Divisible by prime number Q

[ting.cui10]

Source: GMAT Club Test Center Quant Set 5. #16. If (40*x^2*y^2)/z is divisible by prime number Q , is Q an even prime number?
(1) Product of x^2*y^2 is even.
(2) z*Q = 2

Answer is E. The solution says "Statements (1) and (2) combined are insufficient. Either x or y has to be divisible by 3. Pick numbers 4 for x and 3 for y . When we divide by 6, there is still no way to tell if or is equal to 2." I don't understand their explanation. I'm taking your 9 week course - could you explain how to solve this problem using the strategies taught in the course? Thanks

[abemartin87]

Question is asking whether Q=2
(1)

[(40*x^2*y^2)/z]/Q=(40*2k)/(z*Q)=(2^3*5*2k)/(z*Q)=some integer

Now we can pick Q=2 (A prime & even) and we still get an integer

we can also pick Q=5 and we still get an integer since the numerator has both 2 and 5 as prime in it. Hence, INSUFF.

(2)

(40*x^2*y^2)/z*Q=(2^3*5*x^2*y^2)/2=2^2*5*x^2*y^2=some integer

For Z*Q= we can have Z=1 and Q=2, in which case the answer is yes, or Z=2/5 and Q=5, in which case the answer is no. INSUFF.


(1) & (2)

(40*x^2*y^2)/z*Q=(2^3*5*2k)/2=2^3*5

Same argument as in statement (2) For Z*Q= we can have Z=1 and Q=2, in which case the answer is yes, or Z=2/5 and Q=5, in which case the answer is no. INSUFF

[jnelson0612]

Great work, abe!