When positive integer x is divided by 44, the remainder is 28

Question

When positive integer x is divided by 44, the remainder is 28. When positive integer y is divided by 22, the remainder is 14. If N = x+y, what is the remainder when N is divided by 11?

A) 1
B) 3
C) 5
D) 7
E) 9

*kudos for all correct solutions

chetan2u · Accepted Answer

Good Question Brent..
 
When x is divided by 44, remainder is 28...
So the number x is 44t+28, where t is integer..

When y is divided by 22, remainder is 14..
So the number y is 22s+14, where s is integer..
 
N=x+y = 44t+28+22s+14
So when N is divided by 11,  \frac{44t+22s+42}{11} 
44t and 22s are div by 11..
42=11*3+9..
So 9 is the remainder

E

rohit8865 · Answer

x = 44a+28( a = any integer)
Let a =1 then x = 44+28= 72
similarly 
y=22b+14 (b=any integer)
let b=1
then y= 36

thus N=x+y =72+36=108
108/11 = 9 9/11
thus 9is correct answer

ans E

origen87 · Answer

x=44a+28;y=14+22b
For a=1 and b=1 
x=72,y=36
n=x+5=108
remainder-9

gracie · Answer

least values of x and y are 28 and 14 respectively
x+y=42=N
N/11 gives a remainder of 9
E

Hatakekakashi · Answer

remainder 28 when divided by 44

so 44a + 28

remainder 14 when divided by 22

so 22b + 14

now N = x+y

44a + 22b + 42

N/11

as we know 44 and 22 are divisible by 11 only 42 is remaining

42/11 remainder = -2 or 9

44- 2 = 42
33+9 = 42

E

susheelh · Answer

HI!

Did it by number picking

Possible value of x = 28, 72, 100...
Possible values of y = 14, 36, 58....

Since there can be only one unique solution, add to find the smallest possible value of n = 28 + 14 = 42. Remainder of 42/11 = 9

Correct answer: E

Is the Kudos for correct solution still valid?

Abhishek009 · Answer

Let  x = 28  and  y = 14

So,  N = 28 + 14  =>  42

\frac{N}{11} = 11*3 + 9 , Thus Answer must be (E) 9

jotapepe · Answer

Two equations: 
 
(1)  x  = k +28 --->  x= 44k+28 
 44

Applying same logic to second equation: 
 
(2) y = 22k +14

Substitute into the provided equation N = x+y

= 44k + 28 + 22k +14

= 66k + 42

66k + 42  = ? 
 11

At this point I saw that 66 is divisible by 11 so I looked for the remainder when 42 is divided by 11.  Ans. 9

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When positive integer x is divided by 44, the remainder is 28

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When positive integer x is divided by 44, the remainder is 28

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