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If x is an integer greater than 0, what is the remainder when x is div
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Updated on: 09 Sep 2019, 06:05
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Bunuel wrote:
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
Target question:What is the remainder when x is divided by 4 ?
Statement 1: The remainder is 3 when x + 1 is divided by 4. ------ASIDE---------------------- 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 -------------------------------- We don't know how many times 4 divides into x+1. So, let's just say 4 divides into x+1 k times. So, we can write: x + 1 = 4k + 3 (for some integer k) Subtract 1 from both sides to get x = 4k + 2 Since 4k is a multiple of 4, we can see that x is 2 greater than some multiple of 4 So, when we divide x by 4, the remainder will be 2 Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The remainder is 0 when 2x is divided by 4. We can write: 2x = 4k (for some integer k) Divide both sides by 2 to get: x = 2k This tells us that x is an even integer. There are several values of x that satisfy statement 2. Here are two: Case a: x = 2. In this case, the answer to the target question is when we divide x by 4, the remainder will be 2 Case b: : x = 4. In this case, the answer to the target question is when we divide x by 4, the remainder will be 0 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers, Brent
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Re: If x is an integer greater than 0, what is the remainder when x is div
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26 Apr 2019, 06:11
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The question is asking "x is how much larger than a multiple of 4". If, from Statement 1, we know x+1 is 3 greater than a multiple of 4, then x itself must be 2 greater than a multiple of 4, so Statement 1 is sufficient.
Statement 2 tells us that 2x is divisible by 4, but that will be true any time x is even. So the remainder can be 0 or 2 when we divide x by 4, and Statement 2 is not sufficient. _________________
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Re: If x is an integer greater than 0, what is the remainder when x is div
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16 May 2019, 13:24
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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) 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
Re: If x is an integer greater than 0, what is the remainder when x is div
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01 Jul 2020, 15:11
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Expert Reply
hemantbafna wrote:
Bunuel wrote:
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,
While you have selected the correct answer, your explanation is incomplete.
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.