Is Statement one sufficient?

[OluwaseunMakinde]

Hello house,

I came across this question in the 2016 OG and the answer was given as D. In my opinion the answer is B, Please help determine if statement one is sufficient.

Max has $125 consisting of bills each worth either $5 or $20. How many bills
worth $5 does Max have?
(1) Max has fewer than 5 bills worth $5 each.
(2) Max has more than 5 bills worth $20 each.

[MartyMurray]

The total quantity of money Max has is $125.

If he has fewer than 5 $5 bills, then he has less than $25 in $5 bills. The next multiple of 5 below 25 is 20.

125-20 = 105

5 x 20 = 100

So 5 $20 bills won't get him to the total if he has fewer than 5 $5 bills.

Now what do you think about Statement 1?

[ceilidh.erickson]

This question is testing INTEGER CONSTRAINTS. If we have $5 bills and $20 bills, we have to have a whole number of each.

With these types of problems in DS, it's useless to set up an equation. 5x + 20y = 125 will look unsolvable, as algebraic equations can't account for integer constraints. Instead, make a CHART:

Start with the maximum # of 20's - it's usually easier to start with the bigger one:


You don't have to fill in everything, but just enough to notice patterns to start. Then, fill in the # of 5's that would add up to $125 total:


Now when you're looking at the statements, here's your goal:
See if the statements restrict it to a single scenario in your chart.

(1) Max has fewer than 5 bills worth $5 each.
Cross off any scenarios in your chart that don't apply:


This leaves us with a single scenario:


That's sufficient!

(2) Max has more than 5 bills worth $20 each.
Do the same thing here: eliminate the scenarios that don't fit.


Once again, there's only one scenario left that fits:


That's also sufficient.

The answer is D.

[ceilidh.erickson]

Here's another example of how to use a chart with integer constraints:
https://www.beatthegmat.com/a-factory-p ... tml#765462