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

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Math Expert
Joined: 02 Sep 2009
Posts: 52296
If xy = 0 and y not divisible by 6, which of the following is the grea  [#permalink]

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23 Nov 2016, 02:17
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25% (medium)

Question Stats:

75% (01:11) correct 25% (01:10) wrong based on 184 sessions

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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

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Re: If xy = 0 and y not divisible by 6, which of the following is the grea  [#permalink]

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23 Nov 2016, 02:37
Bunuel wrote:
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

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
Intern
Joined: 11 Jan 2016
Posts: 32
Re: If xy = 0 and y not divisible by 6, which of the following is the grea  [#permalink]

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23 Nov 2016, 07:16
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.
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Re: If xy = 0 and y not divisible by 6, which of the following is the grea  [#permalink]

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23 Nov 2016, 07:26
1
1
Bunuel wrote:
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

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

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Intern
Joined: 18 Nov 2016
Posts: 7
Re: If xy = 0 and y not divisible by 6, which of the following is the grea  [#permalink]

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27 Nov 2016, 22:04
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
Intern
Joined: 28 Mar 2018
Posts: 46
Re: If xy = 0 and y not divisible by 6, which of the following is the grea  [#permalink]

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20 Apr 2018, 05:59
Abhishek009 wrote:
Bunuel wrote:
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

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

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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Joined: 22 May 2016
Posts: 2353
If xy = 0 and y not divisible by 6, which of the following is the grea  [#permalink]

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21 Apr 2018, 06:14
4
Bunuel wrote:
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

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.

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.

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If xy = 0 and y not divisible by 6, which of the following is the grea &nbs [#permalink] 21 Apr 2018, 06:14
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