buoyant wrote:Hi Mitch,
Thank you for a nice explanation.
Won't testing several numbers in such questions be time consuming? Also, how to know in such questions that an equation with two variables is going to be sufficient.
Is there any other way to approach such questions?
When an equation with two variables is restricted to POSITIVE INTEGERS, we must check whether it can be satisfied by more than one combination of values.
If the equation can be satisfied by only ONE combination of values, then we have SUFFICIENT information to solve for each variable.
An alternate approach to the problem above:
Let D = the number of directors and S = the number of salespeople.
Statement 1 implies the following:
150D + 80S = 2200
15D + 8S = 220.
The units digit of 15D must be 5 or 0.
To yield a sum of 220, the units digit of 8S must also be 5 or 0.
Since 8S is even, its units digit cannot be 5.
Implication:
Both 15D and 8S must have a units digit of 0.
Options:
15D = 30, 60, 90, 120, 150, 180, 210.
8S = 40, 80, 120, 160, 200.
Two combinations will yield a sum of 220:
15D + 8S = 60+160 = 220.
15D + 8S = 180+40 = 220.
The latter equation is not valid, since it implies more directors than salespeople.
Thus, we know that 15D=60 and that 8S=160, implying that D=4 and S=20.
You are correct:
Statement 1 requires a bit of a time investment.
But statement 2 compensates:
It can be evaluated without almost no work at all.
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