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Logic and Proofs Videos 13 videos

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Logical Reasoning (Problem) 290 Views


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Description:

Sounds logical to us!

Language:
English Language
Common Core Standards:

Transcript

00:07

Adam, Bob, and Charles want to lose weight so they can look their most fabulous for the [Adam, Bob and Charles dressed in bright purple and pink clothing]

00:11

Mardi Gras drag parade.

00:13

When they first got fitted for their purple-and-green feathered jumpsuits, Adam was heavier than [Adam, Bob and Charles being fitted for their costumes]

00:17

Bob, who was heavier than Charles.

00:19

If Adam loses forty pounds, Bob loses fifteen pounds, and Charles loses twenty-five pounds

00:24

by Mardi Gras…

00:26

… which of the following cannot be true of their weights on the big day?

00:30

And here are the potential answers…

00:33

Based on the wording of the question, any answer that might be true… is an incorrect

00:37

answer.

00:38

Starting from the bottom...

00:40

For this example, we'll say that Adam weighed three-hundred pounds, Bob weighed one-hundred-ninety-nine [Adam, Bob and Charles in a line with their weights by their side]

00:45

pounds and Charles weighed one-hundred-fifty pounds...

00:48

After Adam loses forty pounds and Charles only loses twenty-five pounds, Charles will

00:52

still weigh less than Adam...

00:54

This situation could be true, so “E” is wrong.

00:57

By the same logic, if Bob lost 15 pounds and Adam lost forty, Bob would still weigh less than Adam [Adam and Bob stood together with boards of their weight loss]

01:03

So D is also wrong

01:05

Now, consider a case where Adam only weighs one pound more than Bob at the start.[Adam and Bob on either side of a weighing scale]

01:09

This satisfied the initial condition that Adam is heavier than Bob.

01:12

However, after Adam loses forty pounds...

01:15

…by taking off that giant beehive wig...

01:18

…and Bob only loses fifteen pounds, Adam will weigh less than Bob. [Adam weighing less than Bob on the weighing scale]

01:22

“C” is possible, and therefore…it’s not the choice we’re looking for.

01:26

Similar to option “C”, consider a case where Adam is one pound heavier than Bob,

01:30

who is one pound heavier than Charles.

01:33

After Adam loses an insane forty pounds...

01:35

Adam will now weigh less than both Bob and Charles.

01:37

“B” is possible, and wrong [Answer B ruled out with a red cross]

01:40

Finally, “A” must be the correct answer by process of elimination.

01:43

Just to check… can this statement be proven false as well?

01:48

Because Charles is losing more weight than Bob, and because he's already lighter, he

01:52

can never end up heavier... so there you go.

01:56

Now that this problem's solved, we're off to get more beads. [Adam Bob and Charles waving in their drag costumes]

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