Last visit was: 19 Apr 2025, 07:06 It is currently 19 Apr 2025, 07:06
Home
GMAT
Messages
Tests
Schools
Reviews
Rewards
Chat
My Profile
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
555-605 Level|   Algebra|      
User avatar
fattty
User avatar
Joined: 29 Nov 2015
Last visit: 31 Jan 2016
Posts: 11
Own Kudos:
418
 [56]
Given Kudos: 1
Posts: 11
Kudos: 418
 [56]
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 18 Jan 2016, 22:32
Kudos
Add Kudos
56
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

75% (01:44) correct 25% (01:53) wrong based on 1179 sessions

History

Date
Time
Result
Not Attempted Yet
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
davedekoos
User avatar
Joined: 09 Jul 2013
Last visit: 11 Apr 2025
Posts: 97
Own Kudos:
319
 [18]
Given Kudos: 11
Posts: 97
Kudos: 319
 [18]
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 19 Jan 2016, 13:17
10
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
fattty
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14


When dealing with remainders and equations, it is often helpful to translate the words into formulas.

"When x is divided by 2, remainder is 1" --> This means that x is 1 more than a multiple of 2 --> \(x = 2a+1\), where \(a\) is an integer.
"y is divided by 8, remainder is 2" --> This means that y is 2 more than a multiple of 8 --> \(y = 8b+2\), where \(b\) is an integer.

Now if we plug those expressions into 2x + y we get:

\(2x + y = [2(2a+1)] + [8b+2]\)
\(= 4a+2 + 8b+2\)
\(= 4(a+2b+1)\)

So 2x + y = 4*(some integer), and is therefore a multiple of 4. The only answer choice that is a multiple of 4 is C) 12.

Answer: C
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Apr 2025
Posts: 15,889
Own Kudos:
72,688
 [6]
Given Kudos: 462
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 15,889
Kudos: 72,688
 [6]
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 18 Jan 2016, 22:39
2
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
fattty
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10 B) 11 C) 12 D) 13 E) 14

Use some quick logic to eliminate the options:

"When x is divided by 2, remainder is 1" - means x is odd

"y is divided by 8, remainder is 2" - y is not divisible by 8. It could be 2, 10, 18... (all even numbers)

2x + y -> x is odd but 2x will be even. y is even. So 2x+y will be even. Options (B) and (E) are out.

Consider (A) 10 - y can be 2 but then x will be 4 (even); y can be 10 but then x will be 0(even) - Not possible
Consider (C) 12 - y can be 2 then x will be 5 (odd) - Works

Answer (C)
General Discussion
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 19 Apr 2025
Posts: 11,324
Own Kudos:
40,160
 [2]
Given Kudos: 333
Status:Math and DI Expert
Products:
My Reviews
Expert
Expert reply
Posts: 11,324
Kudos: 40,160
 [2]
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 18 Jan 2016, 23:20
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
fattty
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14

Hi,

Apart from the method stated above..
lesser error prone way would be
1) if x is divided by 2, the remainder is 1, that is x is odd.
So, 2x will be a multiple of 2 but not 4, that is 2x = 2(2a+1) = 4a+2.

2) now if y divided by 8 leaves a remainder 2, y when divided by 4 will also give a remainder of 2.., that is y=8b+2=4(2b)+2=4c+2.
so if 2x+y is divided by 4, it should give us a remainder of 2+2=4, meaning 2x+y should be div by 4..
only C fits in
OR
2x+y=4a+2+4c+2=4a+4c +4 or a multiple of 4.
C
avatar
hari1985
avatar
Joined: 06 Jul 2015
Last visit: 22 Mar 2019
Posts: 19
Own Kudos:
11
Given Kudos: 9
Products:
My Reviews
Posts: 19
Kudos: 11
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 19 Jan 2016, 12:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasPrepKarishma
fattty
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10 B) 11 C) 12 D) 13 E) 14

Use some quick logic to eliminate the options:

"When x is divided by 2, remainder is 1" - means x is odd

"y is divided by 8, remainder is 2" - y is not divisible by 8. It could be 2, 10, 18... (all even numbers)

2x + y -> x is odd but 2x will be even. y is even. So 2x+y will be even. Options (B) and (E) are out.

