Oct 18 08:00 AM PDT  09:00 AM PDT Learn an intuitive, systematic approach that will maximize your success on Fillintheblank GMAT CR Questions. Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions)
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 25 Sep 2018
Posts: 425
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
13 Jul 2019, 06:39
If n is a positive integer less than 400, what is the number of n such that when n is divided by 4, the remainder is 3 and when n is divided by 7, the remainder is 1? A. 10 B. 12 C. 13 D. 14 E. 15 Solution: By remainder theory we can conclude that , n= 4Q+ 3, & n= 7P + 1 we can apply this theory and find the various values of n by testing values of Q & P. Since n is less than 400, n can be 15, 43, 71, 99,127, 155,183,211,239,267,295,323,351,379 since there are 14 numbers in total which satisfy the above condition , Hence answer choice D must be the correct answer.
_________________
Why do we fall?...So we can learn to pick ourselves up again



Senior Manager
Joined: 25 Jul 2018
Posts: 266

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
13 Jul 2019, 07:37
If n is a positive integer less than 400, what is the number of n such that when n is divided by 4, the remainder is 3 and when n is divided by 7, the remainder is 1?
(1)if we divide n (0<n<400)by 4, the remainder is 3, n could be 3,7,11,15,19,23,27,31,35,39,43.... (2)if we divide n (0<n<400)by 7, the remainder is 1, n could be 1,8,15,22,29,36,43,50,57,64,71....
let's pay attention in what numbers n matches appropriately>> they are 15,43,71....
In the second condition(which n is divided by 7...),matches is repeated every 4th number except the first one. the first one came in the 3rd position.
when n is divided by 7 (0<n<400)by 4, the remainder is 1, n could be 1,8,15,22,29,36,43,50,57,64,71...393(400 is not included) and n comes 57 times between 0<n<400. So, we can calculate the number of n (3+4+4+4+4+4+4+4+4+4+4+4+4+4=55) which is 14 times.
Answer choice is D



Manager
Joined: 22 Oct 2018
Posts: 73

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
13 Jul 2019, 07:39
If n is a positive integer less than 400, what is the number of n such that when n is divided by 4, the remainder is 3 and when n is divided by 7, the remainder is 1?
A. 10 B. 12 C. 13 D. 14 E. 15
Solution: According to Remainder Theory we are getting two equations:
n=4Q+3 and n=7Q+1
The value of n less than 400 for both of the cases when n divided by 4 leaving a remainder of 4 and when divided by 7 leaving a remainder 1 can b arrived by substituting various values of Q as 1,2,3,4,5,6,...…...till we get a value less than 400 in both equations. We get the following values for both the equations:
For the first equation the various vales are=7,11,15,19,23,27,31,35,39,43,47,51,55,59,63,67,71,75,79,83,..................99,.......127,.........155,...183,....211....,239,.....267......295.....323,....351,.....379....399. For the second equation the various value of n are=8,15,22,29,36,43,50,57,64,71,78,85,92,....99,....113,......127,.....134,.....155,.....162,...169,.......183,.....190,....211,...218,...239,......246,....260,...267,...281,....295,.....302,.....323,.....351,......358,.....365,...379,.....393.
so from above we see that the values of n for which when n divided by 4 leaves a remainder 3 and when divided by 7 leaves a remainder 1 are=15,43,71,99,127,155,183,211,239,267,295,323,351,379 .
The above numbers are 14 in count .Hence answer is D IMO.



Intern
Joined: 17 Jul 2017
Posts: 34

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
13 Jul 2019, 07:53
I don't have a proper approach or formula. I started by counting the multiples of 7 and +1. That will give remainder as 1 when divided by 7 8  remainder as 1 when divided by 7, rem=0 when divided by 4 15 remainder as 1 when divided by 7, rem=3 when divided by 422  remainder as 1 when divided by 7, rem=2 when divided by 4 29  remainder as 1 when divided by 7, rem=1 when divided by 4 36  remainder as 1 when divided by 7, rem=0 when divided by 4 43  remainder as 1 when divided by 7, rem=3 when divided by 4We have a pattern starting from 15 and increasing the number by 28 we have the number that satisfies this condition. Last number in the pattern less than 400 is 379.Total number of 'n' that satisfies the condition is = 14 (D)
_________________
I am alive, because I have a dream Give kudos if it helped. Comment if I am wrong to help me learn more.



