Tricky Problem Scenarios Flashcards

1
Q

You are given a 7 letter word such as BANANA. You need to find out the number 3 letter of groupings. How do you solve

A

19 - List out each possible 3 letter grouping, calculate the number of possible permutations to arrange each one, and add the permutations together

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2
Q

You are given 8 people total to form a team of 5 people, but 2 people cannot be together on the team of 5. How do you calculate the number of team configurations?

A

Total Number Of Teams = Total Number Of Teams With Both + Total Number Of Teams With One OR Neither

Total Number Of Teams With One OR Neither = Total Number Of Teams - Total Number Of Teams With Both

8C5 - 6C3 = 36

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3
Q

In a set with an even number of items, how many elements are between the first element and the median (incl. first element excluding median)?

A

N/2 and n/2 + 1 are median indices, n/2 - 1 elements separated between the middle elements

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4
Q

In a set with an odd number of items, how many elements are between the first element and the median (incl. first element excluding median)?

A

n+1/2 is median index n+1/2 - 1 elements before or n-1/2 elements total

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5
Q

What are the conditions for two triangles to be similar/proportional to each other

A
  1. All three angles are the same measurement
  2. All three sides have the same proportions
  3. An angle of one triangle is the same measure as an angle of another triangle and the sides surrounding these angles are in the same ratio.
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6
Q

Let’s say we have a right triangle and an altitude bisects the triangle into two smaller triangles. What is the similarity

A

All 3 triangles in this case are similar

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7
Q

How do you find average rate?

A

Distance = Rate x Time
Avg Rate = Total Dist / Total Time

Multiple Parts
Avg Rate = (D1 + D2) / (T1 + T2)

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8
Q

What is the converging rate equation?

A

When two objects are moving towards each other, the distances will always add to a concrete total?

distance1 + distance2 = total distance 1&2

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9
Q

How do you solve a “catch up and pass” problem?

A

Time = Delta Distance / Delta Rate

Delta Distance = Extra Distance Faster Object Must Travel over Slower Object
Delta Rate = Rate of Faster Object - Rate of Slower Object

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