Hi All,
This question can certainly be solved as a "system" question (as Bunuel showed). If you don't see that "pattern" though, there IS another approach (although it will take more note-taking and some extra work to get to the correct answer) and there are some useful Number Properties in this prompt that would save you some time.
We're told that candy bars come in packs of 2; this is important because it means that the TOTAL number of each type of candy bar will be EVEN.
Rasheed handed out 2/3 of the chocolate bars; since we can't have an ODD number of chocolate bars, we know that the total number of chocolate bars will be a MULTIPLE of 6 (and the total that he HANDED OUT will be a MULTIPLE OF 4). The number of PACKAGES of chocolate bars MUST be a MULTIPLE of 3.
Rasheed handed out 3/5 of the toffee bars; since we can't have an ODD number of toffee bars, we know that the total number of toffee bars will be a MULTIPLE of 10 (and the total that he HANDED OUT will be a MULTIPLE OF 6). The number of PACKAGES of toffee bars MUST be a MULTIPLE of 5.
To make the above easier to reference, here's the essential info:
Chocolate:
Total packages = multiple of 3
Total bars = Multiple of 6
Total handed out = multiple of 4
Toffee:
Total packages = multiple of 5
Total bars = multiple of 10
Total handed out = multiple of 6
We're asked how many PACKAGES of chocolate bars Rasheed bought?
Fact 1: Rasheed bought 1 fewer package of toffee bars than chocolate bars.
Using the deductions from earlier, the number of packages of chocolate MUST be a multiple of 3 and the number of packages of toffee MUST be a multiple of 5...
9 packages of chocolate and 10 packages of toffee
OR
24 packages of chocolate and 25 packages of toffee
Fact 1 is INSUFFICIENT
Fact 2: Rasheed handed out the same NUMBER of each type of candy bar.
Again, using the deductions from earlier, we need a MULTIPLE of 4 that EQUALS a MULTIPLE of 6....so we need a MULTIPLE of 12 bars given of each type....
We could have (among many options)....
12 bars given --> 9 packages of chocolate
24 bars given --> 18 packages of chocolate
Fact 2 is INSUFFICIENT
Combined, we can use the limitations in each of the two Facts against one another:
Using the "multiple of 12s" from Fact 2, we can do a quick comparison...
12 bars given --> 9 packs chocolate, 10 packs toffee --> difference is 1 PACKAGE
24 bars given --> 18 packs chocolate, 20 packs toffee --> difference is 2 PACKAGES
36 bars given --> 27 packs chocolate, 30 packs toffee --> difference is 3 PACKAGES
Etc.
The pattern here proves that as Rasheed gives out MORE chocolate bars, the DIFFERENCE in the number of packages INCREASES.
Thus, there's only 1 situation in which both of the Facts combine....When Rasheed buys 9 packs of chocolate bars.
Combined, SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich