GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Sep 2019, 19:52

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

If n is a positive integer less than 400, what is the number of n such

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 24 Mar 2019
Posts: 22
If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post Updated on: 13 Jul 2019, 06:03
1
When you have since question there is a general formula which we can use.
We are given n=4X+3 and n=7Y+1
And the first of this number is 15.

We will get these number using this general equation

Number=(4*7)a+ 15
Number =28a+15

If we substitute the value of a from 1 we can find 13 more values before it passes the value of 400. So 13+1=14 is the answer

Posted from my mobile device

Originally posted by DarshBakshi on 12 Jul 2019, 08:48.
Last edited by DarshBakshi on 13 Jul 2019, 06:03, edited 1 time in total.
Manager
Manager
User avatar
S
Joined: 18 Sep 2018
Posts: 100
CAT Tests
Re: If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post 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
VP
User avatar
D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1029
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

New post 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
Intern
avatar
B
Joined: 26 May 2018
Posts: 45
Re: If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post 12 Jul 2019, 08:59
1
Answer is D

15/4=3._ and r=3; 15/7=2._ and r=1

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
Manager
Manager
avatar
S
Joined: 30 May 2019
Posts: 108
If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post Updated on: 13 Jul 2019, 02:09
1
n=4q+3, so n can be 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43......................
n=7q+1, n can be 1, 8, 15, 22, 29, 36, 43..................
Common integers are 15, 43,....... and the difference is 43-15=28, this means that after 28 numbers we get one number that fits to both of our equations above. Accordingly, 15, 43, 71, 99, etc. We can manually add 28 and then we will finally reach some number less than 400 OR we can do a smart calculation by dividing 400/28 to see how many 28th we have in 400. It is a little more than 14, which is our answer (D)

Originally posted by mira93 on 12 Jul 2019, 09:02.
Last edited by mira93 on 13 Jul 2019, 02:09, edited 1 time in total.
Manager
Manager
User avatar
S
Joined: 06 Jun 2019
Posts: 118
If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post Updated on: 13 Jul 2019, 05:28
1
First number for "when n is divided by 4, the remainder is 3" is 3, second is 7, 11, 15, ,,,,,,,,,,,, 43 (add 4 to each term)

First number for "when n is divided by 7, the remainder is 1" is 1, second is 8, 15,........, 43 (add 7 to each term)

If we count manually we will observe pattern that we have same n for every other 14 numbers (or 28 in total). we can add 28 to 43 and see which numbers overlap. So, 43+28=71, 99, 127, 155, 183, 211, 239, 267, 295, 323, 351, 379. Overall 14 numbers.

While solving, however, I didn't manually added 28 to each number, I rather added to 43 (140, 28*5), so I got, 183, 323, 463 (nope, little more). Let's count till 323, we have 15, 43 2 numbers) 183 (since was multiplied by 5, we have 5 numbers in it), so 2+5+5=12 until 323. Add 56 to get 379 (our last number) and we have overall 12+2=14

Hence D
_________________
Bruce Lee: “I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times.”
GMAC: “I fear not the aspirant who has practiced 10,000 questions, but I fear the aspirant who has learnt the most out of every single question.” :lol:

Originally posted by JonShukhrat on 12 Jul 2019, 09:04.
Last edited by JonShukhrat on 13 Jul 2019, 05:28, edited 1 time in total.
Intern
Intern
avatar
B
Joined: 13 Mar 2019
Posts: 28
Location: India
GMAT ToolKit User
Re: If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post 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
Manager
avatar
G
Joined: 08 Jan 2018
Posts: 145
Location: India
Concentration: Operations, General Management
WE: Project Management (Manufacturing)
Re: If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post 12 Jul 2019, 09:08
1
IMO-D

n=4p+3
n=7q+1

Therefore, 4p+3=7q+1 [p,q are positive integers ]
q=(4p+2)/7

p=3, q=2
p=10, q=6
similarly , p=17, 24, ......

n<400
4p+3<400
p max=99

p: 3,10,17,24,........99
3+(x-1)*7=99
x=96/7 +1 = 14 (nearest integer)
Manager
Manager
avatar
S
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

New post 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
Senior Manager
User avatar
P
Joined: 20 Mar 2018
Posts: 334
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

New post 12 Jul 2019, 09:15
n<400
n= 4q+3.......(1)
n=7p+1........(2)

n=4q+3=7p+1
4q= 7p-2 —> q= (7p-2)/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
Manager
Manager
avatar
B
Joined: 24 Jun 2019
Posts: 108
Re: If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post 12 Jul 2019, 09:15
1
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?

Caution: We do NOT have to find A VALUE OF N. We have to find the NUMBER OF POSSIBLE VALUES of N that will satisfy the conditions. I made that mistake on my first attempt!

We need a value for N such that... N/7 has remainder 1, N/4 has remainder 3.

