## Challenge Problem of the Month

I will choose one person out of all the people who answer correctly to win a free Manhattan GRE Strategy Guide. If you're keen on calculations or on winning free things, you should try your hand this month.

### This Month's Problem: "These Three Integers"

x, y, and z are positive integers.
$y< 1 5 z MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy Ubqee0evGueE0jxyaibaieYhNi=xH8yiVC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8 A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaakeaaca WG5bGaeyipaWZaaSaaaeaacaqGXaaabaGaaeynaaaacaWG6baaaa@3C5C@$ $1 3 x− 3 4 y= 1 6 z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy Ubqee0evGueE0jxyaibaieYhNi=xH8yiVC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8 A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaakeaada WcaaqaaiaabgdaaeaacaqGZaaaaiaadIhacqGHsisldaWcaaqaaiaa iodaaeaacaaI0aaaaiaadMhacqGH9aqpdaWcaaqaaiaabgdaaeaaca qG2aaaaiaadQhaaaa@414D@$

Quantity A

x

Quantity B

z

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.