When 100 is divided by positive integer x, the remainder is

Question

When 100 is divided by positive integer x, the remainder is 2. What is the remainder when 198 is divided by x?
A) 2
B) 3
C) 4
D) 6
E) 8

Bunuel · Accepted Answer

When 100 is divided by positive integer x, the remainder is 2 --> 100 is 2 greater than a multiple of x, so 98 IS a multiple of x.

198 = 100 + 98 = 100 + {a multiple of x}, thus the remainder when 198 is divided by x is 2.

Answer: A.

kusena · Answer

if100/x leaves a reminder 2 then (100-2) i.e. 98 is divisible by x
So (100+98)/x leaves a reminder rem(100/x)+rem(98/x)=> 2+0=2

Ans 2..Hope it helps

LinaNY · Answer

Kusena, why is 98 divisible by 2? if you are using the formula 100=xq+2, then xq=98? what am I missing here?

kusena · Answer

Yes, i am using the formula 100=x*quotient+2(remainder)

100-2=x*quotient
98=x*Quotient
so 98 is a multiple of X,hence the remainder will be zero when 98 is divided by x...

LinaNY · Answer

thanks, kusena. I totally overlooked that 98 will be a multiple of x

ajdse22 · Answer

Ok ,, 
We can do it in two ways. 
1) Select a factor for 98 , since 2 is a remainder. So one factor is 7 and another is 49
198/7 = > quotient of 28 and remainder of 2
198/49 => quotient of 4 and remainder of 2.. and likewise. infact when the question says what is the remainder, it is intuitively like we should get only one remainder no matter what the divisor is. So we can take any divisor of 98 and arrive at the same answer. 98*2 = 196 and remainder of 2!

2) Algebra -- 
98 = x*p+0
198 = 100+98
=> 198 = x*p + 2 + x*p
=> 198 = 2(x*p)+2.. Here we go with remainder of 2.

adiagr · Answer

100 can be written as:

100 = ax+2; where a is any integer not equal to zero.

This means ax = 98

100+98 = ax+2+ax
 198 = 2ax+2

when 198 is divided by x, it cane be seen from above that remainder would be 2.

A is the answer.

stonecold · Answer

Give me an algebraic Solution 
Anyone ?

gracie · Answer

let x=100-2=98
198/98 leaves a remainder of 2
A

ScottTargetTestPrep · Answer

One possible value of x is 98. , Using that value for x, the remainder of 198/98 is 2.

Alternate Solution:

Since the remainder when 100 is divided by x is 2, 98 is divisible by x. Since 98 is divisible by x, 98*2 = 196 is also divisible by x. Since 196 is divisible by x, 198 will produce a remainder of 2 when divided by x.

Answer: A

Abhishek009 · Answer

Least possible value of x = 98 ( as 100 divided by 98 remainder will be 2)

198 divided by 98 remainder will be 2, Thus Answer must be (A) 2

BrushMyQuant · Answer

When 100 is divided by positive integer x, the remainder is 2. What is the remainder when 198 is divided by x?
 
Let's solve the problem using two methods:

Method 1: Substitution

When 100 is divided by positive integer x, the remainder is 2. 
Let x = 98, as 100 when divided by 98 will give us 2 remainder

What is the remainder when 198 is divided by x? 
=> Remainder of 198 divided by 98 = 2

So,  Answer will be A

Method 2: Algebra

When 100 is divided by positive integer x, the remainder is 2.

Dividend = Divisor * Quotient + Remainder

=> 100 = x*k + 2 (where k is the quotient)
=> 100 = xk + 2

What is the remainder when 198 is divided by x?

=> 198 = 200 - 2 = 2*100 - 2 = 2*(xk + 2) - 2 = 2xk + 4 - 2 = 2xk + 2
=> 198 when divided by x gives 2k as the quotient and 2 as the remainder

So,  Answer will be A 
Hope it helps!

Watch the following video to MASTER Remainders

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

bumpbot · Answer

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When 100 is divided by positive integer x, the remainder is

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