Hi parulmahajan89,
You can certainly TEST Values on this question and get the solution, but there are some hidden Number Properties that would make the work considerably easier:
We're told that candy bars are purchased in packs of 2, so we're going to end up with an even number of chocolate bars and an even number of toffee bars. We're also told that he handed out 2/3 of the chocolate and 3/5 of the toffee bars. Since those denominators are "odd", we need to convert the fractions to make the math easier.
2/3 = 4/6 of the chocolate handed out
3/5 = 6/10 of the toffee handed out
This also tells us that he bought the items in "multiples":
Chocolate was bought in multiples of 3 "packs"
Toffee was bought in multiples of 5 "packs"
These limitations will severely limit the possibilities....
The question asks how many packs of toffee he bought?
Fact 1: 1 fewer pack of chocolate than toffee.
In other words:
Number of chocolate packs + 1 = Number of toffee packs.
Keep in mind that chocolate is bought in sets of 3-packs and toffee is bought in sets of 5-packs
So a (multiple of 3) + 1 = (multiple of 5)
TESTING Values gives us some options...
Chocolate = 9 packs, Toffee = 10 packs
Chocolate = 24 packs, Toffee = 25 packs
There are other options, but you don't need to find them.
Fact 1 is INSUFFICIENT
Fact 2: Same NUMBER of each kind of bar were handed out.
So, the number of chocolate bars given = the number of toffee bars given
Let's choose some variables:
X = TOTAL number of chocolate bars
Y = TOTAL number of toffee bars
X(4/6) = Y(6/10)
4X/6 = 6Y/10
40X = 36Y
10X = 9Y
This equation has multiple solutions...
X = 9, Y = 10
X = 18, Y = 20
X = 27, Y = 30,
Etc.
Fact 2 is INSUFFICIENT
Combined, there's an overlap worth noting:
In Fact 1, the numbers must differ by 1
In Fact 2, the numbers differ by an ever increasing value (first by 1, then by 2, then by 3, etc.)
So, there's only one set of values that fits BOTH: X = 9, Y = 10
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
