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

It is currently 15 Nov 2019, 06:49

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

10^x + 10^y + 10^z = n, where x, y, and z are positive integers. Which

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59073
10^x + 10^y + 10^z = n, where x, y, and z are positive integers. Which  [#permalink]

Show Tags

New post 28 Oct 2018, 23:56
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

29% (02:05) correct 71% (02:02) wrong based on 91 sessions

HideShow timer Statistics

\(10^x + 10^y + 10^z = n\), where x, y, and z are positive integers. Which of the following could be the total number of zeroes, to the left of the decimal point, contained in n?

I. x + y
II. y – z
III. z

A. III only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

_________________
Manager
Manager
User avatar
P
Joined: 09 Jun 2018
Posts: 185
Location: United States
GPA: 3.95
WE: Manufacturing and Production (Energy and Utilities)
GMAT ToolKit User
10^x + 10^y + 10^z = n, where x, y, and z are positive integers. Which  [#permalink]

Show Tags

New post 30 Oct 2018, 13:14
1
Afc0892 wrote:
Since x,y and z are positive integers. min value of x+y is 2. But if x is 1 and y is 1 and z is 2. then n = 120. only 1 zero. cannot be possible.
Statement 1 is not possible.



Statement 1 is also possible. Consider x = 1, y = 1, z = 3.

Then you have 10 + 10 + 1000 = 1020
1020 has 2 zeros to the left of the decimal point, i.e. in the units place and the hundred's place and hence Statement 1 is also possible.

I think the catch is "total" number of zeros. The question does not ask number of zeros until you reach a non-zero number starting from the units digit and going left.

Statement 2 is possible. Consider, x = 1, y = 3, z = 2, hence n = 1110, y-z = 1 is satisfied.

Statement 3 is possible. Consider, x = 3, y = 2, z = 1, hence n = 1110, z = 1 is satisfied.

Hence all three statements are possible.

Option E
_________________
If you found this relevant and useful, please Smash that Kudos button!
NUS School Moderator
avatar
V
Joined: 18 Jul 2018
Posts: 1017
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Reviews Badge
Re: 10^x + 10^y + 10^z = n, where x, y, and z are positive integers. Which  [#permalink]

Show Tags

New post 29 Oct 2018, 01:02
Consider x as 1, y as 3, z as 2. Then n = 1110. the total number of zeros to the left of the decimal point is 1.

Statement 2 is possible as y-z = 3-2 = 1.

Since x,y and z are positive integers. min value of x+y is 2. But if x is 1 and y is 1 and z is 2. then n = 120. only 1 zero. cannot be possible.
Statement 1 is not possible.

If x is 3, y is 2 and z is 1. then n will contain 1 zero. Hence statement 3 is possible.

Only 2 and 3 are possible.

D is the answer.
_________________
Press +1 Kudos If my post helps!
GMAT Club Bot
Re: 10^x + 10^y + 10^z = n, where x, y, and z are positive integers. Which   [#permalink] 29 Oct 2018, 01:02
Display posts from previous: Sort by

10^x + 10^y + 10^z = n, where x, y, and z are positive integers. Which

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





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