M03-37

Question

If  z  is a positive integer, is 2 a factor of  z ?

(1) 22 is a factor of  15z 
 
(2) 22 is a factor of  16z

hatemnag · Answer

I think in ST>1 z must be even and contains 11 as well. assume that z is 2 then 15 x 2 = 30 which is not divisible by 22 so even fact is not enough for ST> 1 to be true

Bunuel · Answer

The question asks: is z an even number?

Now, ask yourself, if z is odd for (1), can 22 be a factor of 15z? No. Because if z is odd, then 15z is odd too, and 22 (even) cannot be a factor of an odd number. Thus z must be even.

TheNightKing · Answer

(1) 22 is a factor of  15z

22=2*11 
15z=3*5*z

Since there is nothing common between known factors of the two numbers, It can be inferred that z has to have at least a 2 and a 11.

Sufficient

Answer is either A or D.

(2) 22 is a factor of  16z

22=2*11
16z=(2^4)*z

Since 2 is common we cannot infer whether z has a 2 or not. We can be sure that z has at least one 11 because that is not common.

Not Sufficient.

Answer (A)

Godsent · Answer

Good question.

MHIKER · Answer

(1) As 15 is an odd number so z must be an even number and is divisible by 2. Sufficient.

(2) As 16 is even then z can be odd or can be even, for example; z is 11 the 16z is divisible by 2 but z is not divisible 2, but z can be 22 and is divisible by 2. Yes and No. Insufficient.

The answer is A

r_putra_rp · Answer

My take on this question

is  2  a factor of  Z ?

(1):
 22  is a factor of  15Z 
or in other words

\frac{(3 * 5 *Z)}{(2 * 11)} = integer

since  15  is not a multiple of 2 nor 11, thus  Z  must be a multiple of  2  and a multiple of  11 , otherwise the premise doesn't hold
Sufficient

(2):
 22  is a factor of  16Z

or in other words

\frac{(2^4 *Z)}{(2 * 11)} = integer 
 \frac{(2^3 *Z)}{(11)} = integer

now  Z  does not be a multiple of  2  for this to hold, for example:
 Z = 11  then the result is  2^3  is an integer => statement is FALSE
 Z = 22  then the result is  2^3 * 2  is also an integer => statement is TRUE
Insufficient

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.

M03-37

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