Last visit was: 23 May 2024, 05:37 It is currently 23 May 2024, 05:37
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
SORT BY:
Date
Math Expert
Joined: 02 Sep 2009
Posts: 93417
Own Kudos [?]: 626023 [9]
Given Kudos: 81940
Send PM
Most Helpful Reply
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5986
Own Kudos [?]: 13504 [6]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
General Discussion
Manager
Manager
Joined: 20 Feb 2017
Posts: 154
Own Kudos [?]: 450 [1]
Given Kudos: 489
Location: India
Concentration: Operations, Strategy
WE:Engineering (Other)
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5350
Own Kudos [?]: 4016 [1]
Given Kudos: 160
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Re: The numbers 400, 536 and 645, when divided by a positive integer N, gi [#permalink]
1
Bookmarks
Bunuel wrote:
The numbers 400, 536 and 645, when divided by a positive integer N, give the remainders of 22, 23 and 24 respectively. What is the greatest possible value of N?

A. 9
B. 18
C. 21
D. 27
E. 54

Are You Up For the Challenge: 700 Level Questions


400modN = 22
536modN = 23
645modN = 24

136modN=1
109modN=1

27modN=0
N = 27k

Let N = 54;
400mod54= 22
536mod54 = -4mod54 = 50
645mod54 = -3mod54 = 51

Largest value of N = 27

IMO D
Senior Manager
Senior Manager
Joined: 12 Dec 2015
Posts: 468
Own Kudos [?]: 544 [0]
Given Kudos: 84
Send PM
Re: The numbers 400, 536 and 645, when divided by a positive integer N, gi [#permalink]
The numbers 400, 536 and 645, when divided by a positive integer N, give the remainders of 22, 23 and 24 respectively. What is the greatest possible value of N?

A. 9
B. 18
C. 21
D. 27 --> correct
E. 54

Solution:
400 = N*d1 + 22 => N*d1=378 = 3^3*14 ---(i)
536 = N*d2 + 23 => N*d2=513 = 3^3*19---(ii)
645 = N*d3 + 24 => N*d3=621 = 3^3 *23--(iii)

HCF of (i), (ii) & (iii) => 3^3=27

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3723
Own Kudos [?]: 17013 [1]
Given Kudos: 165
Send PM
Re: The numbers 400, 536 and 645, when divided by a positive integer N, gi [#permalink]
1
Kudos
Expert Reply

Solution



Given
In this question, we are given that
    • The numbers 400, 536 and 645, when divided by a positive integer N, give the remainders of 22, 23 and 24 respectively

To find
We need to determine
    • The greatest possible value of N

Approach and Working out
When 400 is divided by N, the remainder is 22
    • Hence, 400 – 22 = 378 should be completely divisible by N

When 536 is divided by N, the remainder is 23
    • Hence, 536 – 23 = 513 should be completely divisible by N

When 645 is divided by N, the remainder is 24
    • Hence, 645 – 24 = 621 should be completely divisible by N

Now, the greatest possible value of N = the greatest number that divides 378, 513, 621 = GCD (378, 513, 621) = 27

Thus, option D is the correct answer.

Correct Answer: Option D
Manager
Manager
Joined: 26 Apr 2019
Posts: 247
Own Kudos [?]: 168 [0]
Given Kudos: 135
Location: India
Concentration: Finance, Leadership
GMAT 1: 690 Q49 V34
GMAT 2: 700 Q49 V36
GMAT 3: 720 Q50 V37
GMAT 4: 740 Q50 V40
GPA: 3.99
Send PM
Re: The numbers 400, 536 and 645, when divided by a positive integer N, gi [#permalink]
easiest way to solve this problem is by substracting remainder from given number for example do 400-22 =388 and then match from the options.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10152
Own Kudos [?]: 16719 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: The numbers 400, 536 and 645, when divided by a positive integer N, gi [#permalink]
Expert Reply
400 = pN+22 => 378 = pN (p is quotient)
536 = qN+23 => 513 = qN (q is quotient)
645 = rN+24 => 621 = rN (r is quotient)

378 = 2 * 3^3 * 7
513 = 3^3 * 19
621 = 3^3 * 23

So common factor dividing all the three numbers (378,513, and 621) is 3^3 = 27

Answer D
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10152
Own Kudos [?]: 16719 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: The numbers 400, 536 and 645, when divided by a positive integer N, gi [#permalink]
Expert Reply
400 = pN+22 => 378 = pN (p is quotient)
536 = qN+23 => 513 = qN (q is quotient)
645 = rN+24 => 621 = rN (r is quotient)

378 = 2 * 3^3 * 7
513 = 3^3 * 19
621 = 3^3 * 23

So the common factor dividing all the three numbers (378,513, and 621) is 3^3 = 27

Answer D
Director
Director
Joined: 05 Jan 2020
Status:Admitted to IIM Shillong (PGPEx 2023-24)
Affiliations: CFA Institute; ICAI; BCAS
Posts: 586
Own Kudos [?]: 566 [1]
Given Kudos: 694
Location: India
WE 2: EA to CFO (Consumer Products)
GPA: 3.78
WE:Corporate Finance (Commercial Banking)
Send PM
Re: The numbers 400, 536 and 645, when divided by a positive integer N, gi [#permalink]
1
Kudos
To add my inputs to above solutions, remainder is always less than divisor. So options A to C are out straight away.

Between D and E, we may use the approach mentioned above.
Tutor
Joined: 11 May 2022
Posts: 1091
Own Kudos [?]: 712 [1]
Given Kudos: 81
Send PM
Re: The numbers 400, 536 and 645, when divided by a positive integer N, gi [#permalink]
1
Kudos
Expert Reply
Bunuel wrote:
The numbers 400, 536 and 645, when divided by a positive integer N, give the remainders of 22, 23 and 24 respectively. What is the greatest possible value of N?

A. 9
B. 18
C. 21
D. 27
E. 54

Are You Up For the Challenge: 700 Level Questions



Look at the answer choices. This is a variation of PITA (Plugging In The Answers)
A. If we were dividing by 9, how on earth would we end up with a remainder of 22?!? 22 would just mean that we have two more multiples of 9 and then a remainder of 4. A is wrong.
B. If we were dividing by 18, how on earth would we end up with a remainder of 23?!? 23 would just mean we have another multiple of 18 and then a remainder of 5. B is wrong.
C. If we were dividing by 21, how on earth would we end up with a remainder of 24?!? 24 would just mean we have another multiple of 21 and then a remainder of 3. C is wrong.
D. I don't know. Leave it.
E. If we're dividing 645 (an odd number) by 54 (an even number), we'd end up with a remainder that's odd. 24 is not odd. E is wrong.

Answer choice D.


ThatDudeKnowsPITA
Intern
Intern
Joined: 25 Apr 2023
Posts: 5
Own Kudos [?]: [0]
Given Kudos: 6
Location: Italy
GMAT 1: 580 Q49 V21
GMAT 2: 680 Q49 V34
GPA: 3.6
Send PM
Re: The numbers 400, 536 and 645, when divided by a positive integer N, gi [#permalink]
The numbers 400, 536 and 645, when divided by a positive integer N, give the remainders of 22, 23 and 24 respectively. What is the greatest possible value of N?

A. 9
B. 18
C. 21
D. 27
E. 54

The reminder cannot be higher than the dividend so A, B and C are wrong. Try to use the solution D and E but only 27 works so the answer is D.
You can do it in less than 30 seconds and reducing the operation done
GMAT Club Bot
Re: The numbers 400, 536 and 645, when divided by a positive integer N, gi [#permalink]
Moderator:
Math Expert
93417 posts