If the integer s is divided by 9, the remainder is 1. If s is divided

Question

If the integer s is divided by 9, the remainder is 1. If s is divided by 4, the remainder is 2. If s is between 30 and 90, what is the sum of all possible values of s?

(A) 46
(B) 72
(C) 82
(D) 128
(E) 132

rajatchopra1994 · Answer

Explanation:

Numbers are : 46 & 82

Sum = 46 +92 = 128

IMO-D

yashikaaggarwal · Answer

If the integer s is divided by 9, the remainder is 1. 
The set follow is = 10,19,28,37,46,55,64,73,82 
 
Among the set ( 10,19,28,37,46,55,64,73,82 )
If s is divided by 4, the remainder is 2.
the set = ( 10, 46, 82)

If s is between 30 and 90, Set S = 46 & 82

The sum of all possible values of s = 46+82 = 128

Answer is D

chipsy · Answer

First, we will find the first value of s which satisfies both condition i.e. remainder 1 when divided by 9 and remainder 2 when divided by 4.

10 is such number which satisfies the conditions.

Now, next number = 10+ (9*4) = 46
 next number = 46+ (9*4) = 82

as 30<s<90 , means only two numbers are in that range i.e. 46 and 82

Sum of all possible values of s = 46+ 82
 = 128

Option D

Chethan92 · Answer

When s is divided by 9, the remainder is 1.
When s is divided by 4, the remainder is 2.

We can now write,  \frac{9x+1}{4}  gives a remainder of 2.

The above equation is satisfied when x = 1, 5, 9...etc
The numbers are 10, 46, 82.

30<s<90 , i.e, 46+82 = 182.

D is the answer.

Babineaux · Answer

30 < s < 90

In first case s = 9q1 + 1;
The set is {37, 46, 55, 64, 73, 82};

In the second case s = 4q2 + 2;
The set is {34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86};

After satisfying all conditions set of possible values of s = {46, 82};

Hence required sum = 46 + 82 = 128

IMO ans is D.

gracie · Answer

s/9=q+1
s/4=p+2
→9q-4p=1
q=1;p=2
least value of s=10 no too low
product of divisors=36
10+36=46 yes
46+36=82 yes
82+36=118 no too high
46+82=128
D

aggvipul · Answer

S=9q+1
S=4q+2
By rule- S=36q+10
lsince, 30<S<90
S= 42 and 82
Sum= 128
Answer D

satya2029 · Answer

Find the first value that matches both the conditions
S=9Q+1
S=4P+2
S=10
Next Value will be 10+LCM(4,9)
=46
NEXT 46+LCM(4,9)
=46+36
=82
Since S is between 30 and 90
Desired value= 46+82
=128
D:)

sujoykrdatta · Answer

A remainder of 1 when divided by 9 is satisfied by 10 which also leaves remainder 2 when divided by 4.

Thus, the set of numbers after 10 will be obtained by adding the lcm of the divisors 4 and 9 ie 36

Thus, the numbers are 10, 10+36=46, 46+36=82

Required sum = 46+82=128

Answer D

If the integer s is divided by 9, the remainder is 1. If s is divided

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If the integer s is divided by 9, the remainder is 1. If s is divided

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