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# Thanks for challenging us. I am sure it is going to be

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Thanks for challenging us. I am sure it is going to be [#permalink]  26 Jun 2004, 20:22
Thanks for challenging us. I am sure it is going to be useful to us .

Is 75/(Z+1) an integer?

1. Z is a multiple of 75.

2. 0 <= Z <=75.

Explanation to this question in the site is given below.

Explanation

Statement 1 states that Z is one of the following: -75, 0, 75, 150, etc
it is not sufficient since when Z is 0, the expression is an integer, in all other cases it is not. INSUFFICIENT.

Statement 2 gives a range of numbers where again, the expression may or may not be an integer (e.g. 4 and 5). INSUFFICIENT.

Combining both statements together, z can be 0 or 75 - sufficient.

Although, I did it wrong, I am not able to accept the answer C. The problem is if Z is 0, 75/(0+1) = 75. Integer; sufficient to say yes. However, if Z is 75, the answer is 75/(75+1) = 75/76 . Not an integer. However, here it is sufficient to say No. Therefore, for the answer has to be E. Can some one help me to understand whether I am wrong or the challenge question's explantaion is wrong?

Thanks.
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Re: April-June GMAT Club Challenge Question 5 [#permalink]  26 Jun 2004, 23:51
dhandaydham wrote:
Thanks for challenging us. I am sure it is going to be useful to us .

Is 75/(Z+1) an integer?

1. Z is a multiple of 75.

2. 0 <= Z <=75.

Explanation to this question in the site is given below.

Explanation

Statement 1 states that Z is one of the following: -75, 0, 75, 150, etc
it is not sufficient since when Z is 0, the expression is an integer, in all other cases it is not. INSUFFICIENT.

Statement 2 gives a range of numbers where again, the expression may or may not be an integer (e.g. 4 and 5). INSUFFICIENT.

Combining both statements together, z can be 0 or 75 - sufficient.

Although, I did it wrong, I am not able to accept the answer C. The problem is if Z is 0, 75/(0+1) = 75. Integer; sufficient to say yes. However, if Z is 75, the answer is 75/(75+1) = 75/76 . Not an integer. However, here it is sufficient to say No. Therefore, for the answer has to be E. Can some one help me to understand whether I am wrong or the challenge question's explantaion is wrong?

Thanks.

Yes, I answered E as well, you are right, dhandaydham. This happened to me too.
Joined: 31 Dec 1969
Location: India
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GMAT 1: 710 Q49 V0
GMAT 2: 740 Q40 V50
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[#permalink]  27 Jun 2004, 09:45
Hi Emmanuel

Thanks for letting me know that. I am new to the forum. Hope to contribute to the forum.

Thanks
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Re: April-June GMAT Club Challenge Question 5 [#permalink]  27 Jun 2004, 13:37
Expert's post
dhandaydham wrote:
Thanks for challenging us. I am sure it is going to be useful to us .

Is 75/(Z+1) an integer?

1. Z is a multiple of 75.

2. 0 <= Z <=75.

Explanation to this question in the site is given below.

Explanation

Statement 1 states that Z is one of the following: -75, 0, 75, 150, etc
it is not sufficient since when Z is 0, the expression is an integer, in all other cases it is not. INSUFFICIENT.

Statement 2 gives a range of numbers where again, the expression may or may not be an integer (e.g. 4 and 5). INSUFFICIENT.

Combining both statements together, z can be 0 or 75 - sufficient.

Although, I did it wrong, I am not able to accept the answer C. The problem is if Z is 0, 75/(0+1) = 75. Integer; sufficient to say yes. However, if Z is 75, the answer is 75/(75+1) = 75/76 . Not an integer. However, here it is sufficient to say No. Therefore, for the answer has to be E. Can some one help me to understand whether I am wrong or the challenge question's explantaion is wrong?

Thanks.

Thank you for catching it.
My appologies, I failed to catch it when I was going through it.

Actually Kpadma was the first to catch it. The scores have been modified to reflect this change. We will start a discussion specifically for the challenge and will appreciate reports of any inconsistencies.

-Thank you.
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Intern
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[#permalink]  27 Jun 2004, 18:45
probably a stupid question, but how is 0 a multiple of 75.
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[#permalink]  27 Jun 2004, 21:44
Maneesh wrote:
probably a stupid question, but how is 0 a multiple of 75.

Maneesh, you forgot about Z+1 = 1 in the lower part of the fraction.
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[#permalink]  28 Jun 2004, 19:08
Posted: Sun Jun 27, 2004 6:45 pm Post subject:

--------------------------------------------------------------------------------

probably a stupid question, but how is 0 a multiple of 75.

