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

 It is currently 21 Feb 2019, 14:37

### 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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

# For integers x, y, and z, if (3^x) (4^y) (5^z) = 3,276,800,0

Author Message
TAGS:

### Hide Tags

Manager
Joined: 12 Dec 2012
Posts: 217
GMAT 1: 540 Q36 V28
GMAT 2: 550 Q39 V27
GMAT 3: 620 Q42 V33
GPA: 2.82
WE: Human Resources (Health Care)
For integers x, y, and z, if (3^x) (4^y) (5^z) = 3,276,800,0  [#permalink]

### Show Tags

Updated on: 17 Mar 2013, 00:05
11
00:00

Difficulty:

55% (hard)

Question Stats:

68% (02:30) correct 32% (02:47) wrong based on 191 sessions

### HideShow timer Statistics

For integers x, y, and z, if (3^x) (4^y) (5^z) = 3,276,800,000 and x + y + z = 15, what is the value of xy/z?

(A) undefined
(B) 0
(C) 3
(D) 5
(E) 15

http://www.veritasprep.com/blog/2010/09 ... -opponent/

_________________

My RC Recipe
http://gmatclub.com/forum/the-rc-recipe-149577.html

My Problem Takeaway Template
http://gmatclub.com/forum/the-simplest-problem-takeaway-template-150646.html

Originally posted by TheNona on 16 Mar 2013, 09:01.
Last edited by Bunuel on 17 Mar 2013, 00:05, edited 1 time in total.
Renamed the topic and edited the question.
SVP
Joined: 24 Jul 2011
Posts: 1530
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740

### Show Tags

16 Mar 2013, 09:27
2
2
3,276,800,000 = 32,768 x 100,000 = 2^15 x 100,000 = 2^15 x 5^5 x 2^5 = 2^20 x 5^5

Therefore x =0, y =10, z = 5

xy/z = 0

The answer is B. Although this detailed explanation has been provided, you can straightaway reach the answer by realizing that x=0 since the large number given does not have 3 as a factor, and so xy/z has to be 0.
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Manager
Joined: 12 Dec 2012
Posts: 217
GMAT 1: 540 Q36 V28
GMAT 2: 550 Q39 V27
GMAT 3: 620 Q42 V33
GPA: 2.82
WE: Human Resources (Health Care)

### Show Tags

16 Mar 2013, 10:22
GyanOne wrote:
3,276,800,000 = 32,768 x 100,000 = 2^15 x 100,000 = 2^15 x 5^5 x 2^5 = 2^20 x 5^5

Therefore x =0, y =10, z = 5

xy/z = 0

The answer is B. Although this detailed explanation has been provided, you can straightaway reach the answer by realizing that x=0 since the large number given does not have 3 as a factor, and so xy/z has to be 0.

Thanks but how did you get that the big number = 2^15? and why the absence of 3 from the factors would lead the fraction to be = zero?
_________________

My RC Recipe
http://gmatclub.com/forum/the-rc-recipe-149577.html

My Problem Takeaway Template
http://gmatclub.com/forum/the-simplest-problem-takeaway-template-150646.html

Intern
Joined: 03 Sep 2011
Posts: 17

### Show Tags

16 Mar 2013, 14:02
1
If we know that 3,276,800,000 is not divisible by 3 (which by the way you can quickly test by adding the digits of the number together and seeing whether they are divisble by 3) , this implies that when it is expressed in the form (3^x) (4^y) (5^z) the x=0. Hence xy/z =0
Concerning the 2^15, either you know the powers of 2 or you don't. This one is indeed very high so it seems unlikely to know it by heart. But if you divide 32768 by 8 for example you land on 4096 (which is 2^12) so you eventually figure out that it's 2^15. But again, this was not necessary in order to solve the question.
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1431
Location: India
Re: For integers x, y, and z, if (3^x) (4^y) (5^z) = 3,276,800,0  [#permalink]

### Show Tags

07 Sep 2013, 12:48
'x' is the easiest to check here.. just add the digits of the number, sum is 26, thus this is not a multiple of 3.. since 'x' is an integer it must be '0'..
now neither of 'y' or 'z' could be '0' because just by looking we see that this number has trailing zeroes so it must have both 2 and 5...

so simply since 'x' is '0' the given solution is '0'. Hence B
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1820
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: For integers x, y, and z, if (3^x) (4^y) (5^z) = 3,276,800,0  [#permalink]

### Show Tags

26 Feb 2014, 20:44
1
Jut observe the RHS, 3,276,800,000 can be written as 32768 x 100000

32768 is not divisible by 3, so x = 0

xy/z = 0 = Answer = B; no need to calculate the rest
_________________

Kindly press "+1 Kudos" to appreciate

VP
Joined: 09 Mar 2018
Posts: 1001
Location: India
For integers x, y, and z, if (3^x) (4^y) (5^z) = 3,276,800,0  [#permalink]

### Show Tags

26 Jan 2019, 19:52
TheNona wrote:
For integers x, y, and z, if (3^x) (4^y) (5^z) = 3,276,800,000 and x + y + z = 15, what is the value of xy/z?

(A) undefined
(B) 0
(C) 3
(D) 5
(E) 15

http://www.veritasprep.com/blog/2010/09 ... -opponent/

$$2^{10} = 1024$$, you can remember this, multiply 5 more times with 2, you will get the value as 32768

$$(3^x) (2^{2y}) (5^z)$$ and there are 5 zero's, this can be written as $$(2*5)^5$$, After this just compare LHS and RHS

x + y + z = 15, This will translate into 0 + 10 + 5

0*10/5

B
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

For integers x, y, and z, if (3^x) (4^y) (5^z) = 3,276,800,0   [#permalink] 26 Jan 2019, 19:52
Display posts from previous: Sort by