Last visit was: 15 Jul 2025, 06:37 It is currently 15 Jul 2025, 06:37
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: 102,576
Own Kudos:
Given Kudos: 98,190
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,576
Kudos: 741,554
 [10]
2
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
avatar
SavageBrother
Joined: 18 Dec 2014
Last visit: 03 Oct 2015
Posts: 95
Own Kudos:
51
 [1]
Given Kudos: 5
Posts: 95
Kudos: 51
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
AmoyV
User avatar
Retired Moderator
Joined: 30 Jul 2013
Last visit: 09 Nov 2022
Posts: 248
Own Kudos:
708
 [1]
Given Kudos: 134
Status:On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Products:
Posts: 248
Kudos: 708
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
User avatar
lipsi18
Joined: 26 Dec 2012
Last visit: 30 Nov 2019
Posts: 131
Own Kudos:
Given Kudos: 4
Location: United States
Concentration: Technology, Social Entrepreneurship
WE:Information Technology (Computer Software)
Posts: 131
Kudos: 55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
n is +ive integer; n/4=R=reminder=?

1.n/8=R=1, assume n =1,9,17...; so n/8 = 1/8 =R=1=9/8=17/8; 1/4=9/4=17/4=R=1 For all numbers remainder =1; so sufficient.

2. n/2=R=1, assume n=1,3,5,7,9...; so n/2=1/2=R=1=3/2=5/2=7/2; but for 1/4=5/4=R=1, 3/4=7/4=R=3; so not sufficient.

Hence answer is A

Thanks,
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,788
Own Kudos:
12,493
 [3]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,788
Kudos: 12,493
 [3]
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
SavageBrother
What is the remainder when positive integer n is divided by 4?

(1) When n is divided by 8, the remainder is 1.

(2) When n is divided by 2, the remainder is 1.


Picked a number

1)
9 / 8 = 1 remainder 1
17 / 8 = 2 remainder 1

9 / 4 = 2 remainder 1
17 / 4 = 4 remainder 1

Sufficient.

2)
9 / 2 = 4 remainder 1
17 / 2 = 8 remainder 1

9 / 4 = 2 remainder 1
17 / 4 = 4 remainder 1

Both sufficient, D?

Hi SavageBrother,

When dealing with the individual Facts in a DS question, you have to be careful about assuming that the logic/examples you use for one are the only options that you can use for the other.

Here, Fact 2 tells us: when N is divided by 2, the remainder is 1.

You should start here by TESTing the easiest values possible (not just the ones you used in Fact 1).

Here, N could be 1, 3, 5, 7, 9 etc.

IF...
N = 1
1/4 = 0 remainder 1

IF....
N = 3,
3/4 = 0 remainder 3
Fact 2 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich
User avatar
Lucky2783
Joined: 07 Aug 2011
Last visit: 08 May 2020
Posts: 418
Own Kudos:
1,990
 [1]
Given Kudos: 75
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT 1: 630 Q49 V27
Posts: 418
Kudos: 1,990
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the remainder when positive integer n is divided by 4?

(1) When n is divided by 8, the remainder is 1.

(2) When n is divided by 2, the remainder is 1.


Kudos for a correct solution.

Option a
n=8k+1
Will always give remainder 1 when divided by 4

Option b
n=2k+1
if k is even remainder will be 1
if k is odd remainder will be 3

Option A answer
User avatar
Harley1980
User avatar
Retired Moderator
Joined: 06 Jul 2014
Last visit: 14 Jun 2024
Posts: 1,002
Own Kudos:
6,617
 [3]
Given Kudos: 178
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT 2: 740 Q50 V40
Posts: 1,002
Kudos: 6,617
 [3]
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
What is the remainder when positive integer n is divided by 4?

(1) When n is divided by 8, the remainder is 1.

(2) When n is divided by 2, the remainder is 1.


Kudos for a correct solution.

