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If x, y, and z are consecutive integers and x < y < z, which of the fo
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Updated on: 19 Jan 2020, 21:24
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If x, y, and z are consecutive integers and x < y < z, which of the following must be true? I. xyz is even II. x + y + z is even III. (x + y)(y + z) is odd A. none B. I only C. II only D. I and II only E. I and III only
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Originally posted by Mozart721 on 19 Jan 2020, 15:39.
Last edited by Bunuel on 19 Jan 2020, 21:24, edited 2 times in total.
Renamed the topic and edited the question.



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Re: If x, y, and z are consecutive integers and x < y < z, which of the fo
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19 Jan 2020, 20:50
Mozart721 wrote: If x,y, and z are consecutive integers and x < y < z, which of the following must be true?
I) xyz is even II) x+y+z is even III)(x+y)(y+z) is odd Please post the answer choices too



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Re: If x, y, and z are consecutive integers and x < y < z, which of the fo
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19 Jan 2020, 20:56
Sorry for my mistake. I already posted the options. Thanks for the message.
Posted from my mobile device



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Re: If x,y, and z are consecutive integers and x < y < z
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19 Jan 2020, 22:06
Given that x < y < z, where x, y, and z are consecutive integers. In the first case, z =4, y=3, x = 2
I) xyz = 2*3*4 =even II) x+y+z = 2 + 3 +4 = Odd III) (x+y)(y+z) = (2 +3) * (3+4) = 5*7 = Odd
In the second case, z =5, y=4, x = 3 I) xyz = 3*4*5 =even II) x+y+z = 3 +4+ 5 = Even III) (x+y)(y+z) = (3 +4) * (4+5) = 7*9 = Odd
In both cases, (I), and (III) are true.(E)



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Re: If x, y, and z are consecutive integers and x < y < z, which of the fo
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19 Jan 2020, 22:56
If x, y, and z are consecutive integers and x < y < z, which of the following must be true?
I. xyz is even II. x + y + z is even III. (x + y)(y + z) is odd
We know that x,y,z are integers that are consecutive. What we should know next is that there are 3 cases to consider in this question. (because there is a possibility that the middle number would be even, odd, or even zero)
1. even, odd, even 2. odd, even, odd 3. 1,0,1
For me, I believe that input the number is the easiest way to solve this question. This is because we can see that the question I,II,III are all about +,,*,/ which are not that complicated, so input number could be the right way to do. My input number will be 1. even, odd, even = 2,3,4 2. odd, even, odd = 1,2,3 3. 1,0,1
I. xyz is even 1. 2*3*4 = 24 even 2. 1*2*3 = 6 even 3. 1*0*1 = 0 even Then I is OK
II. x + y + z is even 1. 2+3+4 = 9 odd The question ask about "MUST be true" which means that every cases must suffice. So we dont have to waste time calculate other options Then II is NOT OK
III. (x + y)(y + z) is odd 1. (2+3)(3+4) = 5*7 = 35 odd 2. (1+2)(2+3) = 3*5 = 15 odd 3. (1+0)(0+1) = 1*1 = 1 odd Then III is OK
So I,III is OK then we choose E.
More tricks We may be able to calculate more 20+ secs faster if we can remember these patterns since we may not waste time to calculate or input simple numbers  even * any integers = even (because there is gonna be 2 as factors for sure so that the product will be even) This could help us be able to skip question "I" since we know that there is even integer for sure in the answer.  same type (eveneven, oddodd) that is + or  will have even even + even = even odd + odd = even but different type will have odd even + odd = odd odd  even = odd  But in the end, to input could be a very effective strategy in these kind of questions and not waste that much time.



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Re: If x, y, and z are consecutive integers and x < y < z, which of the fo
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20 Jan 2020, 00:35
I don't get one thing. The question is saying consecutive integers, Not just even consecutive integers. So we can select 1,3 and 5. Then xyz=15 which is odd.



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Re: If x, y, and z are consecutive integers and x < y < z, which of the fo
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20 Jan 2020, 00:39
Hea234ven wrote: I don't get one thing. The question is saying consecutive integers, Not just even consecutive integers. So we can select 1,3 and 5. Then xyz=15 which is odd. "Consecutive integers" ALWAYS mean integers that follow each other in order with common difference of 1: ... x3, x2, x1, x, x+1, x+2, .... For example: 7, 6, 5 are consecutive integers. 2, 4, 6 ARE NOT consecutive integers, they are consecutive even integers. 1, 3, 5 ARE NOT consecutive integers, they are consecutive odd integers.
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Re: If x, y, and z are consecutive integers and x < y < z, which of the fo
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20 Jan 2020, 00:43
Hea234ven wrote: I don't get one thing. The question is saying consecutive integers, Not just even consecutive integers. So we can select 1,3 and 5. Then xyz=15 which is odd. 1. Consecutive integers = ...,3,2,1,0,1,2,3,... 2. Consecutive even integers = ...,4,2,0,2,4,... 3. Consecutive odd integers = ...5,3,1,1,3,5,... So the question is saying " Consecutive integers" which means that it could be ...,3,2,1,0,1,2,3,... we CAN NOT select 1,3,5 since 1,3,5 are " Consecutive ODD integers" Not sure if its help?




Re: If x, y, and z are consecutive integers and x < y < z, which of the fo
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20 Jan 2020, 00:43






