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

 It is currently 18 Oct 2019, 19:06 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.  If x, y, and k are positive integers, is k < 10 ?

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

Hide Tags

Intern  G
Joined: 18 Nov 2013
Posts: 46
If x, y, and k are positive integers, is k < 10 ?  [#permalink]

Show Tags

15 00:00

Difficulty:   95% (hard)

Question Stats: 22% (02:44) correct 78% (02:17) wrong based on 206 sessions

HideShow timer Statistics

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

(1) $$45! = x(10^k)$$

(2) $$y=\sqrt{1.25*10^k}$$

Originally posted by harish1986 on 08 Oct 2018, 08:53.
Last edited by chetan2u on 14 Oct 2018, 18:10, edited 3 times in total.
Renamed the topic, corrected the OA
Math Expert V
Joined: 02 Aug 2009
Posts: 7978
Re: If x, y, and k are positive integers, is k < 10 ?  [#permalink]

Show Tags

4
2
If x, y, and k are positive integers, is k < 10 ?

1. $$45! = x(10^k)$$
Max possible value of k is when x does not have any 10s in it..
So number of 10s in 45! is number of 5s = $$\frac{45}{5}+\frac{45}{25}=9+1=10$$
So if x does not have any 5s then k is 10, otherwise it will be <10
Insufficient

2. y=$$3\sqrt{1.25(10^k)}$$
I believe it is the cube root ..
So $$y^3=1.25*10^k=5^3*10^{k-2}$$
So minimum value of k is 2 or k can be 5,8,11 and so on
Insufficient

Combined k cannot be 10 as per statement II and $$k\leq{10}$$
So k<10
Sufficient

C

Editing the OA as it cannot be A
_________________
General Discussion
Manager  S
Joined: 10 Sep 2015
Posts: 67
Location: India
Concentration: Finance, Human Resources
GMAT 1: 640 Q47 V31 GMAT 2: 660 Q47 V35 GMAT 3: 700 Q49 V36 GPA: 4
Re: If x, y, and k are positive integers, is k < 10 ?  [#permalink]

Show Tags

Hi chetan2u,
I took the statement 2 as 3*(1.25(10k))^-2
and hence i got E. Please confirm if my understanding is incorrect or question is written in a bad format.
GMATH Teacher P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If x, y, and k are positive integers, is k < 10 ?  [#permalink]

Show Tags

harish1986 wrote:
If x, y, and k are positive integers, is k < 10 ?

(1) $$45! = x(10^k)$$

(2) $$y$$ is the cubic root of $$1.25*(10^k)$$

$$x,y,k\,\, \ge 1\,\,\,{\rm{ints}}\,\,\,\left( * \right)$$

$$k\,\,\mathop < \limits^? \,\,10$$

$$\left( 1 \right)\,\,45! = x \cdot {10^k}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,k\,\,\, \le \,\,\,\left\lfloor {{{45} \over 5}} \right\rfloor + \left\lfloor {{{45} \over {25}}} \right\rfloor \, = 10\,\,\,\,\,\left( {**} \right)\,\,$$

$$\left( {**} \right)$$ See my explanation (and notation) here:
https://gmatclub.com/forum/if-n-is-the- ... 75460.html

$$\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {k{\kern 1pt} \,;\,x} \right) = \left( {10\,;\,\,{{45!} \over {{{10}^{10}}}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\,\left( {x = {{45!} \over {{{10}^{10}}}}\,\, \ge 1\,\,{\mathop{\rm int}} \,\,\,{\rm{by}}\,\,\left( {**} \right)} \right)\,\, \hfill \cr \,{\rm{Take}}\,\,\left( {k\,;\,x} \right) = \left( {1\,;\,\,{{45!} \over {10}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,\,\, \hfill \cr} \right.$$

