When positive integer x is divided by 20, the remainder is 8. What is

Question

When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?

A. 1
B. 3
C. 5
D. 8
E. Cannot be determined

rohit8865 · Answer

since x is positive and 20 is multiple of 5 ,
we can divide 8 by 5 to get 3 remainder

Ans B

BrentGMATPrepNow · Answer

There's a nice rule that say, "  If N divided by D equals Q with remainder R, then N = DQ + R  "
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

In this case, we aren't told how many times 20 divides into x, but this isn't a problem. 
Let's just say that 20 divides into x k times. 
In other words,  x divided by 20 equals k with remainder 8 
Applying the above   rule  , we can then say: x = 20k + 8 for some positive integer k

What is the remainder when x is divided by 5?   
We know that: x = 20k + 8 
Rewrite as: x =  20k + 5  +  3  
And the factor to get: x =    5  (4k + 1 ) +  3 
So, we can see that  x is  3  greater than some multiple of   5   
This tells us that, if we divide x by   5  , the remainder will be  3

Answer: B

Cheers,
Brent

Abhishek009 · Answer

Lest possible value of x = 28.

Is, 3
  
Hence, correct aswer must be (B) 3

warriorguy · Answer

Isn't least possible value 8 when quotient is 0

BrentGMATPrepNow · Answer

Another approach:

When it comes to remainders, we have a nice rule that says: 
  If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.    
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

When positive integer x is divided by 20, the remainder is 8.   
So, the possible values of x are: 8, 28, 48, 68, 88,... 
Let's  test  a few values

8 divided by 5 equals 1 with remainder  3 
28 divided by 5 equals 5 with remainder  3 
48 divided by 5 equals 9 with remainder  3 
68 divided by 5 equals 13 with remainder  3 
88 divided by 5 equals 17 with remainder  3 
.
.
.
It certainly LOOKS like the remainder will always be  3

Answer: B

Cheers,
Brent

awdxzs · Answer

To add to this least possible value of x is 8 not 28.

Sent from my iPad using  GMAT Club Forum mobile app

Mo2men · Answer

You are correct.

x=20q +8

When q=0......x=8 when divided by 5 the reminder is 3.

Abhishek009 · Answer

Admit that its 8...

tapabrata · Answer

When x is divided by 20, the remainder is 8.
therefore x is of the form 20k+8 where k is an integer.

so x=20k+8=20k+5+3=5(4k+1)+3

When x is divided by 5, the component 5(4k+1) is divisible by 5. Hence remainder when x is divided by 5 = remainder(3/5) = 3.

Answer B

ehsan090 · Answer

check least possible value for which x results in remainder 8 
28/20 results in remainder 8
then divide 28/5 the result is 3 
choice B
**Experts Please respond as I am a beginner

ScottTargetTestPrep · Answer

We can create the equation:

x/20 = Q + 8/20

x = 20Q + 8

When 20Q + 8 is divided by 5 we have:

(20Q + 8)/5 = 4Q + 8/5

Since 8/5 = 1 3/5, the remainder is 3.

Alternate Solution:

Since we have a remainder of 8 when x is divided by 20, x could equal 28. When we divide 28 by 5, the quotient is 5 with a remainder of 3.

Answer: B

SidKan · Answer

since x is positive and 20 is multiple of 5 ,
we can divide 8 by 5 to get 3 remainder

Ans B

BrushMyQuant · Answer

When positive integer x is divided by 20, the remainder is 8

Theory: Dividend = Divisor*Quotient + Remainder

x -> Dividend
20 -> Divisor
a -> Quotient (Assume)
8 -> Remainders
=> x = 20*a + 8 = 20a + 8

What is the remainder when x is divided by 5

x = 20a + 8 = 5*4a + 5 + 3 = 5*(4a+1) + 3

=> x when divided by 5 gives 3 remainder

So,  Answer will be B 
Hope it helps!

Watch the following video to learn the Basics of Remainders

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

bumpbot · Answer

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When positive integer x is divided by 20, the remainder is 8. What is

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