Consider (A) 10 - y can be 2 but then x will be 4 (even); y can be 10 but then x will be 0(even) - Not possible
Consider (C) 12 - y can be 2 then x will be 5 (odd) - Works

Answer (C)


Hi Karishma,

We know 2 is not divisible by 8. But it does not satisfy the condition stated in the question "y is divided by 8 remainder is 2"?
I could not connect why you have chosen y as 2. Can you please help me in understanding it?
User avatar
davedekoos
User avatar
Joined: 09 Jul 2013
Last visit: 11 Apr 2025
Posts: 97
Own Kudos:
319
 [1]
Given Kudos: 11
Posts: 97
Kudos: 319
 [1]
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 19 Jan 2016, 13:01
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
hari1985

Hi Karishma,

We know 2 is not divisible by 8. But it does not satisfy the condition stated in the question "y is divided by 8 remainder is 2"?
I could not connect why you have chosen y as 2. Can you please help me in understanding it?


Hi Hari,

2 is a valid choice for y because when you divide 2 by 8, the answer is 0 with remainder 2.

In general, any time you divide a smaller integer by a larger integer, the result will be 0 with the remainder equal to the smaller number. If integer \(a\) is smaller than integer \(b\), then \(\frac{a}{b}\) = 0 with remainder \(a\).

I hope that helps!

Cheers,
User avatar
mahakmalik
User avatar
Joined: 30 Apr 2015
Last visit: 08 May 2016
Posts: 71
Own Kudos:
77
 [3]
Given Kudos: 30
Status:Build your own dreams,Otherwise some one else will hire you to build there's.
Location: India
Concentration: Finance
Schools: BYU-Marriott'18
GMAT 1: 590 Q45 V26
GMAT 2: 660 Q47 V34
GPA: 3.68
Schools: BYU-Marriott'18
GMAT 2: 660 Q47 V34
Posts: 71
Kudos: 77
 [3]
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 22 Feb 2016, 10:02
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I got it in 1 min by:
X=2a+1..i
Y=8b+2...ii

we want 2X+Y
Multiply eqi by 2
2X=4a+2 And we have Y=8b+2
add both
2X+Y=4(a+2b)+4
only c option is divisible by 4..hence the answer.
User avatar
Ekland
User avatar
Joined: 15 Oct 2015
Last visit: 30 Apr 2023
Posts: 359
Own Kudos:
1,723
Given Kudos: 342
Concentration: Finance, Strategy
Schools: Fordham '18 Schulich Jan '18 Desautels '19 Haskayne(Calgary) Alberta"19 Jindal '19 Owen '19 Olin '19 (I) Queens"18
GPA: 3.93
WE:Account Management (Education)
Schools: Fordham '18 Schulich Jan '18 Desautels '19 Haskayne(Calgary) Alberta"19 Jindal '19 Owen '19 Olin '19 (I) Queens"18
Posts: 359
Kudos: 1,723
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 25 Feb 2016, 04:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fattty
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14

I had to go back to the good old number testing method for this
\(2x + y\)
pick numbers for x and y that fulfils the conditions given.
2(3) + 2
6 + 2
8. Not in the option! :(

raise x to the next level
2(5) + 2
10 + 2
12
That's in the option! :-D :-D :-D
Defnily their CANNOT be more than one possible value for \(2x + y\) in the options.
C.
User avatar
Probus
User avatar
Joined: 10 Apr 2018
Last visit: 22 May 2020
Posts: 181
Own Kudos:
508
Given Kudos: 115
Location: United States (NC)
Posts: 181
Kudos: 508
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 07 Sep 2018, 12:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
fattty
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14

Hi,

Apart from the method stated above..
lesser error prone way would be
1) if x is divided by 2, the remainder is 1, that is x is odd..
if the same x multiplied by 2, ( 2x), and divided by 4 will give a remainder 2..

[b]now if y divided by 8 leaves a remainder 2, y when divided by 4 will also give a remainder of 2..[/b]
so if 2x+y is divided by 4, it should give us a remainder of 2+2=4, meaning 2x+y should be div by 4..
only C fits in
C

Hi chetan2u,
Can you explain me property for the highlited portion. I get that when 18/8 reminder is 2 and 18/ 4 reminder is 2 but can you explain me logic behind the same.

