If the positive integer x leaves a remainder of 2 when divided by 8,

Question

If the positive integer x leaves a remainder of 2 when divided by 8, what will the remainder be when x+9 is divided by 8?

A. 0
B. 1
C. 2
D. 3
E. 4

msk0657 · Answer

This is how I did...

x is a number and leaves a remainder of 2 when divided by 8

x = 8q+2 , here q is quotient.

Now asked to find x+9 values

Sub 8q+2 value in x+9 then we get 8q+11 and now divided this value by 8 , we get 3 as reminder ( 11/8).

gracie · Answer

if x/8 leaves a remainder of 2,
then (x+6)/8 leaves a remainder of 0,
and (x+9)/8 leaves a remainder of 3

Divyadisha · Answer

x/8 leaves a reminder of 2

(x+9)/8 can be written as x/8 +9/8

x/8 leaves a reminder of 2 and 9/8 will leave a reminder of 1

Total reminder= 2+1= 3

KarishmaB · Answer

"If the positive integer x leaves a remainder of 2 when divided by 8" - means from x balls we make groups of 8 balls each and are left with 2 balls. When we bring another 9 balls in the mix, we will make 1 more group of 8 balls and now we will have 3 balls remaining. Answer (D) Check this concept here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/04 ... unraveled/ https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/04 ... y-applied/

abani · Answer

x = 8q +2
x +9 =8q+2+9
8q+11 this can be furthur written as 8q +8 +3 = 8(q+1)+3

Remainder 3. Ans D.

PolarisTestPrep · Answer

Hey guys,

One way to think about this that is interesting is that multiples of a number tend to repeat their units in a pattern

Take the multiples of 8 as an example:

8 16 24 32 40 48 56 64 72 80 88 96 etc...

As you can see, the multiples of 8 end with the units number repeating in a pattern 8 6 4 2 0 8 6 4 2 0 etc...

If the remainder is 2 that means there must be 2 left over after the number is divided by 8. That means the number is a multiple of 8 plus 2

It could be either 10, 18, 26, 34, 42, 50, etc

In each of those numbers, the remainder would be two if you were to divide by eight

Now what if you added 9 to those numbers?

19, 27, 35, 43, 51, 59

Each of these numbers has a remainder of 3 when divided by 8

The answer is D

Just another way of looking at it

BrushMyQuant · Answer

If the positive integer x leaves a remainder of 2 when divided by 8

Theory: Dividend = Divisor*Quotient + Remainder

x -> Dividend
8 -> Divisor
a -> Quotient (Assume)
2 -> Remainders
=> x = 8*a + 2 = 8a + 2

what will the remainder be when x+9 is divided by 8

x + 9= 8a + 2 + 9 = 8a + 8 + 3 = 8*(a+1) + 3

=> x+9 when divided by 8 gives 3 remainder

So,  Answer will be D 
Hope it helps!

Watch the following video to learn the Basics of Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

If the positive integer x leaves a remainder of 2 when divided by 8,

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