BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
Live EA class + 6 months of EA OnDemand
  • Expert-led weekly online sessions
  • EA Masterclass access between classes
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

130-point score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

P is the product of positive integers 1 through 30. How many consecutive 0’s are ther

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times
by Max@Math Revolution » Mon Jun 15, 2020 2:47 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

[GMAT math practice question]

P is the product of positive integers 1 through 30. How many consecutive 0’s are there in the units digit of P?

A. 4
B. 5
C. 6
D. 7
E. 8
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times

Re: P is the product of positive integers 1 through 30. How many consecutive 0’s are ther

by Max@Math Revolution » Wed Jun 17, 2020 12:52 am
=>

Let P be the product of integers 1 through 30.
Then the prime factorization of P is P = 2^a3^b5^c7^d·…·29.
Define [x] as the greatest integer less than or equal to x.
Then the number of the prime factors of 2 is 26 = 15 + 7 + 3 + 1,
since [30/2] = 15, [30/2^2] = 7, [30/2^3] = 3 and [30/2^4] = 1.
The number of prime factors of 5 is 7 = 6 + 1,
since [30/5] = 6 and [30/5^2] = 1.

Then we have P = 2^26·3b·5^7·7d·…·29 = 2^{7+19}·3b·5^7·7d·…·29 =2^72^19·3b·5^7·7d·…·29 = 2^7·5^7·2^19·3b·7d·…·29 =10^7·2^19·3b·7d·…·29, and P has 7 consecutive zeros in the units digit.

Since we have 10 = 2*5 and more 2’s than 5’s, we can count the number of 5’s only.

Therefore, D is the answer.
Answer: D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8176
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

Re: P is the product of positive integers 1 through 30. How many consecutive 0’s are ther

by Scott@TargetTestPrep » Thu Jun 18, 2020 2:49 pm
Max@Math Revolution wrote: ↑
Mon Jun 15, 2020 2:47 am
 [GMAT math practice question]

P is the product of positive integers 1 through 30. How many consecutive 0’s are there in the units digit of P?

A. 4
B. 5
C. 6
D. 7
E. 8
Solution:

We are assuming the question intended to ask for the greatest number of consecutive 0’s at the end of P.

We see that P = 30! and we are looking for 2-and-5 pairs in 30!. Since there are fewer factors of 5 than 2, we need to determine the number of factors of 5 in 30! (since that is the number of consecutive 0’s at the end of the number P.)

We see that in 30!, the factors 5, 10, 15, 20, and 30 each contributes one factor of 5, whereas 25 contributes two factors of 5. Therefore, the total number of factors of 5 is 5 + 2 = 7. Since there are 7 factors of 5 (and also at least 7 factors of 2), there are 7 consecutive 0’s at the end of the number P.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1