Last visit was: 14 Jul 2025, 15:39 It is currently 14 Jul 2025, 15:39
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Jul 2025
Posts: 102,570
Own Kudos:
Given Kudos: 98,182
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,570
Kudos: 741,408
 [14]
2
Kudos
Add Kudos
12
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Jul 2025
Posts: 102,570
Own Kudos:
741,408
 [1]
Given Kudos: 98,182
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,570
Kudos: 741,408
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
General Discussion
User avatar
cs15811581
Joined: 08 Aug 2021
Last visit: 23 Dec 2021
Posts: 31
Own Kudos:
120
 [2]
Given Kudos: 3
Location: India
Posts: 31
Kudos: 120
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 14 Jul 2025
Posts: 11,294
Own Kudos:
41,743
 [2]
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert
Expert reply
Posts: 11,294
Kudos: 41,743
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If x is a two-digit positive odd integer, is (x - 7)(x - 5)(x - 3)(x - 1) divisible by 1920?

(1) x + 7 is a factor of 150

(2) x + 17 is actor of 120

Great question Bunuel


We can say that whatever be the value of x, the terms (x - 7), (x - 5), (x - 3) and (x - 1) are 4 consecutive even integers as x is odd.
Now, we will surely have one of the four consecutive evens to be a multiple of 8, one of 4 and other two of 2.
We could even have multiple of 16, 32 but we are looking at the least possible 2s in the product.

For example 22, 24, 26, 28: 22 and 26 are multiple of 2 only, while 24 is multiple of 8 and 28, a multiple of 4.

Thus the product of these four consecutive evens will be a multiple of 2*2*4*8 or \(2^7\). Also one of them will surely be a multiple of 3.

For, this product to be a multiple of 1920, the product should be divisible by all factors of 1920 => \(1920=2^7*3*5\)

Product is divisible by \(2^7*3\)

Now, let us check for divisibility by 5: the units digit should be 5 or 0, since we are looking at even, the units digit should be 0.

If x ends with 7, 5, 3 or 1, then (x - 7), (x - 5), (x - 3) or (x - 1) will give units digit 0.

What are we finally checking then?: Is the units digit of X 9?


(1) x + 7 is a factor of 150
Let us check for even factors of 150 as x+7 is even.
Does any 2-digit even factor of 150 has 9+7 or 16 or 6 as units digit.
150=2*3*5*5
All 2-digit even factors will be multiple of 5 and end with 0.
So answer is YES.
Sufficient

(2) x + 17 is actor of 120
Let us check for even factors of 120 as x+17 is even.
Does any 2-digit even factor of 150 has 9+17 or 26 or 6 as units digit.
120=2*2*3*5
2-digit even factors will be multiple of 5 and end with 0 or it will be 12
So answer is YES.
Sufficient


D
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,398
Own Kudos:
Posts: 37,398
Kudos: 1,013
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderator:
Math Expert
102570 posts