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:

Re: If x, y and z are integers, what is y – z? [#permalink]

Show Tags

21 Jul 2013, 07:41

1

This post received KUDOS

If x, y and z are integers, what is y – z?

(1) \(100^x = 2^y5^z\) \(2^{2x}5^{2x}=2^y5^z\) so \(y-z=2x-2x=0\). Sufficient

(2) \(10^y = 20^x5^{z+1}\) \(2^y5^y=2^{2x}5^x5^{z+1}\) so \(y=2x\) and \(y=x+z+1\). We cannot determine y-z. Consider y=4,x=2 and z=1 so y-z=3; or y=8,x=4 and y=3 so y-z=5. Not sufficient

A _________________

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

Re: If x, y and z are integers, what is y – z? [#permalink]

Show Tags

01 May 2016, 09:54

Bunuel wrote:

vishalrastogi wrote:

I could not get the explanation here, can anybody explain this, please ?

If x, y and z are integers, what is y – z?

(1) \(100^x = 2^y5^z\) --> \(2^{2x}5^{2x}=2^y5^z\) --> equate the exponents: \(2x=y\) and \(2x=z\) --> thus \(2x-2x=y-z=0\). Sufficient.

(2) \(10^y = 20^x5^{z+1}\) --> \(2^y5^y=2^{2x}*5^{x+z+1}\) --> \(y=2x\) and \(y=x+z+1\). We cannot get the value of y-z from this. Not sufficient,

Answer: A.

Hope it's clear.

How can 1 be sufficient??? In the given statement, its 5 raise to the power 2. And the solution you have provided considers it as 5 raise to the power z.

I could not get the explanation here, can anybody explain this, please ?

If x, y and z are integers, what is y – z?

(1) \(100^x = 2^y5^z\) --> \(2^{2x}5^{2x}=2^y5^z\) --> equate the exponents: \(2x=y\) and \(2x=z\) --> thus \(2x-2x=y-z=0\). Sufficient.

(2) \(10^y = 20^x5^{z+1}\) --> \(2^y5^y=2^{2x}*5^{x+z+1}\) --> \(y=2x\) and \(y=x+z+1\). We cannot get the value of y-z from this. Not sufficient,

Answer: A.

Hope it's clear.

How can 1 be sufficient??? In the given statement, its 5 raise to the power 2. And the solution you have provided considers it as 5 raise to the power z.

It's 5^z both in the question and in the solution.
_________________

Re: If x, y and z are integers, what is y – z? [#permalink]

Show Tags

02 May 2016, 15:58

I think what's confusing some folks is the second equation is giving y = x+z+1 bringing z to the left side. y-z = x+1. This still doesn't give a value for y-z. Question is asking for a value for y-z and not if you can deduce an expression for y-z. I made this silly mistake once in the heat of the moment so sharing it here.
_________________

Re: If x, y and z are integers, what is y – z? [#permalink]

Show Tags

17 Nov 2016, 17:58

Bunuel wrote:

vishalrastogi wrote:

I could not get the explanation here, can anybody explain this, please ?

If x, y and z are integers, what is y – z?

(1) \(100^x = 2^y5^z\) --> \(2^{2x}5^{2x}=2^y5^z\) --> equate the exponents: \(2x=y\) and \(2x=z\) --> thus \(2x-2x=y-z=0\). Sufficient.

Answer: A.

Hope it's clear.

If y-z=0, then y=z. If i put the value of y=z, how can we legitimate the statement 1? statement 1: \(100^x = 2^y5^z\) \(2^{2x}5^{2x}=2^z5^z\) To legitimate the statement 1 we still need the value of x and z. But, they are still unknown here. How can you make known it for all? Then, how can we conclude it? Bunuel Thank you...
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow

I could not get the explanation here, can anybody explain this, please ?

If x, y and z are integers, what is y – z?

(1) \(100^x = 2^y5^z\) --> \(2^{2x}5^{2x}=2^y5^z\) --> equate the exponents: \(2x=y\) and \(2x=z\) --> thus \(2x-2x=y-z=0\). Sufficient.

Answer: A.

Hope it's clear.

If y-z=0, then y=z. If i put the value of y=z, how can we legitimate the statement 1? statement 1: \(100^x = 2^y5^z\) \(2^{2x}5^{2x}=2^z5^z\) To legitimate the statement 1 we still need the value of x and z. But, they are still unknown here. How can you make known it for all? Then, how can we conclude it? Bunuel Thank you...

