Hi All,
This prompt gives us lots of information to work with. We’re told:
X and Y are POSITIVE INTEGERS
Y is a multiple of 5
3X + 4Y = 200
We’re then asked what X MUST be a multiple of. This question can be solved with a bit of Arithmetic and TESTing VALUES. There’s also a subtle Number Property Rule built into this question that can save you some time if you recognize it. If you don’t immediately spot the Number Property, then you can still solve this problem with a bit of ‘brute force.’
Let’s start by TESTing the simplest multiple of 5…
IF…. Y = 5…..
3X + 20 = 200
3X = 180
X = 60
60 is a multiple of both 6 and 10, so the correct answer has to be either B or E.
Next, let’s work up through the next few multiples of 5….
IF…. Y = 10
3X + 40 = 200
3X = 160
160 is NOT evenly divisible by 3 though (meaning that X would be a non-integer, which is not allowed)
IF…. Y = 15
3X + 60 = 200
3X = 140
140 is NOT evenly divisible by 3 though (meaning that X would be a non-integer, which is not allowed)
IF…. Y = 20
3X + 80 = 200
3X = 120
X = 40
Between the two remaining answers, 40 is only a multiple of 10.
Final Answer:
The Number Property in this question is if you add a multiple of 5 to another multiple of 5, then the sum will be a multiple of 5.
Since Y is a MULTIPLE of 5, then 4Y will also be a multiple of 5. The sum of the two terms (200) is ALSO a multiple of 5, so the remaining term (the 3X) must ALSO be a multiple of 5. The answers are written in such a way that there’s only one multiple of 5 among them (re: the correct answer).
GMAT Assassins aren’t born, they’re made,
Rich
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