this case the answer would be C.

2 questions:

1) What is +ves? 2) If the stem read that x & y could be positive OR negative, that would mean that only statement one is sufficient. Is that correct?

My reasoning being, the second inequality could become \(x<+-10<y\). Meaning, x would have to be less than -10, lets call it -25 and y would have to be 4 which would yield a "no" for the question. Additionally, if we took the positive squareroot, the question stem would yield a yes. Am I thinking about this the right way?

(1) x < y and xy = 100. Since both \(x\) and \(y\) are positive AND \(x < y\), then in order \(xy=100\) to hold true, one multiple must be less than 10 and another greater than 10, thus \(x < 10 < y\). Sufficient.

(2) x^2 < 100 < y^2. Take the square root from all three parts: \(|x|<10<|y|\). Again, since both \(x\) and \(y\) are positive, then it transforms to \(x < 10 < y\). Sufficient.

Answer: D.

What If GMAT twist it by not giving that x and y are +ves?

In this case the answer would be C.

2 questions:

1) What is +ves? 2) If the stem read that x & y could be positive OR negative, that would mean that only statement one is sufficient. Is that correct?

My reasoning being, the second inequality could become \(x<+-10<y\). Meaning, x would have to be less than -10, lets call it -25 and y would have to be 4 which would yield a "no" for the question. Additionally, if we took the positive squareroot, the question stem would yield a yes. Am I thinking about this the right way?

1. +ve = positive.

2. If we were not told that x and y are positive, then the answer would be C, not A: Is x < 10 < y?

(1) x < y and xy = 100. If x=-20 and y=-5, then the answer is NO but if x=5 and y=20, then the answer is YES. Not sufficient. Notice that from xy = 100 we can deduce that x and y have the same sign.

(2) x^2 < 100 < y^2 --> -10 < x < 10 and |y|>10. So, y can be more than 10 as well as less than -10. Not sufficient.

(1)+(2) Since x < y, then y < -10 is not possible, thus y > 10. So, we have that x < 10 < y. Sufficient.

Re: If x and y are positive, is x < 10 < y? [#permalink]

Show Tags

04 May 2014, 07:21

Bunuel wrote:

russ9 wrote:

2 questions:

1) What is +ves? 2) If the stem read that x & y could be positive OR negative, that would mean that only statement one is sufficient. Is that correct?

My reasoning being, the second inequality could become \(x<+-10<y\). Meaning, x would have to be less than -10, lets call it -25 and y would have to be 4 which would yield a "no" for the question. Additionally, if we took the positive squareroot, the question stem would yield a yes. Am I thinking about this the right way?

1. +ve = positive.

2. If we were not told that x and y are positive, then the answer would be C, not A: Is x < 10 < y?

(1) x < y and xy = 100. If x=-20 and y=-5, then the answer is NO but if x=5 and y=20, then the answer is YES. Not sufficient. Notice that from xy = 100 we can deduce that x and y have the same sign.

(2) x^2 < 100 < y^2 --> -10 < x < 10 and |y|>10. So, y can be more than 10 as well as less than -10. Not sufficient.

(1)+(2) Since x < y, then y < -10 is not possible, thus y > 10. So, we have that x < 10 < y. Sufficient.

Answer: C.

Hope it's clear.

Hi Bunuel,

I see how you can prove that 1 is NOT sufficient although I'm having a hard time with #2. The equality reads x^2 < 100 < y^2. Doesn't that yield that x < +/- 10? Wouldn't that make it is x<10 or -x>10? I can tell that my signs are off but if I follow the math, they seem fine. What am I missing here? Assuming that this part of the problem is resolved(as I can see the light at the end of the tunnel), I still don't see how you get insufficient.

Assuming that the correct inequalities are -10<x<10 and 10<y<-10, are you saying that since the final inequality can be y<-10<x or x<10<y, therefore insufficient? But wouldn't we say that only x<10<y pertains to the main equation and therefore sufficient?

