When x is divided by 10, the quotient is y with a remainder of 4. If x

Question

When x is divided by 10, the quotient is y with a remainder of 4. If x and y are both positive integers, what is the remainder when x is divided by 5?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

Chethan92 · Answer

X = 10Y+4.
When X is divided by 5, then X= 2Y+4. Hence 4 is the remainder.

NandishSS · Answer

x=10y+r ==> 10y+4

If x is divided by 5 then the remainder is 4

Hence E

CounterSniper · Answer

can be written as 
x=10y+4
the following values are possible 
x=14,24,34,44,54...(essentially a unit digit of 4)
all of the above values when divided by 5 gives 4 as its remainder.
E

Abhishek009 · Answer

x = 10y + 4

Plug in some value of y ( say y = 1)

Thus, x = 10 + 4 => 14

Now, When xy/5 = 14*1/5 = Remainder 4, Answer must be (E) 4

KSBGC · Answer

Approach 1:

\frac{x}{10} = y + 4

x = 10y + 4

Now we have to divide x by 5 .

10y is divisible by 5 but 4 is not. Thus 4 is remainder.

Approach 2 :

probable value of x.

x could be 14 as per the condition stated in the question.

\frac{14}{5} = 5*2 + 4

4 is remainder here.

The best answer is E.

JeffTargetTestPrep · Answer

We can create the equation:

x = 10y + 4

So when x is divided by 5 we have:

(10y + 4)/5 = 2y + 4/5, so the remainder is 4.

Answer: E

Kinshook · Answer

Given: When x is divided by 10, the quotient is y with a remainder of 4.
Asked: If x and y are both positive integers, what is the remainder when x is divided by 5?

When x is divided by 10, the quotient is y with a remainder of 4.
x = 10y + 4

x = 5(2y) + 4

IMO E

dimri10 · Answer

I usually pick numbers:
14/10= 1. + R of 4
24/10=2 + R of 4

14/5 R is 4 24/5 R is 4.

https://gmatclub.com/static/posted_from.png     Posted from    GMAT ToolKit

I believe that when a number is divided by 10 the reminder after dividing by 5 will be the same

BrentGMATPrepNow · Answer

APPROACH #1 : Test a possible value of x
When it comes to remainders, we have a nice property 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.

So, from the given information, the possible values of x are: 4, 14, 24, 34, 44, 54,....
If you divide any of these possible x-values by 5, you'll always get a remainder of 4.

Answer: E

APPROACH #2 : Use algebra
There's a nice rule that says, "  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

From the given information we can write: x = 10y + 4
We can rewrite this as: x = (  5  )(2x) + 4
We know that (  5  )(2x) is a multiple of  5 , which means (  5  )(2x)  + 4  is   4 MORE THAN   a multiple of  5 
So, when we divide (  5  )(2x) + 4 by  5 , the remainder will be  4

Answer: E

RELATED VIDEO 
 https://www.youtube.com/watch?v=XCxgIR042tE

BrushMyQuant · Answer

When x is divided by 10, the quotient is y with a remainder of 4

Theory: Dividend = Divisor*Quotient + Remainder

x -> Dividend
10 -> Divisor
y -> Quotient (Assume)
4 -> Remainders
=> x = 10*y + y = 10y + 4

what is the remainder when x is divided by 5

x = 10y + 4
Remainder of x by 5 = Remainder of 10y + 4 by 5 = Remainder of 10y by 5 + Remainder of 4 by 5 = 0 + 4 = 4

So,  Answer will be E 
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 x is divided by 10, the quotient is y with a remainder of 4. If x

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When x is divided by 10, the quotient is y with a remainder of 4. If x

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