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

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LinaNY
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When 100 is divided by positive integer x, the remainder is [#permalink] When 100 is divided by positive integer x, the remainder is   22 Sep 2013, 11:01
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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
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kusena
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Re: When 100 is divided by positive integer x, the remainder is [#permalink] When 100 is divided by positive integer x, the remainder is   22 Sep 2013, 11:19
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LinaNY wrote:
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


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
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Re: When 100 is divided by positive integer x, the remainder is [#permalink] When 100 is divided by positive integer x, the remainder is   23 Sep 2013, 00:34
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LinaNY wrote:
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


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.
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Re: When 100 is divided by positive integer x, the remainder is [#permalink] When 100 is divided by positive integer x, the remainder is   22 Sep 2013, 11:29
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Kusena, why is 98 divisible by 2? if you are using the formula 100=xq+2, then xq=98? what am I missing here?
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kusena
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Re: When 100 is divided by positive integer x, the remainder is [#permalink] When 100 is divided by positive integer x, the remainder is   22 Sep 2013, 12:32
LinaNY wrote:
Kusena, why is 98 divisible by 2? if you are using the formula 100=xq+2, then xq=98? what am I missing here?



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...
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Re: When 100 is divided by positive integer x, the remainder is [#permalink] When 100 is divided by positive integer x, the remainder is   22 Sep 2013, 13:17
thanks, kusena. I totally overlooked that 98 will be a multiple of x
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Re: When 100 is divided by positive integer x, the remainder is [#permalink] When 100 is divided by positive integer x, the remainder is   21 Jun 2016, 22:36
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.
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Re: When 100 is divided by positive integer x, the remainder is [#permalink] When 100 is divided by positive integer x, the remainder is   21 Jun 2016, 23:13
LinaNY wrote:
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



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.
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Re: When 100 is divided by positive integer x, the remainder is [#permalink] When 100 is divided by positive integer x, the remainder is   18 Oct 2016, 11:16
Give me an algebraic Solution
Anyone ?
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When 100 is divided by positive integer x, the remainder is [#permalink] When 100 is divided by positive integer x, the remainder is   Updated on: 25 Oct 2018, 18:23
LinaNY wrote:
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


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

Originally posted by gracie on 08 Dec 2017, 11:44.
Last edited by gracie on 25 Oct 2018, 18:23, edited 1 time in total.
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Re: When 100 is divided by positive integer x, the remainder is [#permalink] When 100 is divided by positive integer x, the remainder is   25 Oct 2018, 09:27
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LinaNY wrote:
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


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
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Re: When 100 is divided by positive integer x, the remainder is [#permalink] When 100 is divided by positive integer x, the remainder is   26 Oct 2018, 08:12
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LinaNY wrote:
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

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
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When 100 is divided by positive integer x, the remainder is [#permalink] When 100 is divided by positive integer x, the remainder is   28 Dec 2023, 03:53
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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!

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When 100 is divided by positive integer x, the remainder is [#permalink]
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