The question asks the value of y - z, not the individual value of x, y, and z. From the solution we got that y - z = 0.
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow

x, y, and z are given to be integers. We have \(2^{2x}5^{2x}=2^y5^z\) --> equate the exponents of 2 and 5: \(2x=y\) and \(2x=z\). Thus 2x = y = z.
_________________

x, y, and z are given to be integers. We have \(2^{2x}5^{2x}=2^y5^z\) --> equate the exponents of 2 and 5: \(2x=y\) and \(2x=z\). Thus 2x = y = z.

This is the first time i learn that i can equate the exponent after having multiple variables on both side. I, normally, equate the exponent when i have only one part in the right hand side and the other one in the left hand side. like below... 2^{2x}=2^y --> 2x=y it is ok. But when it is something like below then it is the first time i learn. \(2^{2x}5^{2x}=2^y5^z\) \(2x=y\) and \(2x=z\). Anyway, many many thanks with 'kudos'
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow

x, y, and z are given to be integers. We have \(2^{2x}5^{2x}=2^y5^z\) --> equate the exponents of 2 and 5: \(2x=y\) and \(2x=z\). Thus 2x = y = z.

This is the first time i learn that i can equate the exponent after having multiple variables on both side. I, normally, equate the exponent when i have only one part in the right hand side and the other one in the left hand side. like below... 2^{2x}=2^y --> 2x=y it is ok. But when it is something like below then it is the first time i learn. \(2^{2x}5^{2x}=2^y5^z\) \(2x=y\) and \(2x=z\). Anyway, many many thanks with 'kudos'

We can only do this here because we know that x, y, and z are integers.
_________________

Re: If x, y and z are integers, what is y – z? [#permalink]

Show Tags

20 Nov 2016, 02:30

Bunuel wrote:

iMyself wrote:

Bunuel wrote:

x, y, and z are given to be integers. We have \(2^{2x}5^{2x}=2^y5^z\) --> equate the exponents of 2 and 5: \(2x=y\) and \(2x=z\). Thus 2x = y = z.

This is the first time i learn that i can equate the exponent after having multiple variables on both side. I, normally, equate the exponent when i have only one part in the right hand side and the other one in the left hand side. like below... 2^{2x}=2^y --> 2x=y it is ok. But when it is something like below then it is the first time i learn. \(2^{2x}5^{2x}=2^y5^z\) \(2x=y\) and \(2x=z\). Anyway, many many thanks with 'kudos'

We can only do this here because we know that x, y, and z are integers.

That means: we can't equate this type of things if the variable is NOT integer, right Bunuel?
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow

Re: If x, y and z are integers, what is y – z? [#permalink]

Show Tags

20 Nov 2016, 02:40

Bunuel wrote:

iMyself wrote:

That means: we can't equate this type of things if the variable is NOT integer, right Bunuel?

_______________________ Yes...

Thank you Brother with kudos!
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow

Re: If x, y and z are integers, what is y – z? [#permalink]

Show Tags

29 Nov 2016, 15:33

kingflo wrote:

If x, y and z are integers, what is y – z?

(1) \(100^x = 2^y5^z\)

(2) \(10^y = 20^x5^{z+1}\)

We need to determine the value of y – z.

Statement One Alone:

100^x = 2^y * 5^z

Notice that 100^x = (2^2 * 5^2)^x = 2^(2x) * 5^(2x). Equate this with 2^y * 5^z and we have:

2^(2x) * 5^(2x) = 2^y * 5^z

Therefore, 2^(2x) = 2^y and 5^(2x) = 5^z.

Thus, 2x = y and 2x = z. Therefore, y - z = 2x - 2x = 0.

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

10^y = 20^x * 5^(z+1)

Since 20^x = (2^2 * 5)^x = 2^(2x) * 5^x, that means 20^x * 5^(z+1) = 2^(2x) * 5^x * 5^(z+1) = 2^(2x) * 5^(x+z+1). Notice that 10^y = (2 * 5)^y = 2^y * 5^y, so we have:

2^y * 5^y = 2^(2x) * 5^(x+z+1)

Therefore, 2^y = 2^(2x) and 5^y = 5^(x+z+1).

Thus, y = 2x and y = x + z + 1. From the second equation, we have y - z = x + 1. However, since we do not know the value of x, we cannot determine the value of y - z. Statement two alone is not sufficient to answer the question.

Answer: A
_________________

Jeffrey Miller Scott Woodbury-Stewart Founder and CEO

gmatclubot

Re: If x, y and z are integers, what is y – z?
[#permalink]
29 Nov 2016, 15:33

Campus visits play a crucial role in the MBA application process. It’s one thing to be passionate about one school but another to actually visit the campus, talk...

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Marty Cagan is founding partner of the Silicon Valley Product Group, a consulting firm that helps companies with their product strategy. Prior to that he held product roles at...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...