If xy = 0 and y not divisible by 6, which of the following is the grea

Question

If xy = 0 and y not divisible by 6, which of the following is the greatest integer less than x ?

A. x
B. -2
C. -1
D. 1
E. 0

generis · Accepted Answer

Though it may seem as if there are three cases --

There really is only one case to consider here: 
 x = 0

xy = 0

Either  x  or  y  or both  = 0

If y is not divisible by 6,  y is not 0.

0 is divisible by every integer except 0.

\frac{0}{6}=0 , no remainder*

So  x = 0

The greatest integer less than 0 is -1.

Answer C

lostnumber  , hope that helps

*OR: A is divisible by B if you can write A as the product of B times some integer C. B = 6, A = 0: (6 * 0) = 0.
It does not matter that A = C here. The same is true, e.g., for A = 6, B = 1: (1 * 6) = 6. The property holds.

Vinayak Shenoy · Answer

xy = 0 and y not divisible by 6
this means x=0 and y can be 1, 2, 3, 4, 5, 7, 8, 9, 10, 11.. (basically y is not a multiple of 6. Both positive and negative values of y can exist)
the greatest integer less than x then will be -1 as x=0
IMO C

gracie90 · Answer

I solved it this way, please let me know if I am wrong:

y is not divisible by 6 so it is also not divisible by 2 & 3. From the question I derived that x=0 and y is less than that. So by looking at the answer choices C. -1 was the only valid option.

Abhishek009 · Answer

x*y = o

Since y is not divisible by 6 , it can be any number except multiple of 6 ...

We have 3 possibilities -

1. x = 0 , y = Any number ( not multiple of 6 )
2. x = Any number & y = 0
3. x = 0 & y = 0

Greatest integer less than x is always - x - 1

1. x = 0 , Greatest integer less than x is -1
2. x = Any number , Greatest integer less than - 1
3. x = 0 , Greatest integer less than x is -1
  
Thus answer will be (C) -1

khiemchii · Answer

xy = 0 => x = 0 or y = 0
y not divisible by 6 => y ≠ 0.
=> x = 0
 the greatest integer less than x therefore is -1 =>  C

lostnumber · Answer

I'm missing something here. I got to this part:
1. x = 0 , y = Any number ( not multiple of 6 )
2. x = Any number & y = 0
3. x = 0 & y = 0

But I'm unable to figure out how that leads us to -1 as an answer (I got the question right but ended up guessing). If Y is 0 and X is 100, wouldn't the greatest integer less than x be 99? And since X can be any value I don't understand how we can solve this

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If xy = 0 and y not divisible by 6, which of the following is the grea

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If xy = 0 and y not divisible by 6, which of the following is the grea

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