Last visit was: 21 Apr 2026, 18:03 It is currently 21 Apr 2026, 18:03
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 21 Apr 2026
Posts: 109,728
Own Kudos:
810,469
 [5]
Given Kudos: 105,800
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,728
Kudos: 810,469
 [5]
After the first term, each term in a sequence is five times greater 20 Mar 2022, 03:01
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

50% (02:10) correct 50% (02:31) wrong based on 127 sessions

History

Date
Time
Result
Not Attempted Yet
After the first term, each term in a sequence is five times greater than half the preceding term. If x is the first term of the sequence, and x does not equal zero, is the value of the fourth term minus the second term an integer?

(1) x is a multiple of 12.
(2) x is a multiple of 56.



Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
B
User avatar
ShaikhMoice
User avatar
Joined: 25 Jan 2021
Last visit: 25 Aug 2022
Posts: 94
Own Kudos:
41
Given Kudos: 475
Posts: 94
Kudos: 41
After the first term, each term in a sequence is five times greater 20 Mar 2022, 11:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
After the first term, each term in a sequence is five times greater than half the preceding term. If x is the first term of the sequence, and x does not equal zero, is the value of the fourth term minus the second term an integer?

(1) x is a multiple of 12.
(2) x is a multiple of 56.



Are You Up For the Challenge: 700 Level Questions
Show more

each term in a sequence is five times greater than half the preceding term

1st term X
2nd term 6X/2
3rd term 36X/4
4th term 216X/4

Diff 216X/4-36X/4

Hence both statement 1 & 2 are sufficient
IMO D.

PS: Is my understanding correct to treat five times more as 6X ???
User avatar
IanStewart
User avatar
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 17 Apr 2026
Posts: 4,143
Own Kudos:
11,267
 [3]
Given Kudos: 99
Expert
Expert reply
Posts: 4,143
Kudos: 11,267
 [3]
After the first term, each term in a sequence is five times greater 20 Mar 2022, 12:10
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ShaikhMoice

PS: Is my understanding correct to treat five times more as 6X ???
Show more

I understand why you'd ask, because with percents, that's how things work, but things work differently with numbers. This won't seem logical (and it isn't, really), but when we say one number is five times greater than another, that just means the first number is five times the second number. With percents, on the other hand, if we say one number is 500% greater than another, that means the first number is six times the second. That might seem completely inconsistent, but language is just based on conventions, and that's how these phrases are used in practice (it's also why no one ever says "x is one times greater than y" to mean "x is twice as big as y").

That said, I don't think I've ever seen a real GMAT question use this kind of wording -- it can always be easily avoided, and I only ever it in prep company questions. For GMAT purposes, the important thing to understand is what the phrase "x is 500% greater than y" means (x = 6y), and not what the phrase "x is 5 times greater than y" means (x = 5y).
avatar
inconnu99
avatar
Joined: 09 Aug 2021
Last visit: 20 Apr 2022
Posts: 2
Own Kudos:
2
 [1]
Given Kudos: 29
Posts: 2
Kudos: 2
 [1]
After the first term, each term in a sequence is five times greater Updated on: 03 Apr 2022, 12:07
Originally posted by inconnu99 on 29 Mar 2022, 17:40.
Last edited by inconnu99 on 03 Apr 2022, 12:07, edited 1 time in total.
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The first four terms of the sequence are: x, 5x/2, 25x/4, 125x/8.
We want to know if 125x/8 - 5x/2 = 105x/8 is an integer. 105 and 8 share no common factors. Therefore x must be a multiple of 8 in order for the difference to yield an integer value.

(1) x = 12*k = 2^3 * 3 * k (k > 0) :

We can test two values to see that Statement 1 is not sufficient. If x = 24, then 105x/8 yields an integer. If x = 36 then, no (105*36 is not divisible by 8 - can be deduced from prime factorization).

(2) x = 56 *q = 7 * 2^3 * q (q>0) : x has 8 as a factor. As such, 105x/8 will always be divisible by 8. Sufficient.

Answer: B
User avatar
arvind910619
User avatar
Joined: 20 Dec 2015
Last visit: 18 Oct 2024
Posts: 815
Own Kudos:
615
Given Kudos: 755
Status:Learning
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
GPA: 3.4
WE:Engineering (Manufacturing)
Products:
My Reviews
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
Posts: 815
Kudos: 615
After the first term, each term in a sequence is five times greater 01 Apr 2022, 10:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
inconnu99
The first four terms of the sequence are: x, x/2, 25x/4, 125x/8.
We want to know if 125x/8 - 5x/2 = 105x/8 is an integer. 105 and 8 share no common factors. Therefore x must be a multiple of 8 in order for the difference to yield an integer value.

(1) x = 12*k = 2^3 * 3 * k (k > 0) :

We can test two values to see that Statement 1 is not sufficient. If x = 24, then 105x/8 yields an integer. If x = 36 then, no (105*36 is not divisible by 8 - can be deduced from prime factorization).

(2) x = 56 *q = 7 * 2^3 * q (q>0) : x has 8 as a factor. As such, 105x/8 will always be divisible by 8. Sufficient.

Answer: B
Show more

Kudos for your detailed explanation
User avatar
shivaniilall
User avatar
Joined: 22 Nov 2021
Last visit: 16 Oct 2025
Posts: 27
Own Kudos:
11
Given Kudos: 321
Location: India
Posts: 27
Kudos: 11
After the first term, each term in a sequence is five times greater 02 Apr 2022, 06:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
inconnu99
The first four terms of the sequence are: x, x/2, 25x/4, 125x/8.
We want to know if 125x/8 - 5x/2 = 105x/8 is an integer. 105 and 8 share no common factors. Therefore x must be a multiple of 8 in order for the difference to yield an integer value.

(1) x = 12*k = 2^3 * 3 * k (k > 0) :

We can test two values to see that Statement 1 is not sufficient. If x = 24, then 105x/8 yields an integer. If x = 36 then, no (105*36 is not divisible by 8 - can be deduced from prime factorization).

(2) x = 56 *q = 7 * 2^3 * q (q>0) : x has 8 as a factor. As such, 105x/8 will always be divisible by 8. Sufficient.

Answer: B
Show more

How come the second term here is x/2? Because in the question it says, "five time greater than half the preceding term".
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,956
Own Kudos:
1,117
Posts: 38,956
Kudos: 1,117
After the first term, each term in a sequence is five times greater 04 Mar 2025, 21:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109728 posts
kingbucky
498 posts
Gmat860sanskar
211 posts