1) When some number n is divided x and give some remainder we will receive the same remainder if we divide this number n on factors of x (if factors not less than remainder)
so 8 = 2 * 2 * 2 and if divede n on 2 or 4 or 8 we will receive remainder 1
sufficient

2) We can't say about remainder if want to divide on the number that more than divider which we know.
insufficient

Answer A


Additional example about quality that I mention in 1 statement:
If we have information that n is divided by 30 and the remainder is 1
we can say that all factors of 30 will be give remainder 1 with the number n

for example n = 31
31 / 30 = 1 and remainder 1

factors of 30 = 2 * 3 * 5
31 / 2 = 15 and remainder 1
31 / 3 = 10 and remainder 1
31 / 5 = 6 and remainder 1
User avatar
bagdbmba
User avatar
Retired Moderator
Joined: 27 Aug 2012
Last visit: 10 Dec 2021
Posts: 1,005
Own Kudos:
4,166
 [1]
Given Kudos: 156
Posts: 1,005
Kudos: 4,166
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IMO OA is
avatar
SavageBrother
Joined: 18 Dec 2014
Last visit: 03 Oct 2015
Posts: 95
Own Kudos:
Given Kudos: 5
Posts: 95
Kudos: 51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EMPOWERgmatRichC
SavageBrother
What is the remainder when positive integer n is divided by 4?

(1) When n is divided by 8, the remainder is 1.

(2) When n is divided by 2, the remainder is 1.


Picked a number

1)
9 / 8 = 1 remainder 1
17 / 8 = 2 remainder 1

9 / 4 = 2 remainder 1
17 / 4 = 4 remainder 1

Sufficient.

2)
9 / 2 = 4 remainder 1
17 / 2 = 8 remainder 1

9 / 4 = 2 remainder 1
17 / 4 = 4 remainder 1

Both sufficient, D?

Hi SavageBrother,

When dealing with the individual Facts in a DS question, you have to be careful about assuming that the logic/examples you use for one are the only options that you can use for the other.

Here, Fact 2 tells us: when N is divided by 2, the remainder is 1.

You should start here by TESTing the easiest values possible (not just the ones you used in Fact 1).

Here, N could be 1, 3, 5, 7, 9 etc.

IF...
N = 1
1/4 = 0 remainder 1

IF....
N = 3,
3/4 = 0 remainder 3
Fact 2 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich

Thanks for the explanation. Got it.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Jul 2025
Posts: 102,576
Own Kudos:
Given Kudos: 98,190
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,576
Kudos: 741,554
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the remainder when positive integer n is divided by 4?

(1) When n is divided by 8, the remainder is 1.

(2) When n is divided by 2, the remainder is 1.


Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:
dividingby2and8_text.png
dividingby2and8_text.png [ 19.71 KiB | Viewed 17002 times ]
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,755
Own Kudos:
34,086
 [3]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,755
Kudos: 34,086
 [3]
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Bunuel
What is the remainder when positive integer n is divided by 4?

(1) When n is divided by 8, the remainder is 1.

(2) When n is divided by 2, the remainder is 1.


Kudos for a correct solution.

Target question: What is the remainder when positive integer n is divided by 4?

Statement 1: When n is divided by 8, the remainder is 1.

APPROACH #1
There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2


Statement 1 essentially says, When n is divided by 8, we get some integer (say k) and the remainder is 1.
So, we can use our nice rule to write: n = 8k + 1 (where k is an integer)
At this point, we can take n = 8k + 1 and rewrite it as n = (4)(2)k + 1
We can rewrite THIS as n = (4)(some integer) + 1
This means that n is 1 greater than some multiple of 4.
In other words, if we divide n by 4, we'll get remainder 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

APPROACH #2
Let's test a few possible values of n.
When it comes to remainders, we have another nice rule that says:
If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.


So, if n divided by 8 leaves remainder 1, then some possible values of n are: 1, 9, 17, 25, 33 etc.

Let's test a few of these possible values to see what happens when we divide them by 4
n = 1: n divided by 4 leaves remainder 1
n = 9: n divided by 4 leaves remainder 1
n = 17: n divided by 4 leaves remainder 1
n = 25: n divided by 4 leaves remainder 1
n = 33: n divided by 4 leaves remainder 1
It certainly seems that statement 1 guarantees that the remainder will be 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: When n is divided by 2, the remainder is 1.
In other words, statement 2 tells us that n is ODD
Let's test some possible values of n
Case a: n = 3, in which case n divided by 4 leaves remainder 3
Case b: n = 5, in which case n divided by 4 leaves remainder 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer =
RELATED VIDEO
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,406
Own Kudos:
Posts: 37,406
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
102576 posts