Senior Manager
Joined: 05 Mar 2017
Posts: 261
Location: India
Concentration: General Management, Marketing
GPA: 3.6
WE: Marketing (Hospitality and Tourism)

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
13 Jul 2019, 07:54
If n is a positive integer less than 400, what is the number of n such that when n is divided by 4, the remainder is 3 and when n is divided by 7, the remainder is 1?
A. 10 B. 12 C. 13 D. 14 E. 15
Let's break down the question;
N= 3 or 7 or 11 or 15 keep adding 4 N= 1 or 8 or 15 or 22 or 29 keep adding 7
The key to master this question is pattern recognition So N which falls in both the criteria is 15, 43, 71 difference between each number is 28, so keep adding till 400
So the answer is 14
The answer is D.



Intern
Joined: 24 Mar 2018
Posts: 48
Location: India
Concentration: Operations, Strategy
WE: Project Management (Energy and Utilities)

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
13 Jul 2019, 07:56
n=4a+3 Substituting whole number values for a, we get n=3,7,11,15,19,23,27,31,35,39,43... n=7b+1 Substituting whole number values for a, we get n=1,8,15,22,29,36,43,.. We see that the first common number is 15; then it's 43. So the difference between 2 consecutive numbers is 28. So there are 14 such numbers upto 400.
Answer (D)
Posted from my mobile device



Senior Manager
Joined: 10 Aug 2018
Posts: 335
Location: India
Concentration: Strategy, Operations
WE: Operations (Energy and Utilities)

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
12 Jul 2019, 08:09
If n is a positive integer less than 400, what is the number of n such that when n is divided by 4, the remainder is 3 and when n is divided by 7, the remainder is 1? A. 10 B. 12 C. 13 D. 14 E. 15 15 is the number which leaves 3 and 1 with 4 and 7 respectively. E is the answer
_________________
On the way to get into the Bschool and I will not leave it until I win. WHATEVER IT TAKES. " I CAN AND I WILL"
GMAT:[640 Q44, V34, IR4, AWA5]Need advice: https://gmatclub.com/forum/profileevaluationindian29maleenergysectorneedadvice308286.html



Senior Manager
Joined: 12 Dec 2015
Posts: 428

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
12 Jul 2019, 08:11
If n is a positive integer less than 400, what is the number of n such that when n is divided by 4, the remainder is 3 and when n is divided by 7, the remainder is 1?
given: n = 4*p + 3=7*q + 1, where p & q are integers
A. 10 > 10 = 4*2 + 2 B. 12 > 12 = 4*3 + 0 C. 13 > 13 = 4*3+1 D. 14 > 14 = 4*3+2 E. 15 > correct: 15 = 4*3 + 3 = 7*2+1



Manager
Joined: 29 Nov 2018
Posts: 147
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
12 Jul 2019, 08:19
If n is a positive integer less than 400, what is the number of n such that when n is divided by 4, the remainder is 3 and when n is divided by 7, the remainder is 1?
A. 10 B. 12 C. 13 D. 14 E. 15
The values that satisfy both the condition are 15,43,71. So if we write the equation the number has to satisfy 4x+3 and 7y+1. The values of y which satisfy both the equation are y=2,y=6,y=10,14,18 so we see that it jumps by 4. so last number is going to be y=42 which when put into equation number turns out to be 54. hence total numbers to satisfy the condition is 15.
Hence answer is E



Manager
Joined: 30 May 2018
Posts: 156
Location: Canada
GPA: 3.8

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
12 Jul 2019, 08:28
C
1st condition: n = 4a+3 = 3,7,11,15,19,23... 2nd condition: n=7b+ 1 = 1,8,15,22,...
So, first common integer in both series is 15. GCD of 4 and 7 is 28.
Therefore, n = 28*x + 15. Now, since n has to be less than 400, we have: 28*x + 15 < 4000 => x < 13.5.. So maximum value of x is 13.



