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Solves Problems and Reasons Logically
Lesson 23
Analyze
  Objectives/Vocab/Tips > Examples 1 | 2 | 3 | 4 > Practice: 1 | 2 | 3 | 4 > Reflection

Example 3:

Laurie, Allen, Scott, and Adam all entered their pet frogs in a distance-jumping contest. Laurie's frog finished ahead of Allen's, but was not first. Scott's frog finished behind Laurie's, but was not last.

  • If all of the statements above are true, which conclusion below is definitely true?
  1. Allen's frog did not finish in last place.
  2. Allen's and Scott's frogs finished the contest ahead of Laurie's frog.
  3. Laurie's and Scott's frogs finished first and second in the contest.
  4. Adam's frog finished first while Allen's frog finished last in the contest.

To answer this question, you will want to find the order the frogs finished to determine which of the statements is true. Let's find the order of the contest much like we did in the previous problem with a table to fill in as we reread the clues.

Adam's
 
 
 

As you look over the clues, you will notice that you can find whose frog finished first, Adam's. Let's see how.

After reading the clues, you see that Laurie's frog did not finish first, but did finish ahead of Allen's. Therefore, you know that Allen's frog didn't finish first either. You also know that Scott's frog finished behind Laurie's frog, which didn't come in first. So you can see how the only frog left to place first is Adam's.

Now, look back over the clues and see if you can place the other frogs. You are told that Laurie's frog finished ahead of Allen's and ahead of Scott's. There is only one place that Laurie's frog could have come in and that was second.

Adam's
Laurie's
 
 

With only two places left to fill, you are told that Scott's frog didn't finish last therefore his frog must have finished third and Allen's frog finished last. Here is the correct order:

Adam's
Laurie's
Scott's
Allen's

With the correct order of the contest, you can now look over the four statements to see which is true.

  • Letter A, Allen's frog didn't finish last isn't true since his frog did finish last. Sorry Allen.
  • Letter B, Scott's and Allen's frogs didn't finish ahead of Laurie's so this statement isn't true either.
  • Letter C, Laurie's and Scott's frogs didn't finish in first and second but in second and third, so this statement isn't true as well.
  • With letter D, you know that this statement is true since Adam's frog came in first and Allen's frog came in last. Therefore our final answer to this problem would be letter D.

Example 4 >>

 

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