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If X, Y and Z are three integers...

by CANDOGIRL » Tue Feb 09, 2010 6:11 pm
If X, Y and Z are three integers, are they consecutive integers?
1. z=x+2
2. None of the three integers are multiples of 3.

Statement 1) clearly is insufficient. With Statement 2) am I supposed to rule out negative integer and 0 possibilities? For instance, -2, -1, 0 would be yes, but 4, 7, 8 would be no. Since the question does NOT indicate that they are positive integers, how am I supposed to know that the rule (in any set of 3 consecutive integers, one of three will be a multiple of 3) applies?

The answer is supposed to be B. Any advice?
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by papgust » Tue Feb 09, 2010 9:19 pm
Statement II:

Yes, we need to consider negative integers as well because there is no mention of positive or negative specifically. However, i doubt whether we should ignore 0 in this scenario. I presume that we need to consider 0 as well.

None of the three integers are multiples of 3 - List some multiple of 3 both -ve and +ve for your convenience.

-9, -6, -3
3, 6, 9

Consecutive integers are (... -2, -1, 0, 1, 2, 3 ... ). All integers are evenly spaced with difference of 1.
Consecutive Odd integers are (... -3, -1, 1, 3, 5 ...). All integers are evenly spaced with difference of 2.
Consecutive Even integers are (... -4, -2, 2, 4 ...). All integers are evenly spaced with difference of 2.

If you have only "consecutive integers" in the question, this means that integers must be spaced with 1 unit.
II says "None of the three integers are multiples of 3". So, the three integers COULD be

-4, -2, -1 OR 1, 2, 4 OR anything else. In every 3 consecutive integers, a multiple of 3 is DEFINITELY present. So, X, Y and Z CANNOT be consecutive integers. You get a definite answer here. So, its sufficient.
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by sanjayism » Wed Feb 10, 2010 3:48 am
is o is multiple of 3

if not then set (-1,0, 1),(-2,-1,0) and (0, 1, 2) may be satisfy the above conditions.
kumar sanjay
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by thephoenix » Wed Feb 10, 2010 5:23 am
sanjayism wrote:is o is multiple of 3

if not then set (-1,0, 1),(-2,-1,0) and (0, 1, 2) may be satisfy the above conditions.
no doubt a good observation is raised here , if we will go by def of multiples than indeed 0 is a multiple of 3
infact 0 is the only number which is multiple of all int. we can say its a universal multiple

in order to prove it
any number say n is said to be a multiple of a number say k when n/k=x an integer
now we know that 0 is an integer

when we divide 0 by any number the result is an int and therefore 0 is multiple of that number hence

for the present case we cannot consider -1,0,1 or -2,-1,0 or 0,1,2

and for all other combination of number the result is that the triplets are not consecutive for S2) hence suff
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by shashank.ism » Wed Feb 10, 2010 7:12 am
CANDOGIRL wrote:If X, Y and Z are three integers, are they consecutive integers?
1. z=x+2
2. None of the three integers are multiples of 3.

Statement 1) clearly is insufficient. With Statement 2) am I supposed to rule out negative integer and 0 possibilities? For instance, -2, -1, 0 would be yes, but 4, 7, 8 would be no. Since the question does NOT indicate that they are positive integers, how am I supposed to know that the rule (in any set of 3 consecutive integers, one of three will be a multiple of 3) applies?

The answer is supposed to be B. Any advice?
Statement 1 - insufficient
Statement 2 - you will have to consider negative numbers for sure as integers means both +ve integers and negative integers. now only three possibilities are there where X,Y,Z are consecutive and not divisible by 3.there is no such number 0 is surely divisible by 0.

so they are not consecutive integers -- it is sufficient.
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by harsh.champ » Wed Feb 10, 2010 10:55 pm
CANDOGIRL wrote:If X, Y and Z are three integers, are they consecutive integers?
1. z=x+2
2. None of the three integers are multiples of 3.

Statement 1) clearly is insufficient. With Statement 2) am I supposed to rule out negative integer and 0 possibilities? For instance, -2, -1, 0 would be yes, but 4, 7, 8 would be no. Since the question does NOT indicate that they are positive integers, how am I supposed to know that the rule (in any set of 3 consecutive integers, one of three will be a multiple of 3) applies?

The answer is supposed to be B. Any advice?
Statement 1:-No specific ascending/descending order is given.Hence, insufficient.
Statement 2:-Since none of the integers are multiples of 3 [suppose 7,8,10] then they are not consecutive.Hence,it is clearly sufficient.


Hey CANDOGIRL,
I think what you have your doubt is over here.In case such questions,just plug-in numbers and you will find whether the statement sufffices or not.(like 1,2,3 consecutive but 3(a multiple);1075,1076,1077 but 1077(a multiple))This way you can easily reach to the conclusion.Hope it helps:)

A Note:-For 1 second,I had written insufficient for statement 2.[The fact is that it is not divisible by 3 so the mind registered "NOT" ,hence I wrote insufficient(I better not repeat this mistake in the actual exam)]
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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