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

 It is currently 17 Oct 2019, 06:59 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  x is an integer and x raised to any odd integer is greater

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Director  Joined: 25 Aug 2007
Posts: 673
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
x is an integer and x raised to any odd integer is greater  [#permalink]

Show Tags

6
74 00:00

Difficulty:   95% (hard)

Question Stats: 41% (03:00) correct 59% (03:02) wrong based on 844 sessions

HideShow timer Statistics

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

_________________

Originally posted by ykaiim on 08 Jun 2010, 01:14.
Last edited by Bunuel on 20 May 2012, 11:57, edited 3 times in total.
Edited the question and added the OA
Math Expert V
Joined: 02 Sep 2009
Posts: 58411
Re: DS problem  [#permalink]

Show Tags

12
7
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 = 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.

_________________
General Discussion
Intern  Joined: 12 Feb 2011
Posts: 4
Schools: ISB,Haas,Carnegie,Ross
Re: Is w - z greater than 5 times the quantity 7^x-1 - 5^x  [#permalink]

Show Tags

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?
Intern  Joined: 10 Apr 2012
Posts: 25
Location: India
GMAT 1: 700 Q50 V34 WE: Consulting (Internet and New Media)
Re: Is w - z greater than 5 times the quantity 7^x-1 - 5^x  [#permalink]

Show Tags

1
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:

7^x - z > 5.7^x-1 - 5^(x+1),

Board of Directors D
Joined: 01 Sep 2010
Posts: 3397
Re: Is w - z greater than 5 times the quantity 7^x-1 - 5^x  [#permalink]

Show Tags

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.

2) insufficient

A is the answer.
_________________
Intern  Status: Free Bird
Joined: 23 May 2012
Posts: 26
Location: India
Concentration: General Management, Social Entrepreneurship
GMAT 1: 760 Q50 V44 GPA: 3.2
WE: Project Management (Computer Software)
Re: Is w - z greater than 5 times the quantity 7^x-1 - 5^x  [#permalink]

Show Tags

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 ?
Math Expert V
Joined: 02 Sep 2009
Posts: 58411
Re: Is w - z greater than 5 times the quantity 7^x-1 - 5^x  [#permalink]

Show Tags

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.

Hope it's clear.
_________________
Intern  Status: Free Bird
Joined: 23 May 2012
Posts: 26
Location: India
Concentration: General Management, Social Entrepreneurship
GMAT 1: 760 Q50 V44 GPA: 3.2
WE: Project Management (Computer Software)
Re: Is w - z greater than 5 times the quantity 7^x-1 - 5^x  [#permalink]

Show Tags

Thanks, I misunderstood the question. I thought it was odd int raised to the power x. It is clear now.
Intern  Joined: 20 Jun 2011
Posts: 43
Re: DS problem  [#permalink]

Show Tags

Bunuel wrote:
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 = 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.

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?
Intern  Joined: 20 Apr 2013
Posts: 19
Concentration: Finance, Finance
GMAT Date: 06-03-2013
GPA: 3.3
WE: Accounting (Accounting)
Re: DS problem  [#permalink]

Show Tags

Bunuel wrote:
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 = 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.

Please explain why the lowest value of X is 1.
Math Expert V
Joined: 02 Sep 2009
Posts: 58411
Re: DS problem  [#permalink]

Show Tags

1
Rajkiranmareedu wrote:
Bunuel wrote:
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 = 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.

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.

Hope it's clear.
_________________
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: x is an integer and x raised to any odd integer is greater  [#permalink]

Show Tags

2
3
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.