So it has to be 1 more than multiple of 7... say 8, 15, 22, 29 etc.
Also, it has to be 3 more than multiple of 4... say 7, 11, 15,19, 23, 27 etc...

The lowest value that satisfies this condition is 15 as it appears in both lists. We want to find all such values which will appear in both lists.

After listing few values I realised that values of N start with 15 and then increase by 28 (7x4).

So values are 15, 43, 71, 99, 127, 155, 183, 211, 239, 267, 295, 323, 351, and 379. (each value is previous value + 28.... and it stops at 379 because n is less than 400)

So there are 14 values of n which give remainder 3 when divided by 4 and 1 when divided by 7.


Answer: D - 14


If there is a more elegant solution with some formula, I look forward to learning it tomorrow!
Manager
Manager
User avatar
S
Joined: 10 Sep 2013
Posts: 223
Location: India
GMAT 1: 720 Q50 V38
GPA: 4
Re: If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post 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
Intern
Intern
avatar
S
Joined: 12 Aug 2017
Posts: 42
GMAT ToolKit User CAT Tests
Re: If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post 12 Jul 2019, 09:22
1
1<=n<=400

Applying remainder theorem:
n-3 = 4k and n-1 = 7m (k,m are divisors)

n= 4K+3 and n=7m+1

Only Option E i.e. 15 fits ins.
_________________
The key is not the will to win, it's the will to prepare to win that is important !!
Manager
Manager
avatar
B
Joined: 10 Jun 2019
Posts: 63
CAT Tests
Re: If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post 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.
Manager
Manager
User avatar
G
Joined: 17 Jul 2014
Posts: 128
GMAT ToolKit User CAT Tests
Re: If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post 12 Jul 2019, 09:30
n<400
N = 4Q1 + 3
N could be - 3, 7, 11, 15, 19

N = 7Q2 + 1
N could be 1, 8, 15, 22

So far we have found one number in the above list common 15 that satisfy both above equations and 15 is also in the answer choices

E is the answer
Manager
Manager
avatar
S
Joined: 09 Apr 2017
Posts: 79
GPA: 3.99
GMAT ToolKit User CAT Tests
Re: If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post 12 Jul 2019, 09:53
Use Back-solved,


First, narrow down the answer choices using either N=4Q+3 or N = 7Q + 1

Pick, N = 7Q + 1 , since multiply of 7 is far less divisible compared to multiple of 4

A. 10 = 7Q+1, 9/7=Q not an integer
B. 12=7Q+1, 11/7=Q not an integer
C. 13=7Q+1, 12/7=Q not an integer
D. 14=7Q+1, 13/7=Q not an integer
E. 15=7Q+1, 14/7=Q an integer; definitely, 15=4Q+3, 12/4=Q is an integer

Ans: E
_________________
If you found my post useful,

KUDOS
are much appreciated. Giving Kudos is a great way to thank and motivate contributors, without costing you anything.
Senior Manager
Senior Manager
avatar
P
Joined: 18 Jan 2018
Posts: 308
Location: India
Concentration: General Management, Healthcare
Schools: Booth '22, ISB '21, IIMB
GPA: 3.87
WE: Design (Manufacturing)
GMAT ToolKit User CAT Tests
Re: If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post 12 Jul 2019, 09:59
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?

n/4 reminder = 4 ,then n=4K+3 = 3,7,11,15,19
n/7 reminder= 1 , n = 7k+1 = 1,8,15,22

n = 15 , Option E
Manager
Manager
avatar
S
Joined: 06 Aug 2018
Posts: 98
Re: If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post 12 Jul 2019, 10:03
The first no. We encounter is 15

So next is 7*6
7*10+1
7*14+1
7*18+1
......
7*54+1

We have 15 such numbers (same can be done via 4)

E is correct

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 10 Nov 2018
Posts: 3
Re: If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post 12 Jul 2019, 10:04
The answer is option E

There are two methods to solve this question.

First method :

Look at the answer choices and observe that only number 15gives the required remainders when divided by 4amd 7

The second way is to find the pattern of such numbers.. Luckily no 15 is first such number.. The next will be 43...

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 10 Nov 2018
Posts: 3
Re: If n is a positive integer less than 400, what is the number of n such  [#permalink]

Show Tags

New post 12 Jul 2019, 10:05
The answer is option E

There are two methods to solve this question.

First method :

Look at the answer choices and observe that only number 15gives the required remainders when divided by 4amd 7

The second way is to find the pattern of such numbers.. Luckily no 15 is first such number.. The next will be 43...

Posted from my mobile device
GMAT Club Bot
Re: If n is a positive integer less than 400, what is the number of n such   [#permalink] 12 Jul 2019, 10:05

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

Display posts from previous: Sort by

If n is a positive integer less than 400, what is the number of n such

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne