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Retired Moderator P
Joined: 22 Aug 2013
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What is the remainder when X*Y*Z is divided by 12? (1) X, Y, Z are  [#permalink]

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1 00:00

Difficulty:   45% (medium)

Question Stats: 66% (01:37) correct 34% (02:01) wrong based on 52 sessions

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X, Y, Z are real numbers. What is the remainder when X*Y*Z is divided by 12?

(1) X, Y, Z are consecutive positive integers.

(2) Y - X = Z - Y
Math Expert V
Joined: 02 Aug 2009
Posts: 7971
Re: What is the remainder when X*Y*Z is divided by 12? (1) X, Y, Z are  [#permalink]

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]X, Y, Z are real numbers. What is the remainder when X*Y*Z is divided by 12?

(1) X, Y, Z are consecutive positive integers.
Let the numbers in the order X,Y,Z..
Atleast one will be multiple of 2 and exactly one will be multiple of 3...
So it is surely a multiple of 6, but 12 is not necessary.
If Y is even and a multiple of just 2, answer will be NO. For example 5,6,7.
But otherwise it will be YES, for example 3,4,5 or 6,7,8 and so on
Insufficient

(2) Y - X = Z - Y
This just tells us that Y is the arithmetic mean of the three numbers..
Insufficient

Combined..
The I go if statement I still remains the same..
The order of number is X,Y,Z and the three are consecutive
Insufficient

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Re: What is the remainder when X*Y*Z is divided by 12? (1) X, Y, Z are  [#permalink]

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amanvermagmat wrote:
X, Y, Z are real numbers. What is the remainder when X*Y*Z is divided by 12?

(1) X, Y, Z are consecutive positive integers.

(2) Y - X = Z - Y

#1:
x,y,x can be 13,14,15 remainder yes , 11,12,13 no remainder ; in sufficein

#2:
y-x=z-y
2y= z+x
y=x+z/2
y=mean /avg of x & z
in sufficeint

IMO E Re: What is the remainder when X*Y*Z is divided by 12? (1) X, Y, Z are   [#permalink] 15 Jan 2019, 02:50
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