GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 19 Feb 2020, 23:24

### 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

# The quantity 3^3 4^4 5^5 6^6 - 3^6 4^5 5^4 6^3 will end in how many

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 61303
The quantity 3^3 4^4 5^5 6^6 - 3^6 4^5 5^4 6^3 will end in how many  [#permalink]

### Show Tags

01 May 2018, 04:55
00:00

Difficulty:

45% (medium)

Question Stats:

66% (02:04) correct 34% (02:09) wrong based on 190 sessions

### HideShow timer Statistics

The quantity $$3^3 4^4 5^5 6^6 - 3^6 4^5 5^4 6^3$$ will end in how many zeros ?

A. 3

B. 4

C. 5

D. 6

E. 9

_________________
Manager
Joined: 28 Nov 2017
Posts: 137
Location: Uzbekistan
Re: The quantity 3^3 4^4 5^5 6^6 - 3^6 4^5 5^4 6^3 will end in how many  [#permalink]

### Show Tags

01 May 2018, 05:14
1
1
Bunuel wrote:
The quantity $$3^3 4^4 5^5 6^6 - 3^6 4^5 5^4 6^3$$ will end in how many zeros ?

A. 3

B. 4

C. 5

D. 6

E. 9

Let's rewrite the expression as follows:
$$3^3*4^4*5^5*6^6 - 3^6*4^5*5^4*6^3 = 3^3*4^4*5^4*6^3*(5*6^3 - 3^3*4)$$

$$3^3*4^4*5^4*6^3$$ will end in $$4$$ zeros.
$$(5*6^3 - 3^3*4)$$ will not end in zero (it will end in $$2$$).

Hence, the expression ends in $$4$$ zeros.

_________________
Kindest Regards!
Tulkin.
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2801
Re: The quantity 3^3 4^4 5^5 6^6 - 3^6 4^5 5^4 6^3 will end in how many  [#permalink]

### Show Tags

02 May 2018, 09:22
1
Bunuel wrote:
The quantity $$3^3 4^4 5^5 6^6 - 3^6 4^5 5^4 6^3$$ will end in how many zeros ?

A. 3

B. 4

C. 5

D. 6

E. 9

Simplifying into primes we have:

3^3 x 2^8 x 5^5 x 2^6 x 3^6 - 3^6 x 2^10 x 5^4 x 2^3 x 3^3

3^9 x 2^14 x 5^5 - 3^9 x 2^13 x 5^4

Factoring out we have:

3^9 x 2^13 x 5^4(1 x 2 x 5 - (1 x 1 x 1))

3^9 x 2^13 x 5^4 x 9

We know that each occurrence of 10 in a factorization yields one trailing zero. Note that a “5 and 2” pair in a factorization is equivalent to a 10. Since we have four “5 and 2” pairs,, we have 4 trailing zeros.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Senior Manager
Joined: 03 Sep 2018
Posts: 255
Location: Netherlands
GPA: 4
Re: The quantity 3^3 4^4 5^5 6^6 - 3^6 4^5 5^4 6^3 will end in how many  [#permalink]

### Show Tags

12 Jan 2019, 08:11
Can we not simply ignore every number that does not produce a trailing zero: $$5^5-5^4=5^4(5-1)$$ $$\implies$$ 4 trailing zeros?
_________________
Good luck to you. Retired from this forum.
Manager
Joined: 22 Sep 2018
Posts: 236
The quantity 3^3 4^4 5^5 6^6 - 3^6 4^5 5^4 6^3 will end in how many  [#permalink]

### Show Tags

21 Jan 2019, 21:19
Bunuel wrote:
The quantity $$3^3 4^4 5^5 6^6 - 3^6 4^5 5^4 6^3$$ will end in how many zeros ?

A. 3

B. 4

C. 5

D. 6

E. 9

My reasoning if it helps anyone:

Break everything into primes, then factor out as much as you can to get rid of the subtraction element of this question.

$$3^9 * (2^{14}) * 5^5 - 3^9 * (2^{13}) * 5^4$$

$$3^9 * (2^{13}) * 5^4 (2*5 - 1)$$

The number of zeros a number will have is determined by how many times you multiply 10 to it.

In the above we can multiply 5*2 to get 10. We have four 5's, so we can create four 10's, hence our answer will have 4 zeros.

EDIT: it's supposed to say 2^14 and 2^13. I'm not sure why the math tag isn't working
Math Expert
Joined: 02 Sep 2009
Posts: 61303
Re: The quantity 3^3 4^4 5^5 6^6 - 3^6 4^5 5^4 6^3 will end in how many  [#permalink]

### Show Tags

21 Jan 2019, 21:58
kchen1994 wrote:
EDIT: it's supposed to say 2^14 and 2^13. I'm not sure why the math tag isn't working

When you have more than one character in exponents, put it in { }: 2^{123} --> $$2^{123}$$
_________________
Senior Manager
Joined: 12 Sep 2017
Posts: 313
Re: The quantity 3^3 4^4 5^5 6^6 - 3^6 4^5 5^4 6^3 will end in how many  [#permalink]

### Show Tags

22 Jan 2019, 15:06
1

As we are searching for the number of 0's then we just have to look for the 2 and 5 pairs.

The limiting factor will be the 5's.

Five 0's - Four 0's

100000 - 10000 = 99..0000.

Hence... B
Intern
Joined: 05 Jan 2019
Posts: 10
Re: The quantity 3^3 4^4 5^5 6^6 - 3^6 4^5 5^4 6^3 will end in how many  [#permalink]

### Show Tags

25 Jan 2019, 13:33
Hello,

How I approached answering this question :

To find: Number of trailing 0's after performing subtraction

Approach: I only looked at 2's and 5's on both the sides

4^4 * 5^5 = 2^8 * 5^5 {this will give me 5 trailing 0's at the end (2^5 * 5^5 - need to consider highest power of 5) }
Similarly, 4^5*5*4 = 2^10*5^4 { this will give me 4 trailing 0's at the end (2^4*5^4)}
so, now I have 100000-10000, this gives me 4 trailing 0's at the end.

Ans: B

Re: The quantity 3^3 4^4 5^5 6^6 - 3^6 4^5 5^4 6^3 will end in how many   [#permalink] 25 Jan 2019, 13:33
Display posts from previous: Sort by