Director
Joined: 24 Nov 2016
Posts: 598
Location: United States

If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
Updated on: 15 Jul 2019, 11:11
Quote: If n is a positive integer less than 400, what is the number of n such that when n is divided by 4, the remainder is 3 and when n is divided by 7, the remainder is 1?
A. 10 B. 12 C. 13 D. 14 E. 15 0 < n positive < 400 when n/4 remainder is 3: n={3 7 11 [15] 19 23…[43]…} when n/7 remainder is 1: n={1 8 [15] 22 29 36…[43]…} the pattern of n such numbers that fit the condition has a common difference of 28 [=4315] thus we need to find the last term with a common difference of 28 from 0 to 400, with a first term of 15 and a last term of 15+28(x1)<400: 15+28(x1)<400,…15+28x28<400,…28x<400+2815,…x<413/28,…x<14.75 x=14 Answer (D).
Originally posted by exc4libur on 12 Jul 2019, 08:29.
Last edited by exc4libur on 15 Jul 2019, 11:11, edited 1 time in total.



Manager
Joined: 12 Mar 2019
Posts: 160

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
12 Jul 2019, 08:36
Answer E, Just simply check the options and conclude answer . Only 1 option gives remainder of 3 on dividing by 4 and remainder 1 on diving by 7 i.e 15



Manager
Joined: 30 Nov 2017
Posts: 193
WE: Consulting (Consulting)

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
12 Jul 2019, 08:45
Testing the answers, 15 is the only number in the option that will be divided by 4 to give a remainder of 3 and will also be divided by 7 to give a remainder of 1. Hence answer choice E. Posted from my mobile device
_________________
Be Braver, you cannot cross a chasm in two small jumps...



Manager
Joined: 18 Sep 2018
Posts: 100

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
12 Jul 2019, 08:52
IMO C
Given, n=4q1+3 [where q1 is quotient] => so values of n = 3,7,11,15,19,23,...so on Also given, n=7q2+1 [where q2 is quotient] => so values of n = 1,8,15,22,29,36,...so on The common lowest value is 15 and L.C.M of 4 and 7 is 28 Therefore we can calculate the values of n by the formula n=28k+15 (where k=0,1,2,3,4,...so on) We can now check by the options, from (A) k=10, n=280+15=295 (Too small), [Usually we can try with the middle option C for back calculations) Now from (C) k=13, n=28*13+15=379 (Close!) Let's try one more, from (D) k=14, n=392+15=407 (Greater than 400) C is our winner here.



VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1014
WE: Supply Chain Management (Energy and Utilities)

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
12 Jul 2019, 08:57
n=4k+3 n=7m+1 n<400 when n=15, the above conditions match. Ans. (E)
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Intern
Joined: 13 Mar 2019
Posts: 28
Location: India

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
12 Jul 2019, 09:05
We can find the result easily by the options.From the first statement that when divided by 4 it leaves remainder 3 for sure its a odd no and therefore 3 options A,B,D goes out. Ans is E.



Manager
Joined: 24 Jun 2017
Posts: 71

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
12 Jul 2019, 09:12
A. 10 B. 12 C. 13 D. 14 E. 15 Backsolving is best. Only 15/4 gives 3 as remainder. Therefore divide 15/7. Remainder is 1. So, E
Posted from my mobile device



Senior Manager
Joined: 20 Mar 2018
Posts: 372
Location: Ghana
Concentration: Finance, Real Estate

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
12 Jul 2019, 09:15
n<400 n= 4q+3.......(1) n=7p+1........(2)
n=4q+3=7p+1 4q= 7p2 —> q= (7p2)/4
When p=2 , q= (7(2)2)/4 =3 .: p=2 ,q=3
Substitute p=2 ,n=7(2)+1 =15 Again q=3 ,n=4(3)+3=15
Answer E
Posted from my mobile device



Senior Manager
Joined: 10 Sep 2013
Posts: 307
Location: India
GPA: 4

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
12 Jul 2019, 09:18
The first such number is 15.
Add multiple of 4*7 in 15 to arrive at next such number. =43 and so on
Basically 15+28*13=379. 13 such values are possible.
Posted from my mobile device



Manager
Joined: 10 Jun 2019
Posts: 82

Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
Show Tags
12 Jul 2019, 09:27
The general formula for n would be 28x+15. x can be any positive integer that makes 28x+15 <400. Solving this gives us 28x<385. The least integer value for x that will be < 385 is 13.




Re: If n is a positive integer less than 400, what is the number of n such
[#permalink]
12 Jul 2019, 09:27



Go to page
Previous
1 2 3 4 5
Next
[ 86 posts ]



