GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Positive integer A > 10,000 and B > 20,000. When A is divided by 237,
[#permalink]
28 Apr 2022, 02:00
28 Apr 2022, 02:00
Expert Reply
8
Bookmarks
00:00
Question Stats:
71% (02:12) correct
28% (01:56) wrong based on 49 sessions
Hide Show timer Statistics
Positive integer A > 10,000 and B > 20,000. When A is divided by 237, the remainder is 85. When B is divided by 237, the remainder is 41. What is the remainder when (2A + 3B) is divided by 237?
A. 0
B. 56
C. 123
D. 170
E. 211
A. 0
B. 56
C. 123
D. 170
E. 211
Part of the project: GRE Quantitative Reasoning Daily Challenge - (2022) EDITION
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Positive integer A > 10,000 and B > 20,000. When A is divided by 237,
[#permalink]
28 Apr 2022, 06:15
28 Apr 2022, 06:15
3
2
Bookmarks
Carcass wrote:
Positive integer A > 10,000 and B > 20,000. When A is divided by 237, the remainder is 85. When B is divided by 237, the remainder is 41. What is the remainder when (2A + 3B) is divided by 237?
A. 0
B. 56
C. 123
D. 170
E. 211
A. 0
B. 56
C. 123
D. 170
E. 211
Key property: We can take ANY possible values of A and B (that satisfy the given information) and use them to determine the remainder when (2A + 3B) is divided by 237.
So we can ignore the information that tells us A > 10,000 and B > 20,000, and just use the smallest possible values of A and B.
Another property: 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.
Given: When A is divided by 237, the remainder is 85
So, 85 is the smallest possible value of A.
Given: When B is divided by 237, the remainder is 41
So, 41 is the smallest possible value of B.
Question: What is the remainder when (2A + 3B) is divided by 237?
2A + 3B = 2(85) + 3(41) = 170 + 123 = 293
293 divided by 237 equals 1 with remainder 56
Answer: B
General Discussion
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: Positive integer A > 10,000 and B > 20,000. When A is divided by 237,
[#permalink]
08 Sep 2022, 20:09
08 Sep 2022, 20:09
When A is divided by 237, the remainder is 85
Theory: Dividend = Divisor*Quotient + Remainder
A -> Dividend
237 -> Divisor
a -> Quotient (Assume)
85 -> Remainders
=> A = 237*a + 85 = 237a + 85
When B is divided by 237, the remainder is 41
Let quotient be b
=> B = 237*b + 41 = 237b + 41
What is the remainder when (2A + 3B) is divided by 237
2A + 3B = 2*(237a + 85) + 3*(237b + 41) = 237*2a + 170 + 237*3b + 123 = 237*(2a + 3b) + 237 + 56 = 237*(2a + 3b + 1) + 56
=> 2A + 3B when divided by 237 gives 2a + 3b + 1 as quotient and 56 as remainder.
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Remainders
Theory: Dividend = Divisor*Quotient + Remainder
A -> Dividend
237 -> Divisor
a -> Quotient (Assume)
85 -> Remainders
=> A = 237*a + 85 = 237a + 85
When B is divided by 237, the remainder is 41
Let quotient be b
=> B = 237*b + 41 = 237b + 41
What is the remainder when (2A + 3B) is divided by 237
2A + 3B = 2*(237a + 85) + 3*(237b + 41) = 237*2a + 170 + 237*3b + 123 = 237*(2a + 3b) + 237 + 56 = 237*(2a + 3b + 1) + 56
=> 2A + 3B when divided by 237 gives 2a + 3b + 1 as quotient and 56 as remainder.
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Remainders
