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Re: If y is an integer, is y^2 divisible by 4?
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06 Oct 2015, 05:37
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1. Since Y is even , it must have at least one factor of 2 . \(Y^{2}\)= Y*Y So Y^2 will have at least 2 powers of 2 i.e 2^2 . From each Y , we can factor out a 2. Hence, it will be divisible by 4=2^2
2. \(Y ^ {3}\) is divisible by 4 =2^2 Y^3 is divisible by 4 .So, Y^3 will contain 2^2 . Since , Y is an integer so each Y should contain at least a single factor of 2. Hence, \(Y^{2}\)should contain at least 2^2
So , answer is D
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Re: If y is an integer, is y^2 divisible by 4?
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06 Oct 2015, 06:34
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Bunuel wrote:
If y is an integer, is y^2 divisible by 4?
(1) y is even. (2) y^3 is divisible by 4.
Kudos for a correct solution.
Question : Is y^2 divisible by 4?
Statement 1: y is even. If y is even i.e. a multiple of 2 then y^2 will be a multiple of 2^2 i.e. 4, Hence SUFFICIENT
Statement 2: y^3 is divisible by 4. Since y^3 is divisible by 4 then y must be Even due to being an Integer hence y^2 will be a multiple of 2^2 i.e. 4, Hence SUFFICIENT
Answer: option D
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Re: If y is an integer, is y^2 divisible by 4?
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06 Oct 2015, 10:49
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Bunuel wrote:
If y is an integer, is y^2 divisible by 4?
(1) y is even. (2) y^3 is divisible by 4.
Kudos for a correct solution.
St1: y is even - Zero is also even so it could be 0 in this case 2,4 in any of those cases it's divisible by 4 SUFFICIENT St2: y is an even integer in this case because if it were odd odd*odd*odd is odd and not divisible by 4 - SUFFICIEINT
Answer (D)
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Question Type: Yes/No. This question asks: “Is y^2 divisible by 4.”
Given information in the question stem or diagram: y is an integer.
Statement 1: y is even. With a conceptual understanding of factors, you know that if y is an even number then y^2 will have to be a multiple of 4. If you want to quickly test this you can use some small even numbers. For example, if y = 2, then y^2=4; yes, that is divisible by 4. If y = 4, then y^2 = 16; this is also divisible by 4. Even 0, which is an even number, will work. 0^2 = 0; and yes, 0 is divisible by 4. This confirms what we already knew from our conceptual understanding: an even number when squared is a multiple of 4. The answer is either A or D.
Statement 2: y^3 is divisible by 4. For some, this may not seem sufficient at first glance. y^3 might be divisible by 4 while y^2 is not. For example, y could be the cube root of 4. However, if you leverage properly the information in the question stem (always so important!) then you know that “y is an integer.” So y cannot be the cube root of 4; it must be an integer. Once you have established that y must be an integer then the only way for y^3 to be divisible by 4 is for y to be an even number. In other words, it gives you the same information that you already found sufficient in Statement 1. Thus, the correct answer is D.
Note: This is another good example of “When one statement is easy, the other is hard/counterintuitive.” The first statement is relatively simple so you should be extra careful analyzing the second statement. As is often the case, the key with Statement 2 is to make sure you properly leverage the given information.
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Re: If y is an integer, is y^2 divisible by 4?
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19 Apr 2018, 00:40
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71% (01:26) correct 
