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If x, y, b and t are all positive integers, x = y/5 + 2 [#permalink]
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03 Sep 2015, 13:35
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If x, y, b and t are all positive integers, \(x = \frac{y}{5} + 2\), and \(t = \frac{b}{7} + 4\), is \(b(t^{xy})\) an even number? (1) 3.5t  2 is even (2) b/t is even Source:  Prep4GMAT iOS app
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Last edited by hideyoshi on 04 Sep 2015, 07:14, edited 1 time in total.



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Re: If x, y, b and t are all positive integers, x = y/5 + 2 [#permalink]
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03 Sep 2015, 19:20
hideyoshi wrote: If \(x,y,b\) and \(t\) are all positive integers, \(x = \frac{y}{5} + 2\), and \(t = \frac{b}{7} + 4\), is \(b(t^{xy})\) an even number?
1). \(3.5t  2\) is even 2). \(\frac{b}{t}\) is even When you specify the tag for source of "sourceother please specify", make sure to specify the source.x=y/5 +2, t=b/7 + 4, is \(b(t^{xy})\) = even ? Per statement 1, 3.5t2 = even > 7t/22=even > 7t/2 = even +2 = even > 7t = even*2 = even > t has to be even Also, from the given statements, t=b/7 + 4 > 7t=b+28 > even  28 = b > b = even . Thus for whatever values of x,y, \(bt^{xy}\) = even . Thus this statement is sufficient. Per statement 2, b/t=even > 2 cases possible (think of 6/3 or 4/2) case 1: b=even, t=odd case 2: b = even, t = even Thus, in either of the 2 cases, b = even and hence for whatever values of x,y, \(bt^{xy}\) = even . Thus this statement is sufficient. Both statements are sufficient individually, making D as the correct answer.



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Re: If x, y, b and t are all positive integers, x = y/5 + 2 [#permalink]
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03 Sep 2015, 23:14



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Re: If x, y, b and t are all positive integers, x = y/5 + 2 [#permalink]
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18 Feb 2016, 20:07
hideyoshi wrote: If x, y, b and t are all positive integers, \(x = \frac{y}{5} + 2\), and \(t = \frac{b}{7} + 4\), is \(b(t^{xy})\) an even number?
(1) 3.5t  2 is even (2) b/t is even
Source:  Prep4GMAT iOS app we need to remember that: ee=e oo=e. eo=o oe=o the question really asks whether t is even, since we know 100% that x and y are positive integers. thus, xy must be a positive integer, and the power will neither be negative nor fractional. 1. 3.5t2=e. only ee=e. this only means that 3.5t is even. it can be even only when t is even. sufficient. 2. b/t=e b=7t28 b/t=728/t. this is even. we know that even is only when oo. thus, it must be true that 28/t is odd. therefore, we know for sure that t must be even. (possible variations: 28/1; 28/2; 28/4  we can see that only the last one actually satisfies the condition) sufficient. D



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Re: If x, y, b and t are all positive integers, x = y/5 + 2 [#permalink]
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18 Feb 2016, 20:19
mvictor wrote: hideyoshi wrote: If x, y, b and t are all positive integers, \(x = \frac{y}{5} + 2\), and \(t = \frac{b}{7} + 4\), is \(b(t^{xy})\) an even number?
(1) 3.5t  2 is even (2) b/t is even
Source:  Prep4GMAT iOS app we need to remember that: ee=e oo=e. eo=o oe=o the question really asks whether t is even, since we know 100% that x and y are positive integers. thus, xy must be a positive integer, and the power will neither be negative nor fractional. 1. 3.5t2=e. only ee=e. this only means that 3.5t is even. it can be even only when t is even. sufficient. 2. b/t=e b=7t28 b/t=728/t. this is even. we know that even is only when oo. thus, it must be true that 28/t is odd. therefore, we know for sure that t must be even.(possible variations: 28/1; 28/2; 28/4  we can see that only the last one actually satisfies the condition) sufficient. D Hi, Although you are correct with your solution just two points on your solution .. 1) is \(b(t^{xy})\) an even number? this means any of the b or t, if even, is sufficient... and just not only t 2) related to the above point since b/t is even as per statement 2, this clearly means b is even and we dont require to see any further if t is even or not.. since b is even, the eq \(b(t^{xy})\) will be even
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