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:

x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity \(7^x^-^1 - 5^x\)?

1) z < 25 and w = 7x 2) x = 4

Note: The above expression is 7^(x-1) -5^x.

I guess statement (1) should be: \(z<25\) and \(w=7^x\).

"x is an integer and x raised to any odd integer is greater than zero" means \(x=integer>0\). Q: is \(w-z>5(7^{x-1}-5^x)\)?

(1) \(z<25\) and \(w=7^x\) --> is \(7^x-z>5(7^{x-1}-5^x)\)? --> is \(7^x-z>5*7^{x-1}-5^{x+1}\)? --> is \(7^x-5*7^{x-1}+5^{x+1}>z\)? --> as the lowest value of \(x\) is 1, then the lowest value of LHS is when \(x=1\): \(LHS_{min}=7^x-5*7^{x-1}+5^{x+1}=7-5+25=27\) --> so the lowest value of LHS is 27, which is more than \(z\) as \(z<25\) --> hence \(7^x-5*7^{x-1}+5^{x+1}>z\) is true. Sufficient.

(2) \(x = 4\). No info about \(w\) and \(z\). Not sufficient.

Re: Is w - z greater than 5 times the quantity 7^x-1 - 5^x [#permalink]

Show Tags

20 May 2012, 09:33

Could you please reply with the detailed explanation for the above question. i am confused as to how just Statement I is sufficient to answer the question(A), without knowing the value of X?

Re: Is w - z greater than 5 times the quantity 7^x-1 - 5^x [#permalink]

Show Tags

20 May 2012, 09:52

1

This post received KUDOS

Hello, let me try and explain.

paraphrasing the questions gives us, is w-z > 5.7^(x-1) - 5^(x+1). Further, x is a positive integer as an odd power of x is greater than 0.

taking statement 1, you have the question as 7^x-z > 5.7^(x-1) - 5^(x+1)

Now, for all cases where x is a positive integer, 7^x would be greater than 5.7^(x-1). Next, 5^(x+1) would always be >= 25 as the least value of x can be 1.

So, 7^x > 5.7^x-1 and z < 5^(x+1). Reversing this inequality and adding both the inequalities, we get:

Re: Is w - z greater than 5 times the quantity 7^x-1 - 5^x [#permalink]

Show Tags

20 May 2012, 10:21

Expert's post

the question is not simple but if you think a bit abstract and test number you can arrive to the solution.

The FIRST important thing, breaking the problem, is to understand tha our X is positive. Infact, if a number raised to power of 3 is >0 that means X itself is positive because the odd powr maintain the original sign of the number, so X must be positive.

At this point using the exponent rules we have w - z > 5*7^x-1 - 5^x+1 ----> 7^x - 24 (from stem x<25) > 5*7^x-1 - 5^x+1

testing number 1 ------> 7 -24 > 1 - 25 ---> - 17 > -24 this is TRUE. also if you test some value < 25 positive but also negative the result is the same.

1) sufficient

x = 4 -------> w - z > 5*7^3 - 5^5..........at this point you know nothing about w and z.

Re: Is w - z greater than 5 times the quantity 7^x-1 - 5^x [#permalink]

Show Tags

03 Jun 2012, 01:27

Bunuel wrote:

carcass wrote:

x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^x-1 - 5^x?

1 z < 25 and w = 7^x 2 x = 4

Merging similar topics. Please ask if anything remains unclear.

why can't x be zero apart from even ? any odd number raised to the power zero is 1 which is an interger greater than zero. I think x is given as an interger and not only positive integer. if you work with x = 0 , statement 1 is not sufficient ?

Re: Is w - z greater than 5 times the quantity 7^x-1 - 5^x [#permalink]

Show Tags

03 Jun 2012, 02:38

Expert's post

Kaps07 wrote:

Bunuel wrote:

carcass wrote:

x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^x-1 - 5^x?

1 z < 25 and w = 7^x 2 x = 4

Merging similar topics. Please ask if anything remains unclear.

why can't x be zero apart from even ? any odd number raised to the power zero is 1 which is an interger greater than zero. I think x is given as an interger and not only positive integer. if you work with x = 0 , statement 1 is not sufficient ?

We are told that integer x raised to to any odd integer is greater than zero: \(x^{odd}>0\). Now, if \(x=0\) then \(x^{odd}=0^{odd}=0\) (for odd>0), which violates given condition, so \(x\) cannot be zero.

x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity \(7^x^-^1 - 5^x\)?

1) z < 25 and w = 7x 2) x = 4

Note: The above expression is 7^(x-1) -5^x.

I guess statement (1) should be: \(z<25\) and \(w=7^x\).

"x is an integer and x raised to any odd integer is greater than zero" means \(x=integer>0\). Q: is \(w-z>5(7^{x-1}-5^x)\)?

(1) \(z<25\) and \(w=7^x\) --> is \(7^x-z>5(7^{x-1}-5^x)\)? --> is \(7^x-z>5*7^{x-1}-5^{x+1}\)? --> is \(7^x-5*7^{x-1}+5^{x+1}>z\)? --> as the lowest value of \(x\) is 1, then the lowest value of LHS is when \(x=1\): \(LHS_{min}=7^x-5*7^{x-1}+5^{x+1}=7-5+25=27\) --> so the lowest value of LHS is 27, which is more than \(z\) as \(z<25\) --> hence \(7^x-5*7^{x-1}+5^{x+1}>z\) is true. Sufficient.

(2) \(x = 4\). No info about \(w\) and \(z\). Not sufficient.

Answer: A.

I don't understand the function of statement z<25. If lowest value of LHS is 27 which is more than z, then it doesn't fulfill the condition given?

x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity \(7^x^-^1 - 5^x\)?

1) z < 25 and w = 7x 2) x = 4

Note: The above expression is 7^(x-1) -5^x.

I guess statement (1) should be: \(z<25\) and \(w=7^x\).

"x is an integer and x raised to any odd integer is greater than zero" means \(x=integer>0\). Q: is \(w-z>5(7^{x-1}-5^x)\)?

(1) \(z<25\) and \(w=7^x\) --> is \(7^x-z>5(7^{x-1}-5^x)\)? --> is \(7^x-z>5*7^{x-1}-5^{x+1}\)? --> is \(7^x-5*7^{x-1}+5^{x+1}>z\)? --> as the lowest value of \(x\) is 1, then the lowest value of LHS is when \(x=1\): \(LHS_{min}=7^x-5*7^{x-1}+5^{x+1}=7-5+25=27\) --> so the lowest value of LHS is 27, which is more than \(z\) as \(z<25\) --> hence \(7^x-5*7^{x-1}+5^{x+1}>z\) is true. Sufficient.

(2) \(x = 4\). No info about \(w\) and \(z\). Not sufficient.

x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity \(7^x^-^1 - 5^x\)?

1) z < 25 and w = 7x 2) x = 4

Note: The above expression is 7^(x-1) -5^x.

I guess statement (1) should be: \(z<25\) and \(w=7^x\).

"x is an integer and x raised to any odd integer is greater than zero" means \(x=integer>0\). Q: is \(w-z>5(7^{x-1}-5^x)\)?

(1) \(z<25\) and \(w=7^x\) --> is \(7^x-z>5(7^{x-1}-5^x)\)? --> is \(7^x-z>5*7^{x-1}-5^{x+1}\)? --> is \(7^x-5*7^{x-1}+5^{x+1}>z\)? --> as the lowest value of \(x\) is 1, then the lowest value of LHS is when \(x=1\): \(LHS_{min}=7^x-5*7^{x-1}+5^{x+1}=7-5+25=27\) --> so the lowest value of LHS is 27, which is more than \(z\) as \(z<25\) --> hence \(7^x-5*7^{x-1}+5^{x+1}>z\) is true. Sufficient.

(2) \(x = 4\). No info about \(w\) and \(z\). Not sufficient.

Answer: A.

Please explain why the lowest value of X is 1.

See the highlighted part: x is an integer and x raised to any odd integer is greater than zero means that x is a positive integer, thus its lowest possible value is 1.

Re: x is an integer and x raised to any odd integer is greater [#permalink]

Show Tags

16 Jun 2013, 21:48

1

This post received KUDOS

Expert's post

ykaiim wrote:

x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^(x-1)-5^x?

(1) z < 25 and w=7^x (2) x = 4

Responding to a pm:

What is the meaning of: x is an integer and x raised to any odd integer is greater than zero? It is just a convoluted way of saying 'x is a positive integer'. Since x raised to any odd power is positive, x must be positive. x can take values 1, 2, 3, 4 and so on.

Question: Is \(w - z > 5*7^{x-1}-5^{x+1}\)

Using statement 1: Is \(7^x - 25 > 5*7^{x-1} - 5^{x+1}\)

Even though we are given that z is less than 25, let's assume it to be 25. In case we can prove that left hand side is greater than right hand side for z = 25, we can prove that left hand side will remain greater than right hand side for any other value of z. If z has a smaller value, say 9, left had side will become even larger (since a smaller number will be subtracted) than the right hand side.

Now note that \(7^x\) will be greater than \(5*7^{x - 1}\) since \(7^x\) can be written as \(7*7^{x - 1}\) (x is a positive integer). Also note that minimum value of x is 1 so \(5^{x + 1}\) will always be equal to or larger than 25 (x is a positive integer).

So comparing the left and right hand side expressions, \(7^x\) is greater than \(5*7^{x - 1}\) and 25 is less than or equal to \(5^{x+1}\). So left hand side must be greater than the right hand side in all cases when x is a positive integer.

Re: x is an integer and x raised to any odd integer is greater [#permalink]

Show Tags

05 May 2014, 04:24

paraphrasing the questions gives us, is w-z > 5.7^(x-1) - 5^(x+1). Further, x is a positive integer as an odd power of x is greater than 0.

taking statement 1, you have the question as 7^x-z > 5.7^(x-1) - 5^(x+1)

Now, for all cases where x is a positive integer, 7^x would be greater than 5.7^(x-1). Next, 5^(x+1) would always be >= 25 as the least value of x can be 1.

So, 7^x > 5.7^x-1 and z < 5^(x+1). Reversing this inequality and adding both the inequalities, we get:

Re: x is an integer and x raised to any odd integer is greater [#permalink]

Show Tags

26 Jun 2015, 02:04

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. _________________

So, my final tally is in. I applied to three b schools in total this season: INSEAD – admitted MIT Sloan – admitted Wharton – waitlisted and dinged No...

A few weeks ago, the following tweet popped up in my timeline. thanks @Uber_Mumbai for showing me what #daylightrobbery means!I know I have a choice not to use it...

“This elective will be most relevant to learn innovative methodologies in digital marketing in a place which is the origin for major marketing companies.” This was the crux...