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Bunuel
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If z is a non-negative integer, is 75/(z + 1) an integer? 04 Dec 2020, 06:00
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75% (hard)

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41% (01:19) correct 59% (01:15) wrong based on 183 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) \(0 \leq z\leq 75\)


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Is 75/ (z+1) an integer?

(1) z is a multiple of 75
(2) 0<=z<=75

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If z is a non-negative integer, is 75/(z + 1) an integer? 04 Dec 2020, 20:20
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sanjayparihar16
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If z is a non-negative integer, is \(\frac{75}{z + 1}\) an integer?

\(z\geq{0}\)

(1) z is a multiple of 75
If z is 0, 75/(0+1)=75....Yes
If z is 75, 75/(75+1)=75/76...No
Insufficient

(2) \(0 \leq z\leq 75\)
Same as above, z can be 0 and 75.

Combined
Nothing new.

E
Do we have to consider zero as a multiple of every number in all the cases? Would there be any limitation to this?
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0 is a multiple of all numbers and 1 is a factor of all numbers in all cases.
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If z is a non-negative integer, is 75/(z + 1) an integer? 04 Dec 2020, 06:38
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If z is a non-negative integer, is \(\frac{75}{z + 1}\) an integer?

\(z\geq{0}\)

(1) z is a multiple of 75
If z is 0, 75/(0+1)=75....Yes
If z is 75, 75/(75+1)=75/76...No
Insufficient

(2) \(0 \leq z\leq 75\)
Same as above, z can be 0 and 75.

Combined
Nothing new.

E
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If z is a non-negative integer, is 75/(z + 1) an integer? 04 Dec 2020, 12:48
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chetan2u
If z is a non-negative integer, is \(\frac{75}{z + 1}\) an integer?

\(z\geq{0}\)

(1) z is a multiple of 75
If z is 0, 75/(0+1)=75....Yes
If z is 75, 75/(75+1)=75/76...No
Insufficient

(2) \(0 \leq z\leq 75\)
Same as above, z can be 0 and 75.

Combined
Nothing new.

E
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Do we have to consider zero as a multiple of every number in all the cases? Would there be any limitation to this?
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If z is a non-negative integer, is 75/(z + 1) an integer? 30 Dec 2020, 07:38
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Hi Bunuel, here it is written non-negative integer but zero is an even integer then how can we consider z as zero here ? Zero is neither positive nor negative
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If z is a non-negative integer, is 75/(z + 1) an integer? 30 Dec 2020, 07:41
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abhinavsodha800
Hi Bunuel, here it is written non-negative integer but zero is an even integer then how can we consider z as zero here ? Zero is neither positive nor negative
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Non-negative integers mean integers which are not negative: 0, 1, 2, 3, 4, ... So, 0 and positive integers.
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If z is a non-negative integer, is 75/(z + 1) an integer? 27 Jun 2023, 01:11
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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.

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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If z is a non-negative integer, is 75/(z + 1) an integer? 20 Oct 2024, 04:08
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