Zero is an even integer and considered as a multiple of all the numbers. For example multiples of 5 means, 5, 10, 15, 20 so on. That is, 5 is multiplied by 1, 2, 3, 4, so on. In the same way, if you multiply 5 x 0 (the first integer) the value is zero. Remember this point. I was also perplexed first by this. However, I learned it slowly. Last some points for not knowing this in my diagnostic test.
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gmat2004

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[#permalink]  28 Jun 2004, 19:12
dhandaydham wrote:
Posted: Sun Jun 27, 2004 6:45 pm Post subject:

--------------------------------------------------------------------------------

probably a stupid question, but how is 0 a multiple of 75.

Zero is an even integer and considered as a multiple of all the numbers. For example multiples of 5 means, 5, 10, 15, 20 so on. That is, 5 is multiplied by 1, 2, 3, 4, so on. In the same way, if you multiply 5 x 0 (the first integer) the value is zero. Remember this point. I was also perplexed first by this. However, I learned it slowly. Last some points for not knowing this in my diagnostic test.

No, zero is not a multiple of every non-zero integer, because 5 != 0*z, there is no z, such that: 5 = 0*z..!
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Re: April-June GMAT Club Challenge Question 5 [#permalink]  28 Jun 2004, 19:18
bb wrote:

Thank you for catching it.
My appologies, I failed to catch it when I was going through it.

Actually Kpadma was the first to catch it. The scores have been modified to reflect this change. We will start a discussion specifically for the challenge and will appreciate reports of any inconsistencies.

-Thank you.

Thanks for the forum and bringing in the challenge question section. I am a novice here. I hope to learn, and help others to learn while I learn.
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gmat2004

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[#permalink]  28 Jun 2004, 19:24
Emmanuel wrote:

No, zero is not a multiple of every non-zero integer, because 5 != 0*z, there is no z, such that: 5 = 0*z..!

I could not understand. Do you mind to explain it?
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gmat2004

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[#permalink]  28 Jun 2004, 19:35
dhandaydham wrote:
Emmanuel wrote:

No, zero is not a multiple of every non-zero integer, because 5 != 0*z, there is no z, such that: 5 = 0*z..!

I could not understand. Do you mind to explain it?

BY DEFINITION: a is divided by b if and only if there exists such k - integer, that a = k*b.

5 is divided by 0 if and only if there exists such k - integer, that 5 = 0*k = 0!!! => 5 is NOT divided by 0!
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[#permalink]  29 Jun 2004, 06:36
Emmanuel: then how can you say that from 1st statement the value of Z can be Zero.
As per (1) Z is a multiple of 75 and if Z=0 then is it feasible that still Z is a multiple of 75, bit confused here. I would have picked (A) as the answer.
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[#permalink]  29 Jun 2004, 12:16
Emmanuel wrote:
dhandaydham wrote:
Emmanuel wrote:

No, zero is not a multiple of every non-zero integer, because 5 != 0*z, there is no z, such that: 5 = 0*z..!

I could not understand. Do you mind to explain it?

BY DEFINITION: a is divided by b if and only if there exists such k - integer, that a = k*b.

5 is divided by 0 if and only if there exists such k - integer, that 5 = 0*k = 0!!! => 5 is NOT divided by 0!

Well, if you divide 5 by zero the answer is infinite. Let me put the question in a different way. If zero is not considered as a multiple of every non-zero integer, for what non-zero integers you can consider zero is a multiple? In the explanation for the first statement they give zero is a multiple for 75. In other explanations too, I have seen zero is used as a multiple. Probably, you might be explaining some exceptions. Can you go a little bit down and explain things with some numbers so that we all can understand what you are saying? I hope I am not asking too much of your time. Thanks
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[#permalink]  29 Jun 2004, 13:34
OK..Emmanuel
You wrote the following...

BY DEFINITION: a is divided by b if and only if there exists such k - integer, that a = k*b.

5 is divided by 0 if and only if there exists such k - integer, that 5 = 0*k = 0!!! => 5 is NOT divided by 0!

My conclusion is that
0 is not a multiple of 5. (Is it right or wrong)
what if i replace 5 by 75 here???????????

Answer the following in Y/N
1. 0 is a multiple of 5 (Y/N)
2. 0 is a multiple of 75 (Y/N)

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[#permalink]  29 Jun 2004, 20:38
mdfrahim wrote:
OK..Emmanuel
You wrote the following...

BY DEFINITION: a is divided by b if and only if there exists such k - integer, that a = k*b.

5 is divided by 0 if and only if there exists such k - integer, that 5 = 0*k = 0!!! => 5 is NOT divided by 0!

My conclusion is that
0 is not a multiple of 5. (Is it right or wrong)
what if i replace 5 by 75 here???????????

Answer the following in Y/N
1. 0 is a multiple of 5 (Y/N)
2. 0 is a multiple of 75 (Y/N)

Answer the following in Y/N
1. 0 is a multiple of 5 (Y) bcoz 5*0 = 0
2. 0 is a multiple of 75 (Y) bcoz 75*0 = 0

hope that makes sense

- ash
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I'm crossing the bridge.........

[#permalink] 29 Jun 2004, 20:38
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