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If k is an even integer, what is the smallest possible value of k [#permalink]
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04 Nov 2016, 09:01
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If k is a positive even integer, what is the smallest possible value of k such that 3675*k is the square of an integer? A.3 B.9 C.12 D.15 E.20
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Re: If k is an even integer, what is the smallest possible value of k [#permalink]
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04 Nov 2016, 11:25
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stonecold wrote: If k is an even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?
A.3 B.9 C.12 D.15 E.20 3675*k= 7^2*5^2*3*k Since k is even and the integer should be a square. k=2^2*3=12 C Sent from my iPhone using GMAT Club Forum mobile app



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Re: If k is an even integer, what is the smallest possible value of k [#permalink]
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07 Nov 2016, 11:50
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stonecold wrote: If k is an even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?
A.3 B.9 C.12 D.15 E.20 If 3675*k is a perfect square, then its prime factorization must contain only even exponents. Let’s begin by prime factoring 3,675. 3675 = 25 x 147 = 5 x 5 x 49 x 3 = 5 x 5 x 7 x 7 x 3 = 5^2 x 7^2 x 3^1 We can see that 3,675 is not a perfect square because its prime factorization contains an odd exponent (that is, 3^1). If k only has to be an integer, then the smallest value k can be is 3, since 3675*k would be 5^2 x 7^2 x 3^2, a perfect square. However, since the requirement is that k must be an even integer, we need k to be divisible by an even perfect square (notice that 3675 doesn’t have any even prime factors). Since the smallest even perfect square is 2^2 = 4, the smallest possible value of k is 3 x 4 = 12, so that 3,675*k is a perfect square. In fact, if k = 12, then 3,675*k = 5^2 x 7^2 x 3^2 x 2^2, which is a perfect square. [Note: The smallest possible value of k such that 3675*k is the square of an integer is actually 0, since 3675*0 = 0, which is 0^2. To avoid this case, the problem should be stated as “If k is a positive even integer…such that 3675*k is the square of a positive integer?”] Answer: C
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Re: If k is an even integer, what is the smallest possible value of k [#permalink]
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07 Nov 2016, 12:42
ScottTargetTestPrep wrote: stonecold wrote: If k is an even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?
A.3 B.9 C.12 D.15 E.20 If 3675*k is a perfect square, then its prime factorization must contain only even exponents. Let’s begin by prime factoring 3,675. 3675 = 25 x 147 = 5 x 5 x 49 x 3 = 5 x 5 x 7 x 7 x 3 = 5^2 x 7^2 x 3^1 We can see that 3,675 is not a perfect square because its prime factorization contains an odd exponent (that is, 3^1). If k only has to be an integer, then the smallest value k can be is 3, since 3675*k would be 5^2 x 7^2 x 3^2, a perfect square. However, since the requirement is that k must be an even integer, we need k to be divisible by an even perfect square (notice that 3675 doesn’t have any even prime factors). Since the smallest even perfect square is 2^2 = 4, the smallest possible value of k is 3 x 4 = 12, so that 3,675*k is a perfect square. In fact, if k = 12, then 3,675*k = 5^2 x 7^2 x 3^2 x 2^2, which is a perfect square. [Note: The smallest possible value of k such that 3675*k is the square of an integer is actually 0, since 3675*0 = 0, which is 0^2. To avoid this case, the problem should be stated as “If k is a positive even integer…such that 3675*k is the square of a positive integer?”] Answer: C Absolutely Spot On.!! P.S=> Edited the Question.
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Re: If k is an even integer, what is the smallest possible value of k [#permalink]
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07 Nov 2016, 13:07
stonecold wrote: If k is a positive even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?
A.3 B.9 C.12 D.15 E.20 \(3675 = 3^1 * 5^2 * 7^2\) Now , is the most important part of this question K must be even ( negate options A, B and D ) W e are left with C and E Try one to confirm the answer... Let's try (E) \(20 = 2^2 * 5^1\) \(3675*20 = 2^2 * 3^1 * 5^3 * 7^2\) ( Can not square of an Integer ) So, Answer must be (C).... Double check to be sure  \(3675*12 = 2^2 * 3^2 * 5^2 * 7^2\) (Square of an Integer ) Hope this helps !!
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Re: If k is an even integer, what is the smallest possible value of k [#permalink]
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07 Nov 2016, 13:10
Abhishek009 wrote: stonecold wrote: If k is a positive even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?
A.3 B.9 C.12 D.15 E.20 \(3675 = 3^1 * 5^2 * 7^2\) Now , is the most important part of this question K must be even ( negate options A, B and D ) W e are left with C and E Try one to confirm the answer... Let's try (E) \(20 = 2^2 * 5^1\) \(3675*20 = 2^2 * 3^1 * 5^3 * 7^2\) ( Can not square of an Integer ) So, Answer must be (C).... Double check to be sure  \(3675*12 = 2^2 * 3^2 * 5^2 * 7^2\) (Square of an Integer ) Hope this helps !!
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Re: If k is an even integer, what is the smallest possible value of k [#permalink]
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14 Nov 2016, 15:25
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stonecold wrote: If k is a positive even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?
A.3 B.9 C.12 D.15 E.20 I feel like killing myself for choosing A. If k is a positive even integer EVEN digit...grrr....
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If k is an even integer, what is the smallest possible value of k [#permalink]
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10 Jan 2017, 10:29
stonecold wrote: If k is a positive even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?
A.3 B.9 C.12 D.15 E.20 3675=35*105 if k were odd, then 3 would give us 3*35*105=105^2 so we need an even multiple of 3 12 is only option 4*3*35*105)=(2*105)^2 12 C



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Re: If k is an even integer, what is the smallest possible value of k [#permalink]
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29 Apr 2017, 19:18
Here are my 2 cents on this one >
Given info => K is an even integer. 3675*k=square of an integer.
In a perfect square the power of each prime factor is an even number. Breaking down 3675*k=> 5^2*7^2*3*k => Perfect square. Now the general expression for k will be 3*(Anyprime)^even If the question had not stated that k is even => A would have been sufficient. But here as k is even => Minimum value of k=> 3*2^2 (why 2^2? => Beacuse 2 is the smallest positive even number ) Hence k=>2^2*3=>12
Hence C.
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Re: If k is an even integer, what is the smallest possible value of k [#permalink]
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01 May 2017, 14:10
Ugh, I fell into the trap of forgetting that k is even, and chose A: k=3. I need to remember to always double check the constraints!



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If k is an even integer, what is the smallest possible value of k [#permalink]
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03 Jan 2018, 07:17
sealberg wrote: Ugh, I fell into the trap of forgetting that k is even, and chose A: k=3. I need to remember to always double check the constraints! We all did my friend. We all did.
P.S > Here is the Link to the entire Mock series > https://gmatclub.com/forum/stonecolds ... 6040.html
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