cramya wrote:I always look for opportunities to plug my favourite rule, # of equations vs # of unknowns!
Stuart,
I agree. Is the problem below an exception to this rule(this is the only problem I have seen so far ):
https://www.beatthegmat.com/word-transla ... 15309.html
After solving something similar I try to convince myself each time that 1 equation wiht 2 unknowns in insuffucient by plugging in a few different values rather than convincing myself on a theoritical basis .
Please advice on what the difference is,in the problem posted above(1 equation 2 unknowns but answer is A).
Regards,
Cramya
That question is different because we have an extra piece of information: the two variables have to be positive integers.
Here's the exact wording of the rule:
In order to solve for a system of n variables, one needs n distinct linear equations.
However, there are many occasions on which we can get away with fewer than n variables. Here are the two most common "special" situations:
1) if you're only solving for some of the variables in the system, you may not require all n equations.
For example:
If a + b + c + d = 6, what's the value of d?
(1) a + b + c = 4
Statement (1) gets rid of (a + b + c) all in one shot, so even though we only have 2 equations for our 4 variables, we can solve for d.
2) if you're solving for a relationship among variables instead of the actual value of the variables, you may not require all n equations.
For example:
What's the value of 3x + 2y?
(1) 10 - 4y = 6x
Statement (1) can be rewritten as 6x + 4y = 10; we then divide both sides by 2 to get 3x + 2y = 5, answering the question for us. Note, we have no clue what the value of x or y is (and no way to solve for them), but that's not what the question is asking.
The situation in the question you linked is rarer, but another exception to the general rule. When the types of numbers available are limited, you may not need n distinct equations to solve the system.
Here's another example similar to the one you linked:
If a and b are positive integers, what's the value of b?
(1) 2a + 3b = 5
Well, the only way we can satisfy statement (1) is if both a and b are 1, so it's sufficient to answer the question.
