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

Question

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

prashanths · Accepted Answer

n is divided by 4, the remainder is 3 and when n is divided by 7, the remainder is 1

The numbers would be 15, 43, 71,.....
Its an AP with difference as 28. -> 15 + (n-1)*28

Among the options, if there are 13 numbers, the 13th number would be 
15 + 12*28 = 351.

The 14th number would be 15 + 13*28 = 379.

15th no = 407

14 numbers less than 400.

Option D

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santorasantu · Answer

IMO Answer is D

First number which satisfies the condition is 15, second number which satisfies the condition is 43,

sequence is 15,43,-----

15+(n-1)*28 < 400

n which satisfies the equation is 14.

SO, D

Kinshook · Answer

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

Numbers such that when n is divided by 4, the remainder is 3; 3,7,11,15,19,23,27...
Numbers such that when n is divided by 7, the remainder is 1; 1,8,15,22,29,36,43....

First n = 15
Next n = 15 + 7*4 = 15 +28 = 43
It is an arithmetic progression with a = 15 and d=28
Last such number < 400 = 15 + 13*28 = 379
n=14

IMO D

ancored · Answer

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=4k+3; 3,7,11, 15 ,...
n=7m+1; 1,8, 15 ,22...

Then
n=28t+15; 15....
400-15=385
385/28 = 13,...
Don't forget about 15.
13+1=14

IMO D

RusskiyLev · Answer

I found this question really tricky and spent some time thinking about the concept. 
What we are given: 
n is a positive integer  n > 0  and  n < 400  
 n / 4 = X + 3 
 n / 7 = Y + 1 
We need to find a number of possible "n"s.

From what we are given,  n  is divisable both by  4  and  7  with some remainder in both cases. Thus, the maximum number which satisfies condition  n / 4 = x + 3  is  n = 399  and for  n / 7 = Y + 1  it is  n = 394 . 
Since the number is divisable both by 4 and 7, we need to find out the LCM (least common multiple) of 4 and 7.  LCM of 4 and 7 is the least number smallest positive integer that is divisible by both 4 and 7 , which is  4 * 7 = 28 . 
Now let us find out how many times the number 28 is met in 400 to find the number of "n"s. Since 394 is the smallest of two possible numbers, we need to use it in the calculation:  394 / 28 = 14  and R (remainder) is 2. 
Thus, the answer is  D .

harry89 · Answer

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

Multiples of 4 having remainder 3 are

15, 43, 71 ..... 379 which is less than 400. These are following multiples of 7 ---> 2,6,10.....54. ---> this accounts to total 14 multiples.

IMO. the correct answer is (d)

nick1816 · Answer

n=1 (mod 7)
LCM(4,7)=28
Possibilities
n=1 mod 28
n=8 mod 28
n=15 mod 28
n=22 mod 28

Only 15=3 mod 4

Hence n= 15 mod 28
or n=28k+15, where k is non-negative integer

Maximum value k can take is  =13
Total values n can take= (13-0)+1=14

IMO D

Anki2609 · Answer

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 4 
22 --- 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 4

We 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)

GMATinsight · Answer

n = 4a+3 = {3, 7, 11,  15 , 19, 23, 27, 31, ...}
also
n = 7b+1 = {1, 8,  15 , 22, 29, 36, ...}

First common term = 15

Every terms after the first term will be at a gap of LCM (4 & 7) i.e. 28

Terms are {15, 43, 71....}

Last term = 15 + (n-1)*28 < 400

i.e. n-1 < 13.75
i.e. n < 14.75

i.e. Maximum value of n = 14

Answer: Option D

arora1 · Answer

Used online whiteboard for this question and took 3 mins. Uff!

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

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

Prep Toolkit

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