_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern  Joined: 13 Apr 2014
Posts: 11
Re: x is an integer and x raised to any odd integer is greater  [#permalink]

Show Tags

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:

7^x - z > 5.7^x-1 - 5^(x+1),

tnx for this
_________________
best for iranian
Intern  Joined: 13 Jan 2015
Posts: 3
Location: United States
Concentration: Finance, General Management
WE: Project Management (Commercial Banking)
Re: x is an integer and x raised to any odd integer is greater  [#permalink]

Show Tags

x raised to any odd integer is greater than 0 --> x = integer >0 --> x>=1

(1) --> w-z > 7^x - 5^2 = 7.7^(x-1) - 5^2 > 5.7^(x-1) - 5^2

in order to w-z> 5.7^(x-1) - 5^(x+1), x+1 >=2 --> x >=1 --> sufficient.

(2) insufficient

=> A.
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4006
Re: x is an integer and x raised to any odd integer is greater  [#permalink]

Show Tags

Top Contributor
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

Given: x is an integer and x raised to any odd integer is greater than zero
KEY CONCEPT: A number raised to an ODD power retains its sign.
That is, POSITIVE^ODD = POSITIVE and NEGATIVE^ODD = NEGATIVE
The given info tells us that x^ ODD = POSITIVE
So, it must be the case that x is a POSITIVE integer

Target question: Is w - z > 5[7^(x-1) - 5^x?]
Let's tidy the target question by expanding the right side of the inequality to get....
REPHRASED target question: Is w - z > 5[7^(x-1)] - 5^(x+1)?

Statement 1: z < 25 and w = 7^x
Take the REPHRASED target question and replace w with 7^x to get:
Is 7^x - z > 5[7^(x-1)] - 5^(x+1)?

IMPORTANT: Notice that, on the left side of the inequality, we're subtracting z
We're told that z < 25
So, we can help MINIMIZE the value of the left side by making z as big as possible
So, let's make z = 25 (aside: we could make z equal something really close to 25, like 24.99999999999, but let's make things easy on ourselves and make z EQUAL 25.
We get: Is 7^x - 25 > 5[7^(x-1)] - 5^(x+1)?

Now let's get like terms on the same side of the inequality.
First subtract 5[7^(x-1)] from both sides to get: Is 7^x - 5[7^(x-1)] - 25 > -5^(x+1)?
Then add 25 to both sides to get: Is 7^x - 5[7^(x-1)] > 25 - 5^(x+1)?
Factor 7^(x-1) from left side to get: Is 7^(x-1)[7 - 5] > 25 - 5^(x+1)?
Simplify left side to get: Is 7^(x-1) > 25 - 5^(x+1)?

Now recognize that 7^(x-1) will be POSITIVE for all values of x.
So, 7^(x-1) must be POSITIVE

Now recognize that since x is a POSITIVE integer, 5^(x+1) must be greater than or equal to 25 (since x = 1, is the smallest possible value of x)
So, 25 - 5^(x+1) must be less than or equal to zero.

So, our question becomes Is some POSITIVE number > some number that's less than or equal to zero?
The answer to this REPHRASED target question is a definitive YES
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = 4
Since we have no information about z or w, we cannot answer the REPHRASED target question with certainty.
So, statement 2 is NOT SUFFICIENT

Cheers,
Brent
_________________
Manager  S
Joined: 15 Dec 2016
Posts: 101
x is an integer and x raised to any odd integer is greater  [#permalink]

Show Tags

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.

Hi Karishma,

For this problem, you essentially tried to find if the LHS is ALWAYS greater than the RHS (if you could say Yes, with the information given in S1, you are THEN ONLY saying S1 is sufficient)

For that you minimized the LHS as much as possible which is why x = 1 and z = 25

I understood that part

HOWEVER

My question is

Should you not also check the opposite, i.e. ?

You need to also check if the LHS is ALWAYS lower than the RHS (if you could say Yes, with the information given in S1, you could THEN ONLY also S1 is sufficient as well)

For this new scenario, one would have to maximize the LHS...

Why isn't this scenario part of your calculations

Thank you ! x is an integer and x raised to any odd integer is greater   [#permalink] 25 Jun 2019, 13:14
Display posts from previous: Sort by

x is an integer and x raised to any odd integer is greater

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  