Probus
User avatar
gracie
User avatar
Joined: 07 Dec 2014
Last visit: 11 Oct 2020
Posts: 1,039
Own Kudos:
1,788
Given Kudos: 27
Posts: 1,039
Kudos: 1,788
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 07 Sep 2018, 12:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fattty
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14

next to least value of x=5
least value of y=2
2*5+2=12
C
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 19 Apr 2025
Posts: 11,324
Own Kudos:
40,160
 [1]
Given Kudos: 333
Status:Math and DI Expert
Products:
My Reviews
Expert
Expert reply
Posts: 11,324
Kudos: 40,160
 [1]
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 07 Sep 2018, 20:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Probus
chetan2u
fattty
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14

Hi,

Apart from the method stated above..
lesser error prone way would be
1) if x is divided by 2, the remainder is 1, that is x is odd..
if the same x multiplied by 2, ( 2x), and divided by 4 will give a remainder 2..

[b]now if y divided by 8 leaves a remainder 2, y when divided by 4 will also give a remainder of 2..[/b]
so if 2x+y is divided by 4, it should give us a remainder of 2+2=4, meaning 2x+y should be div by 4..
only C fits in
C

Hi chetan2u,
Can you explain me property for the highlited portion. I get that when 18/8 reminder is 2 and 18/ 4 reminder is 2 but can you explain me logic behind the same.

Probus


1) If x is divided by 2, the remainder is 1 so X=2k+1..
Then 2x=2(2k+1)=4k+2
So when 4k+2 is divided by 4, remainder is 2

2)if y divided by 8 leaves a remainder 2.
So y = 8k+2..
Thus dividing by 4, (8k+2)/4
8k is divisible by 4, therefore remainder is 2

Thus 2x+4 will leave the same remainder as Remainder when 2x divided by 4 + Remainder when y is divided by 4...=> 2+2=4 that is it remainder is div by 4..

In choices only 12 is div by 4, hence C
User avatar
SolankiDas
User avatar
Joined: 21 Jan 2022
Last visit: 01 Jun 2023
Posts: 27
Own Kudos:
3
Given Kudos: 44
Posts: 27
Kudos: 3
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 12 Aug 2022, 06:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fattty
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14

X= 2a+1 , Y= 8b+2
now,

2X = 4a +2 if a=b=1

2X= 6 , Y=10
2X+Y= 16.
What is wrong in this approach?
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 19 Apr 2025
Posts: 11,324
Own Kudos:
40,160
Given Kudos: 333
Status:Math and DI Expert
Products:
My Reviews
Expert
Expert reply
Posts: 11,324
Kudos: 40,160
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 12 Aug 2022, 07:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
SolankiDas
fattty
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14

X= 2a+1 , Y= 8b+2
now,

2X = 4a +2 if a=b=1

2X= 6 , Y=10
2X+Y= 16.
What is wrong in this approach?

There is nothing wrong. But this is COULD BE question means there can be various values.
We know that the answer will be multiple of 4, so 16 will also fit in, but in the given values only 12 will fit in.
User avatar
nazii
User avatar
Joined: 29 Oct 2021
Last visit: 12 Jan 2024
Posts: 58
Own Kudos:
49
Given Kudos: 279
Posts: 58
Kudos: 49
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 05 Nov 2022, 11:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I picked X=9 and Y= 10, which both satisfies the question. 2X+Y= 28, then I looked for answer choice which is multiple of 28, so I chose e. Would you pls explain what is my mistake?
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 16 Dec 2024
Posts: 5,994
Own Kudos:
5,086
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,994
Kudos: 5,086
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 20 Dec 2023, 08:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fattty
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14
Minimum possible value possible value of x = 1 as 1/2 , Rem = 1
Minimum possible value possible value of y = 2 as 1/8 , Rem = 2

So, 2x + y = 2*1 + 1 => 3

Thus, the final answer must be a multiple of 3, among the options only (C) fits in perfectly, Answer must be (C)
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 36,918
Own Kudos:
971
Posts: 36,918
Kudos: 971
When x is divided by 2, remainder is 1 and y is divided by 8, remainde 14 Jan 2025, 21:03
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.
Moderators:
Bunuel
Math Expert
100761 posts
Krunaal
PS Forum Moderator
558 posts