How many positive integers less than 10,000

Expert replies

sachin_yadav: Master | Next Rank: 500 Posts; Posts: 212; Joined: Mon Dec 06, 2010 12:52 amFollowed by: 1 member; Location: India; Thanked: 5 times

by sachin_yadav » Tue Jan 05, 2016 1:27 pm

How many positive integers less than 10,000 are such that the product of their digits is 30?

A. 12
B. 24
C. 36
D. 38
E. 50

OA is E

Please share your approach

Never surrender

Like this post

Source: Beat The GMAT — Problem Solving | Tue Jan 05, 2016 1:27 pm

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Tue Jan 05, 2016 1:46 pm

sachin_yadav wrote:How many positive integers less than 10,000 are such that the product of their digits is 30?

A. 12
B. 24
C. 36
D. 38
E. 50

OA is E

Please share your approach

First, let's lay out the ways we can multiply several positive digits (numbers between 1 and 9) to get 30. (Because the number must be less than 10,000, we know that we want fewer than five digits.)

6 * 5 * 1 will work --> There are 6 ways we can arrange these 3 digits. (Any of the 3 numbers can be in the hundreds place. Any of the 2 remaining numbers can be in the tens place. And the remaining number must be in the units place: 3*2*1 = 6)

3*2*1*5 will work --> There are 24 ways we can arrange these 4 digits: 4*3*2*1 = 24

6*5*1*1 will work ---> There are 12 ways we can arrange these 4 digits. (If all 4 digits are different, there are 24 arrangements. But swapping the 1's will not result in unique numbers, so we need to divide by two to account for the fact that the two 1's are interchangeable.)

6*5 will work ---> 2 ways to arrange these 2 digits

2*3*5 will work ---> 6 ways (3*2*1) to arrange there 3 digits

Now add up the numbers in red: 6 + 24 + 12 + 2 + 6 = 50

Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Jan 05, 2016 2:48 pm

Here's a similar question to practice with: https://www.beatthegmat.com/positive-int ... 83442.html

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Jan 08, 2016 12:59 pm

Casework (as David showed) is probably the best way; this is an approach that is very common for GMAT-level combinatorics questions.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review