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If x, y, b and t are all positive integers, x = y/5 + 2

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If x, y, b and t are all positive integers, x = y/5 + 2 [#permalink]

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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

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Last edited by hideyoshi on 04 Sep 2015, 06:14, 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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New post 03 Sep 2015, 18:20
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 "source-other please specify", make sure to specify the source.

x=y/5 +2,
t=b/7 + 4,

is \(b(t^{xy})\) = even ?

Per statement 1, 3.5t-2 = even ---> 7t/2-2=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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New post 03 Sep 2015, 22:14
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


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

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New post 18 Feb 2016, 19:07
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:
e-e=e
o-o=e.
e-o=o
o-e=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. 3.5t-2=e.
only e-e=e. this only means that 3.5t is even. it can be even only when t is even.
sufficient.

2. b/t=e
b=7t-28
b/t=7-28/t.
this is even.
we know that even is only when o-o.
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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New post 18 Feb 2016, 19:19
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:
e-e=e
o-o=e.
e-o=o
o-e=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. 3.5t-2=e.
only e-e=e. this only means that 3.5t is even. it can be even only when t is even.
sufficient.

2. b/t=e
b=7t-28
b/t=7-28/t.
this is even.
we know that even is only when o-o.
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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Re: If x, y, b and t are all positive integers, x = y/5 + 2 [#permalink]

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Re: If x, y, b and t are all positive integers, x = y/5 + 2   [#permalink] 19 Oct 2017, 03:00
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