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M00-05

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Bunuel
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M00-05 [#permalink] New post   16 Sep 2014, 00:14
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64% (01:22) correct 36% (01:12) wrong based on 171 sessions
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If \(z\) is a non-negative integer, is \(\frac{75}{z+1}\) an integer?


(1) \(z\) is a multiple of 75

(2) \(0 \le z \le 75\)
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Re M00-05 [#permalink] New post   16 Sep 2014, 00:14
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Official Solution:


If \(z\) is a non-negative integer, is \(\frac{75}{z+1}\) an integer?

(1) \(z\) is a multiple of 75.

Since \(z\) is a non-negative integer, the above implies that \(z\) can be 0, 75, 150, and so on. If \(z = 0\), then \(\frac{75}{z+1}=75\), which is an integer. However, if \(z\) is any other number, then \(\frac{75}{z+1}\) will not be an integer. Not sufficient.

(2) \(0 \le z \le 75\).

The above is clearly insufficient.

(1)+(2) Since from (2) \(0 \le z \le 75\), then \(z\) can only be 0 or 75. If \(z=0\), then \(\frac{75}{z+1}=75\), which is an integer. However, if \(z=75\), then \(\frac{75}{z+1}=\frac{75}{76}\), which is not an integer. Not sufficient.


Answer: E
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Re: M00-05 [#permalink] New post   30 May 2016, 09:46
I think this is a high-quality question and I agree with explanation.
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Re: M00-05 [#permalink] New post   27 Jun 2023, 01:09
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M00-05 [#permalink] New post   04 Sep 2023, 23:29
z is a "non negative" integer made all the difference. attention to detail is important here. else we might end up choosing the wrong option! good question!!
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Re: M00-05 [#permalink] New post   25 Sep 2023, 11:04
Z is a non-negative number but as the statement 1 says z is a multiple of 75, then how come 0 is a multiple of 75. Possible multiples of 75 are 75, 150 and so on.. thus statement 1 is should be sufficient. I am not able to understand the official answer.
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Re: M00-05 [#permalink] New post   25 Sep 2023, 11:10
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sumitgupta93 wrote:
Z is a non-negative number but as the statement 1 says z is a multiple of 75, then how come 0 is a multiple of 75. Possible multiples of 75 are 75, 150 and so on.. thus statement 1 is should be sufficient. I am not able to understand the official answer.


ZERO:

1. Zero is an INTEGER.

2. Zero is an EVEN integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. Zero is neither positive nor negative (the only one of this kind).

4. Zero is divisible by EVERY integer except 0 itself (\(\frac{x}{0} = 0\), so 0 is a divisible by every number, x).

5. Zero is a multiple of EVERY integer (\(x*0 = 0\), so 0 is a multiple of any number, x).

6. Zero is NOT a prime number (neither is 1 by the way; the smallest prime number is 2).

7. Division by zero is NOT allowed: anything/0 is undefined.

8. Any non-zero number to the power of 0 equals 1 (\(x^0 = 1\))

9. \(0^0\) case is NOT tested on the GMAT.

10. If the exponent n is positive (n > 0), \(0^n = 0\).

11. If the exponent n is negative (n < 0), \(0^n\) is undefined, because \(0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0}\), which is undefined. You CANNOT take 0 to the negative power.

12. \(0! = 1! = 1\).
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Re: M00-05 [#permalink]
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