Both of these questions test a similar topic - combinations of 2 items with specific prices: "item X costs $x and item Y costs $y." The solutions are different because, well, the questions are different!
#57 is asking us for the total number of item X's + item Y's. In order to find a total number, we often only need the total cost (if there's only one combination of $x and $y that will get us there). Knowing about on X or only Y won't be sufficient.
(1) If the store sold fewer than 10 $10 certificates, we know nothing about the $50 certificates, and therefor nothing about the total. Insufficient.
(2) If the total cost was $460, ask yourself - is there only one pairing that will bet me this total, or are there multiple?
You can quickly chart out the pairings that will add to $460. There are multiple possible pairings, so this is insufficient.
Now combine the statements to see if it restricts it to a single pairing:
We can see that there are 2 options: 1 $10 and 9 $50, or 6 $10 and 8 $50. Insufficient. The answer is
E.
For #132, the question is asking us for the number of a particular item. Once again, it will depend on knowing a total value, and seeing if we can restrict to a single pairing.
(1) If she bought $4.40 worth of stamps, are there multiple pairings that could work? Unlike in the last problem where everything was a multiple of 10, here we have harder-to-work-with numbers. So let's think logically:
- Multiples of the $0.15 stamp will always end in a 0 or a 5. Which multiples of 9, when you add them to 0 or 5, will give you a number that ends in 0? Only $0.29*5, $0.29*10, or $0.29*15 (for products less than $4.40). So you can set up a chart to see if any of these pair with multiples of 0.15:
Here, there's only one pairing of multiples of 0.29 and 0.15 that would work. Sufficient.
(2) Knowing that we have an equal number of each doesn't help if we don't have a total. Insufficient.
The answer is
A.
As you can see, we can use the same method of pairings here. But the answers are different because the information given is different!
