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If x, y, and z are positive integers, is x+y divisible by 5? 1) x+z is

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If x, y, and z are positive integers, is x+y divisible by 5? 1) x+z is [#permalink]

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New post 22 Aug 2017, 01:22
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If x, y, and z are positive integers, is x+y divisible by 5?

1) x+z is divisible by 5
2) y+z is divisible by 5
[Reveal] Spoiler: OA

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Re: If x, y, and z are positive integers, is x+y divisible by 5? 1) x+z is [#permalink]

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Re: If x, y, and z are positive integers, is x+y divisible by 5? 1) x+z is [#permalink]

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New post 23 Aug 2017, 03:32
MathRevolution wrote:
If x, y, and z are positive integers, is x+y divisible by 5?

1) x+z is divisible by 5
2) y+z is divisible by 5


(1) tells us x,z can take (0,5),(5,0).... also no information about y..not sufficient

(2) tells us y,z can take (0,5),(5,0).... also no information about x..not sufficient

on combining
x,y can take (0,0) or (5,5) ...not sufficient

E
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Re: If x, y, and z are positive integers, is x+y divisible by 5? 1) x+z is [#permalink]

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New post 24 Aug 2017, 01:27
=> Consider 1) & 2)

x = 1, y = 1, z = 4 : x + y is not divisible by 5
x = 5, y = 5, z = 0 : x + y is divisible by 5

Ans: E
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Re: If x, y, and z are positive integers, is x+y divisible by 5? 1) x+z is [#permalink]

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New post 24 Aug 2017, 11:28
Q1. When the Q says x, y, z are integers, shouldn't we take all as different numbers but all the explanations here have considered x equal to y to reach to the answers. So is it that, unless explicitly defined as unique there is no need to take different values. Because the Q also doesn't say explicitly that x, y, z can take any value.

Q2. Also under the assumption that they are all different, would E still be the right answer, based on the following:
2+8 & 7+8 both divisible by 5 but 2+7 is not
5+0 & 10+0 both divisible by 5 and so is 5+10

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If x, y, and z are positive integers, is x+y divisible by 5? 1) x+z is [#permalink]

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New post 29 Aug 2017, 21:47
ravjai81 wrote:
Q1. When the Q says x, y, z are integers, shouldn't we take all as different numbers but all the explanations here have considered x equal to y to reach to the answers. So is it that, unless explicitly defined as unique there is no need to take different values. Because the Q also doesn't say explicitly that x, y, z can take any value.

Q2. Also under the assumption that they are all different, would E still be the right answer, based on the following:
2+8 & 7+8 both divisible by 5 but 2+7 is not
5+0 & 10+0 both divisible by 5 and so is 5+10


Answer to Q1
x, y, z might be same or x, y, z might be different.
The point is that there two answers.

Answer to Q2
The example you have shown are good enough to identify that both condition together are not sufficient.
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Last edited by MathRevolution on 06 Sep 2017, 20:47, edited 1 time in total.

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Re: If x, y, and z are positive integers, is x+y divisible by 5? 1) x+z is [#permalink]

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New post 30 Aug 2017, 00:10
Luckisnoexcuse wrote:
(1) tells us x,z can take (0,5),(5,0).... also no information about y..not sufficient
(2) tells us y,z can take (0,5),(5,0).... also no information about x..not sufficient
on combining
x,y can take (0,0) or (5,5) ...not sufficient
E


Hey mate, though your answer is correct, I would like to point out that 0 cannot be considered as the question stems says x,y, and z are positive integers. Appears Luckisnoexcuse got lucky!

Cheers!

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Re: If x, y, and z are positive integers, is x+y divisible by 5? 1) x+z is   [#permalink] 30 Aug 2017, 00:10
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