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If a, b, c are consecutive positive integers and a < b < c, which of
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Updated on: 18 Dec 2017, 22:06
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If a, b, c are consecutive positive integers and a < b < c, which of the following must be true? I. c  a = 2 II. abc is an even integer III. (a + b + c)/3 is an integer A. I B. II C. I and II D. II and III E. I, II and III OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/ifabandc ... 44907.html
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Originally posted by Lolaergasheva on 07 Feb 2011, 22:23.
Last edited by Bunuel on 18 Dec 2017, 22:06, edited 3 times in total.
Renamed the topic, edited the question and added the OA.



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Re: If a, b, c are consecutive positive integers and a < b < c, which of
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07 Feb 2011, 22:58
If a, b, c are consequitive positive integers and a<b<c, which of the following must be true? 1. ca=2 2. abc is an even integer 3. (a+b+c) /3 is an integer 1. a=a b=a+1 c=a+2 ca=a+2a=2. Correct 2. abc a can be either even or odd if a=even; abc=even; if a=odd,b=even; abc=even Rule: multiple of any number of integers if atleast once multiplied by an even number will result in even. even*even=even even*odd=even Correct 3. (a+b+c) /3 is an integer Again; a=a b=a+1 c=a+2 a+b+c=(a+a+1+a+2)=3a+3 3a is always divisible by 3 3 is divisible by 3. Thus "3a+3" is also divisible by 3. Rule: if integer x is divisible by n and integer y is divisible by n then; x+y must be divisible by n Correct. Ans : "E"
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Re: If a, b, c are consecutive positive integers and a < b < c, which of
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08 Feb 2011, 00:22
The sum of three consecutive numbers will always be divisible by 3 <<< It's a helpful result. You might want to commit it to your memory
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Re: If a, b, c are consecutive positive integers and a < b < c, which of
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08 Feb 2011, 02:48
Lolaergasheva wrote: If a, b, and c are consecutive positive integers and a<b<c, which of the following must be true? 1. ca=2 2. abc is an even integer 3. (a+b+c) /3 is an integer
A. 1 B. 2 c. 1 and 2 d. 2 and 3 e. 1, 2 and 3 1. ca=2 > a, b, c are consequitive positive integers and a<b<c then c=a+2 > ca=2. So this statement is always true; 2. abc is an even integer > out of any 3 consecutive integers at least one must be even thus abc=even. So this statement is also always true; 3. (a+b+c)/3 is an integer > the sum of odd number of consecutive integers is ALWAYS divisible by that odd number. So this statement is also always true. Or: (a+b+c)/3=(a+a+1+a+2)/3=(3a+3)/3=a+1=integer. Answer: E. AmrithS wrote: The sum of three consecutive numbers will always be divisible by 3 <<< It's a helpful result. You might want to commit it to your memory Not only that: • If \(k\) is odd, the sum of \(k\) consecutive integers is always divisible by \(k\). Given \(\{9,10,11\}\), we have \(k=3\) consecutive integers. The sum of 9+10+11=30, therefore, is divisible by 3. • If \(k\) is even, the sum of \(k\) consecutive integers is never divisible by \(k\). Given \(\{9,10,11,12\}\), we have \(k=4\) consecutive integers. The sum of 9+10+11+12=42, therefore, is not divisible by 4. • The product of \(k\) consecutive integers is always divisible by \(k!\), so by \(k\) too. Given \(k=4\) consecutive integers: \(\{3,4,5,6\}\). The product of 3*4*5*6 is 360, which is divisible by 4!=24.
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Re: If a, b, c are consecutive positive integers and a < b < c, which of
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18 Dec 2017, 22:07




Re: If a, b, c are consecutive positive integers and a < b < c, which of
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18 Dec 2017, 22:07