$$\left( 2 \right)\,\,\,y = \root {3\,} \of {{5 \over 4}\left( {{{10}^k}} \right)} \,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,{5 \over 4}\left( {{2^k} \cdot {5^k}} \right) = {2^{k - 2}} \cdot {5^{k + 1}}\,\,\,\,{\rm{positive}}\,\,{\rm{perfect}}\,\,{\rm{cube}}\,\,\,\,\,$$

$$\Rightarrow \,\,\,\,\,\,\left\{ \matrix{ \,k - 2 = {\rm{mult}}\,\,{\rm{of}}\,\,{\rm{3}} \hfill \cr k + 1 = \,\,{\rm{mult}}\,\,{\rm{of}}\,\,3 \hfill \cr} \right.\,\,\,\,\,\,\,\,\left( {k \ge 2} \right)\,\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,k \ge 2\,\,\,\,\,{\rm{divided}}\,\,{\rm{by}}\,\,3\,\,\,{\rm{has}}\,\,{\rm{remainder}}\,\,2\,$$

$$\left\{ \matrix{ \,{\rm{Take}}\,\,k = 2\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,k = 2 + 3 \cdot 3\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\, \hfill \cr} \right.$$

$$\left( {1 + 2} \right)\,\,\,\,\,\left\{ \matrix{ \,k \le 10\,\,\,\,{\rm{by}}\,\,\,\,\left( 1 \right) \cap \left( {**} \right) \hfill \cr \,k \ne 10\,\,\,{\rm{by}}\,\,\left( 2 \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMATH Teacher P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If x, y, and k are positive integers, is k < 10 ?  [#permalink]

Show Tags

P.S.: $$y = 3 \cdot \,\,\root {} \of {{5 \over 4}\left( {{{10}^k}} \right)}$$ cannot be an integer, for any given positive integer $$k$$.

Reason:

$$y = \,\,\sqrt {\,9 \cdot {5 \over 4}\left( {{2^k} \cdot {5^k}} \right)} \,\,\,\, = \,\,\,\,\sqrt {\,{2^{k - 2}} \cdot {3^2} \cdot {5^{k + 1}}} \,\,\,\,\,\,\left( {k \ge 1\,\,\,{\mathop{\rm int}} } \right)\,\,\,$$

$${2^{k - 2}} \cdot {3^2} \cdot {5^{k + 1}}\,\,\,{\rm{perfect}}\,\,{\rm{square}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\{ \matrix{ \,k - 2\,\,\, \ge 0\,\,\,{\rm{even}} \hfill \cr \,k + 1\,\,\, \ge 0\,\,\,{\rm{even}} \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{impossible}}!\,$$

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
SVP  V
Joined: 26 Mar 2013
Posts: 2345
Re: If x, y, and k are positive integers, is k < 10 ?  [#permalink]

Show Tags

chetan2u wrote:
If x, y, and k are positive integers, is k < 10 ?

1. $$45! = x(10^k)$$
Max possible value of k is when x does not have any 10s in it..
So number of 10s in 45! is number of 5s = $$\frac{45}{5}+\frac{45}{25}=9+1=10$$
So if x does not have any 5s then k is 10, otherwise it will be <10
Insufficient

2. y=$$3\sqrt{1.25(10^k)}$$
I believe it is the cube root ..
So $$y^3=1.25*10^k=5^3*10^{k-2}$$
So minimum value of k is 2 or k can be 5,8,11 and so on
Insufficient

Combined k cannot be 10 as per statement II and $$k\leq{10}$$
So k<10
Sufficient

C

Editing the OA as it cannot be A

Can you please re-format statement 2? I does not show cubic root.

Thanks
Math Expert V
Joined: 02 Aug 2009
Posts: 7978
Re: If x, y, and k are positive integers, is k < 10 ?  [#permalink]

Show Tags

asthagupta wrote:
Hi chetan2u,
I took the statement 2 as 3*(1.25(10k))^-2
and hence i got E. Please confirm if my understanding is incorrect or question is written in a bad format.

