tricky odds and evens problem

[tonebeeze]

Is z even?

(1) 5z is even
(2) 3z is even

OA = C

[clock60]

really tricky problem, initially i solved it wrong
the most important thing is to notice that we are not given that z is an integer
(1) 5z=even is possible if z any even integer, or z=2/5. then 5*(2/5)=2-even but z is not even integer not suff
(2) the same is true for st 2
3z is even if z is even or z is fraction with even nominator and denominator=3, say z=2/3
then 3*(2/3) =2-even but z=2/3, not suff
both
5z=2k. and 3z=2m
z=(2/5)*k, z=(2/3)*m
(2/5)*k=(2/3)*m cancel 2 amd left with
3k=5m. that is possible if k=m=0 then z=0-even
or k=5. m=3 or k=5a,m=3a where a is +ve integer
let us insert k=5a into the 5z=2k
5z=2*5a. cancel 5 and left with z=2a where a is +ve integer, regardless of the value of a z will always be even integer
the same can be proved with
with 3z=2m, and inserting m=3a
P.S pretty tricky
thanks tonebeeze for posting!!

[tonebeeze]

No worries. Thanks for always responding!

[arnabis2good]

I have read somewhere that GMAT normally won't have choices that are conflicting. In this case, we are assuming the fractions to be 2/3 and 2/5 - and both cannot be true together. Any idea if this kind of question with conflicting choices may come?

[Stuart@KaplanGMAT]

I have read somewhere that GMAT normally won't have choices that are conflicting. In this case, we are assuming the fractions to be 2/3 and 2/5 - and both cannot be true together. Any idea if this kind of question with conflicting choices may come?

Hi,

you're 100% correct that on the GMAT the two statements will never conflict; however, there's no conflict on this particular question.

(1) tells us that z is 2/3 of an even integer; (2) tells us that z is 2/5 of an even integer; however, nowhere does it say that z is 2/3 and 2/5 of the same even integer.

In fact, if it had to be the same even integer, life would be a lot easier, since we could then conclude that z must be 0, giving us a quick "yes" answer to the question.

[cyrwr1]

@Stuart

I have one question regarding this question.

I got the answer as C but am unsure how to apply this for future problems. Can you show me algebraically?

maybe with one of the statements for example having 7z is even?

Please advise.

Thanks

[Stuart@KaplanGMAT]

@Stuart

I have one question regarding this question.

I got the answer as C but am unsure how to apply this for future problems. Can you show me algebraically?

maybe with one of the statements for example having 7z is even?

Please advise.

Thanks

Hi!

I really doubt that I'd even attempt to tackle a question like this algebraically, since the math is a bit on the nutty side. The tougher the questions get, the more you need to use alternative approaches if you want to beat the clock.

In all likelihood, I'd pick numbers until I saw a pattern. Afterwards I might be able to reverse engineer an algebraic solution, but intuition and picking numbers would be my first choices on test day.

[cyrwr1]

@Stuart,

Hi, one more thing.
Since one can derive z as 2/3 or 2/5 of an even number, would it be fair to deduce z is a multiple of 2,3,5 altogether or a multiple of 30 to come to the conclusion that z is even?

Is this deduction valid?

Thanks!

[champmag]

wow...what a tricky question. I got the answer as C in the first attempt.

Excellent explaination clock.