1) What is +ves? 2) If the stem read that x & y could be positive OR negative, that would mean that only statement one is sufficient. Is that correct?

My reasoning being, the second inequality could become \(x<+-10<y\). Meaning, x would have to be less than -10, lets call it -25 and y would have to be 4 which would yield a "no" for the question. Additionally, if we took the positive squareroot, the question stem would yield a yes. Am I thinking about this the right way?

1. +ve = positive.

2. If we were not told that x and y are positive, then the answer would be C, not A: Is x < 10 < y?

(1) x < y and xy = 100. If x=-20 and y=-5, then the answer is NO but if x=5 and y=20, then the answer is YES. Not sufficient. Notice that from xy = 100 we can deduce that x and y have the same sign.

(2) x^2 < 100 < y^2 --> -10 < x < 10 and |y|>10. So, y can be more than 10 as well as less than -10. Not sufficient.

(1)+(2) Since x < y, then y < -10 is not possible, thus y > 10. So, we have that x < 10 < y. Sufficient.

Answer: C.

Hope it's clear.

Hi Bunuel,

I see how you can prove that 1 is NOT sufficient although I'm having a hard time with #2. The equality reads x^2 < 100 < y^2. Doesn't that yield that x < +/- 10? Wouldn't that make it is x<10 or -x>10? I can tell that my signs are off but if I follow the math, they seem fine. What am I missing here? Assuming that this part of the problem is resolved(as I can see the light at the end of the tunnel), I still don't see how you get insufficient.

Assuming that the correct inequalities are -10<x<10 and 10<y<-10, are you saying that since the final inequality can be y<-10<x or x<10<y, therefore insufficient? But wouldn't we say that only x<10<y pertains to the main equation and therefore sufficient?

Hope my question is clear.

\(x^2 < 100\) means that \(|x| < 10\) --> \(-10 < x < 10\) (so x IS less than 10). \(y^2>100\) means that \(|y| > 10\) --> \(y< -10\) or \(y>10\) (so y may be less as well as greater than 10).

For example, if \(x=0\) and \(y=100\), then YES \(x < 10 < y\) but if \(x=0\) and \(y=-100\), then \(x < 10 < y\) dose not hold true.

Re: If x and y are positive, is x < 10 < y? [#permalink]

Show Tags

09 Aug 2015, 11:56

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: If x and y are positive, is x < 10 < y? [#permalink]

Show Tags

19 Apr 2016, 13:16

correct answer is option D statement 1 gives information that as product xy = 100 and x<y , x is less than 10 and y is greater than 10. sufficient statement 2 gives information that |x|<10<|y| but as it is given x<y clearly sufficient

Re: If x and y are positive, is x < 10 < y? [#permalink]

Show Tags

22 May 2016, 14:30

Here we are told both x and y are positive, IS x<10<y?

Before I begin, I say, x could be 9, or .5, or 7.5(if x < 10 < y is true) y could be 10.01 or 100, or 24.5 (if x < 10 < y is true)

So, here we go

1) x<y and xy = 100 since x is less than y, and both x and y are positive, we know that x must be less than 10, and y more then 10 (sufficient) 2) x^2 < 100 < y^2 since x and y are both positive, this is sufficient

D

gmatclubot

Re: If x and y are positive, is x < 10 < y?
[#permalink]
22 May 2016, 14:30

Since my last post, I’ve got the interview decisions for the other two business schools I applied to: Denied by Wharton and Invited to Interview with Stanford. It all...

[rss2posts title=The MBA Manual title_url=https://mbamanual.com/2016/11/22/mba-vs-mim-guest-post/ sub_title=MBA vs. MiM :3qa61fk6]Hey, guys! We have a great guest post by Abhyank Srinet of MiM-Essay . In a quick post and an...

Marketing is one of those functions, that if done successfully, requires a little bit of everything. In other words, it is highly cross-functional and requires a lot of different...