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# If x is an integer greater than 0, what is the remainder when x is div

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Re: If x is an integer greater than 0, what is the remainder when x is div [#permalink]
Bunuel
If x is an integer greater than 0, what is the remainder when x is divided by 4 ?

(1) The remainder is 3 when x + 1 is divided by 4.
(2) The remainder is 0 when 2x is divided by 4.

DS49502.01
OG2020 NEW QUESTION

#1
x= 6, 14 we get remainder 2 sufficeint
#2
remainder is 0 so x= 0 or x = 2,4
insfficient
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Re: If x is an integer greater than 0, what is the remainder when x is div [#permalink]
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Bunuel
If x is an integer greater than 0, what is the remainder when x is divided by 4 ?

(1) The remainder is 3 when x + 1 is divided by 4.
(2) The remainder is 0 when 2x is divided by 4.

DS49502.01
OG2020 NEW QUESTION

We need to determine the remainder when x is divided by 4.

Statement One Alone:

The remainder is 3 when x + 1 is divided by 4.

x + 1 can be values such as 3, 7, 11, 15, and so forth. Thus, x is 2, 6, 10, 14, etc..

When any of those values of x is divided by 4, the remainder is 2.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

The remainder is 0 when 2x is divided by 4.

2x can be values such as 4, 8, 12 ,16, and so forth. Thus, x is 2, 4, 6, 8, etc.

We see that 2/4 = 0 remainder 2 and 4/4 = 1 remainder 0.

Statement two alone is not sufficient to answer the question.

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Re: If x is an integer greater than 0, what is the remainder when x is div [#permalink]
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Hi All,

We're told that X is an INTEGER GREATER than 0. We're asked for the remainder when X is divided by 4. This question is based around some basic Arithmetic rules (and you can TEST VALUES to define the patterns involved). To start, here are the first several positive integers - and what happens when you divide by 4...

1/4 = 0r1
2/4 = 0r2
3/4 = 0r3
4/4 = 1r0
5/4 = 1r1
6/4 = 1r2
7/4 = 1r3
8/4 = 2r0
Etc.

(1) The remainder is 3 when (X + 1) is divided by 4.

Based on the pattern defined above, if we get a remainder of 3 when dividing (X+1) by 4, then removing the "+1" would move us one position 'up' in the pattern - meaning that the remainder when X/4 will ALWAYS equal 2. You can see this in a couple of examples:
IF...
X = 2, then (2+1)/4 = 0r3 and 2/4 = 0r2
X = 6, then (6+1)/4 = 1r3 and 6/4 = 0r2
Etc.
Fact 1 is SUFFICIENT

(2) The remainder is 0 when 2x is divided by 4.

Fact 2 asks us to focus on values that would create a remainder of 0. That will occur with any multiple of 4. However, Fact 2 asks us to consider "2X" and that does not necessarily mean that X is a multiple of 4...
IF...
X = 2, then (2)(2)/4 = 1r0 and 2/4 = 0r2
X = 4, then (2)(4)/4 = 2r0 and 4/4 = 1r0
Thus, the answer to the question could be 2 OR 0.
Fact 2 is INSUFFICIENT

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Re: If x is an integer greater than 0, what is the remainder when x is div [#permalink]
Let's put this in a simple algebra format -

Divider + Remainder = Dividend
Per the question:
Divider = 4
Dividend = x
consider Remainder as y

y + 4 = x
y = x - 4

Statement 1:
y = 3 when x + 1 is divided by 4
3 = x + 1 - 4
x = 6
Therefore, we can find the value of y. Sufficient.

Statement 2:
y = 0 when 2x is divided by 4
0 = 2x + 4
0 = x + 2
x = -2
Based on the question, x is always positive. Therefore, insufficient.

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Re: If x is an integer greater than 0, what is the remainder when x is div [#permalink]
The remainder is 3 when x + 1 is divided by 4.

x + 1 can be values such as 3, 7, 11, 15, and so forth. Thus, x is 2, 6, 10, 14, etc..

When any of those values of x is divided by 4, the remainder is 2.

Statement one alone is sufficient to answer the question.

Statement 2 :

The remainder is 0 when 2x is divided by 4.

2x can be values such as 4, 8, 12 ,16, and so forth. Thus, x is 2, 4, 6, 8, etc.

We see that 2/4 = 0 remainder 2 and 4/4 = 1 remainder 0.

Statement two alone is not sufficient to answer the question.

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Re: If x is an integer greater than 0, what is the remainder when x is div [#permalink]
Bunuel
If x is an integer greater than 0, what is the remainder when x is divided by 4 ?

(1) The remainder is 3 when x + 1 is divided by 4.
(2) The remainder is 0 when 2x is divided by 4.

DS49502.01
OG2020 NEW QUESTION

x>0 When x/4 Remainder=?

(1) x+1/4 Remainder=3. We can think for few numbers that could satisfy this equation only x=14 does justice to it. Sufficient.

(2) 2x/4 Remainder=0. x=8,16, etc. Not Sufficient

Hope that helps!
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Re: If x is an integer greater than 0, what is the remainder when x is div [#permalink]
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hemantbafna
Bunuel
If x is an integer greater than 0, what is the remainder when x is divided by 4 ?

(1) The remainder is 3 when x + 1 is divided by 4.
(2) The remainder is 0 when 2x is divided by 4.

DS49502.01
OG2020 NEW QUESTION

x>0 When x/4 Remainder=?

(1) x+1/4 Remainder=3. We can think for few numbers that could satisfy this equation only x=14 does justice to it. Sufficient.

(2) 2x/4 Remainder=0. x=8,16, etc. Not Sufficient

Hope that helps!

Hi hemantbafna,

With Fact 1, there are LOTS of different values for X that 'fit' the given information, including 2, 6, 10, 14, 18,....keep adding 4 to the total and you'll see some more. The reason why Fact 1 is sufficient is because ALL of those values for X lead to the SAME answer to the given question (re: what is the remainder when X is divided by 4?); the answer is ALWAYS '2.'

With Fact 2, the two values that you listed (X=8 and X=16) would lead to the SAME answer to the question (re: what is the remainder when X is divided by 4?); with these two examples, the answer is 0. You have to consider values that are NOT multiples of 4, such as 2, 6, 10, etc., (which give you an answer of '2') to prove that Fact 2 is insufficient.

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Re: If x is an integer greater than 0, what is the remainder when x is div [#permalink]
Bunuel
If x is an integer greater than 0, what is the remainder when x is divided by 4 ?

(1) The remainder is 3 when x + 1 is divided by 4.
(2) The remainder is 0 when 2x is divided by 4.

DS49502.01
OG2020 NEW QUESTION

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Re: If x is an integer greater than 0, what is the remainder when x is div [#permalink]
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