M00-05

Question

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

Bunuel · Answer

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

Judy1389 · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

vedha0 · Answer

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!!

sumitgupta93 · Answer

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.

Bunuel · 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 .

bumpbot · Answer

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