If z is a non-negative integer, is 75/(z + 1) an integer?

Question

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

Is 75/ (z+1) an integer?

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

chetan2u · Answer

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

sanjayparihar16 · Answer

Do we have to consider zero as a multiple of every number in all the cases? Would there be any limitation to this?

chetan2u · Answer

0 is a multiple of all numbers and 1 is a factor of all numbers in all cases.

abhinavsodha800 · Answer

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

Bunuel · Answer

Non-negative integers mean integers which are not negative: 0, 1, 2, 3, 4, ... So, 0 and positive integers.

Bunuel · Answer

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?

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