Word Problem: Vaul holding gold + silver

[dhl84]

Hi all,
I came across this question and wasn't sure about the given answer and wondered if I could discuss here... The question is stated as follows:

A vault holds only 8 oz tablets of gold and 5 oz tablets of silver. If there are 130 oz of gold and silver total, what is the greatest amount of gold that can be in the vault, in oz?

1. 40
2. 80
3. 120
4. 128
5. 130

Now the answer I came to was 128, because it's the largest number that's a multiple of 8. The answer given states that there must be silver and therefore the answer is 120 (10 oz silver + 120 oz gold). I understand the methodology behind the answer, but in my opinion the question is ambiguous, as it does not necessarily say that there must be silver in the vault... Am I correct in my assumption or should I be looking out for little tricks like these in the questions?
Thanks for your help.

[madboy]

I do not agree that the question needs to expicitly state that there must be silver in the vault. When it says that the vault "holds only 8 oz tablets of gold and 5 oz tablets of silver" it is implied that there is atleast one tablet each of gold and silver in the vault.

Here is how I would approach the problem:
If x is no of gold tablets and y no of silver tablets:
8x + 5y = 130
So x=(130 - 5y)/8
i.e x=5*(26-y)/8
Now the above expression is maximum for the least value of y (greater than 0) which makes (26-y)/8 an integer or, in other words, 26-y a multiple of 8.
Clearly for y=2 , x is maximum and equal to 15
Therefore maximum possible qty of gold = 8*15=120

[kssshah]

While I do agree that the question is sufficient and no additional information needs to be provided, the question does not (and it purposefully does not) state that there is silver in the vault. It could very well have stated that the total weight of gold and silver is 120 oz, in which case the answer would still have been 15 with no silver in the vault. What they have not mentioned and does not need to be mentioned is that the tablets cannot be partial i.e. they cannot be of 2 oz. They can be 8 oz for gold and 5 oz for silver.