Yes, you are correct.
It is bad formatting, which I have corrected now.
_________________
Manager  B
Joined: 04 Oct 2017
Posts: 73
Re: If x, y, and k are positive integers, is k < 10 ?  [#permalink]

Show Tags

[quote="chetan2u"]If x, y, and k are positive integers, is k < 10 ?

1. $$45! = x(10^k)$$
Max possible value of k is when x does not have any 10s in it..
So number of 10s in 45! is number of 5s = $$\frac{45}{5}+\frac{45}{25}=9+1=10$$
So if x does not have any 5s then k is 10, otherwise it will be <10
Insufficient

2. y=$$3\sqrt{1.25(10^k)}$$
I believe it is the cube root ..
So $$y^3=1.25*10^k=5^3*10^{k-2}$$
So minimum value of k is 2 or k can be 5,8,11 and so on
Insufficient

Combined k cannot be 10 as per statement II and [m]k\leq{10}[

Hi,

Please explain Number of 10s in 45! is number of 5s. I didnot understand this. Am lost with factorials. I understood the second statement.

Thanks.
Manager  G
Joined: 21 Jun 2017
Posts: 230
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
If x, y, and k are positive integers, is k < 10 ?  [#permalink]

Show Tags

1
Hi Kezia9

I'll try to explain your query.

In order to find number of zeros or 5 in a complex no , following has to be done.

1. list down numbers ending with 5 and 0
With our case in hand , the list will be
5 10 15 20 25 30 35 40 and 45
2. each of these will have one 5 in them.
3. watchout for perfect squares ...25 will have two.

so 1+1+1+1+2+1+1+1+1= 10 5's

PS: Always remember in order to find zeros or number of 5's you don't need to calculate 2's, because they are plenty. Every alternative number will be even hence, we will just find out the limiting 5.

Posted from my mobile device
_________________
Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Dil ye Ziddi hai !!!

GMAT 1 - 620 .... Disappointed for 6 months. Im back Im back. Bhai dera tera COMEBACK !!!
GMATH Teacher P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
If x, y, and k are positive integers, is k < 10 ?  [#permalink]

Show Tags

1
Kezia9 wrote:
Please explain Number of 10s in 45! is number of 5s. I didnot understand this. Am lost with factorials.
Thanks.

Hi, Kezia9!

I have explained this (step-by-step) here:
https://gmatclub.com/forum/if-n-is-the- ... 75460.html

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Manager  B
Joined: 04 Oct 2017
Posts: 73
Re: If x, y, and k are positive integers, is k < 10 ?  [#permalink]

Show Tags

ShankSouljaBoi wrote:
Hi Kezia9

I'll try to explain your query.

In order to find number of zeros or 5 in a complex no , following has to be done.

1. list down numbers ending with 5 and 0
With our case in hand , the list will be
5 10 15 20 25 30 35 40 and 45
2. each of these will have one 5 in them.
3. watchout for perfect squares ...25 will have two.

so 1+1+1+1+2+1+1+1+1= 10 5's

PS: Always remember in order to find zeros or number of 5's you don't need to calculate 2's, because they are plenty. Every alternative number will be even hence, we will just find out the limiting 5.

Posted from my mobile device

Appreciate your efforts to clarify my doubts. THANK YOU.
Manager  B
Joined: 04 Oct 2017
Posts: 73
Re: If x, y, and k are positive integers, is k < 10 ?  [#permalink]

Show Tags

1
fskilnik wrote:
Kezia9 wrote:
Please explain Number of 10s in 45! is number of 5s. I didnot understand this. Am lost with factorials.
Thanks.

Hi, Kezia9!

I have explained this (step-by-step) here:
https://gmatclub.com/forum/if-n-is-the- ... 75460.html

Regards,
Fabio.

Appreciate your efforts to clarify my doubts. THANK YOU. Re: If x, y, and k are positive integers, is k < 10 ?   [#permalink] 15 Oct 2018, 09:37
Display posts from previous: Sort by

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

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

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