Putting the information in a table makes it easier to solve. We’ll use A for Angie, B for Brenda, T for truth and F (false) for lying.
S
M
T
W
Th
F
S
A
T
F
F
F
T
T
T
B
T
T
T
T
F
F
F
To begin with, there aren’t any days where both of them told the truth and lied the day before, so we know one of them must be lying.
So we have two options, either Angel is lying or Brenda is.
Option 1. Angel is lying.
In order for this to be the case, she needs to be lying today and telling the truth yesterday, so we need two days in a row with T F. And if Brenda is telling the truth, she would need two days with F T. That means we’re looking for two days that have
Angie: T F
Brenda: F T
Option 2. Brenda is lying.
This is just the reverse of the above, so we need to find:
Angie: F T
Brenda: T F
The only day that matches either of the two options is Thursday, and it’s option 2. Brenda is the liar.
I have been hot my entire life. Put me in water or in a freezer for days and I will still be hot. My red color should tell you but don’t be deceived, even when I’m green, I’m still hot. What am I?
At the market you can buy a cow for $10, a pig for $1 and 8 hens for $1. How many animals would you need to buy to get 100 mixed animals for exactly $100?
7 cows, 21 pigs and 72 hens. The trick to this is finding the combination of cows and hens with the same cost and quantity since pigs are already equal. The magic combination is 7 cows and 72 hens, giving you 79 animals that cost $79 ($70 + $9). Then you just add 21 pigs to get to 100 animals.
A dad offered to pay his son $5 for every correct answer on his math test. His son said he would pay his Dad $8 for every incorrect answer. There were 26 questions on the test and no money was exchanged.
The son got 16 questions correct and missed 10. This means he owed his Dad 10 * $8 = $80, but his Dad owed him 16 * $5 = $80, so it was a wash.
Two math equations to solve it are x + y = 26 and 5x = 8y.
Imagine an HIV test that is 95% accurate (false positive rate of 5%) and around 2% of the tested population is infected with HIV. What is the probability that you actually have HIV when your test comes back positive?