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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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03 Sep 2015, 13:35
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Question Stats:

66% (02:34) correct 34% (02:01) wrong based on 71 sessions

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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
[Reveal] Spoiler: OA

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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 "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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03 Sep 2015, 23:14
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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if-r-s-and-t-are-all-positive-integers-what-is-the-136746.html
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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:
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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Joined: 02 Aug 2009
Posts: 5724
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:
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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19 Oct 2017, 04:00
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Re: If x, y, b and t are all positive integers, x = y/5 + 2   [#permalink] 19 Oct 2017, 04:00
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