Word Problems

Question 1

RECOGNITION:

1) What is this Q testing?
2) Solve the Q without looking at the answer

Answer 1

1) Overlapping Sets! (it’s testing a technique)
2) Lol look at GMATClub, I actually don’t know of the top

Question 2

RECOGNITION:

1) What technique can be used to solve the problem in the attached image?
2) Solve the Q, what’s the answer?

Answer 2

1) Overlapping sets!
* When things are categorized (e.g., “GMAT test takers <650 vs. 650+”), that is a clue to use overlapping sets*

Keys here:

• Since not given any numbers in problem (and since not given for Total), pick a Smart Number for Total (in this case 100 is best since %s)
• Careful with the phrasing (20% of Test Takers who take the exam only once) –> in this case, set a variable for Total folks who take it only once (X)… THEN once you finish reading the problem, you realize X = 60

Question 3

Overlapping Sets:
What is the process for overlapping sets problems?

Answer 3

1. Recognize the problem
   
   • Look for “categorization” of items in the Q text
2. Set up matrix
3. Think: What are we solving for?
4. Fill out the Total Box!
   
   • Ideally, use a # given to us for Total
   • If not pinned down to a number, use a smart number
   • OR you can use a variable (if they DO pin you down with a number in Q Text)

Question 4

How shoudl you tackle the rates of two different things (vehicles, people, etc.) in these 2 scenarios:

1) When 2 things are working together (moving towards each other / travelling in opposite directions)
2) When 2 things are working against each other (1 thing is catching up to another)

Answer 4

1) ADD the rates!

IE…If X and Y are travlling towards each other at 20 MPH and 30 MPH respectively, they cut the rate down at 50MPH!

2) Subtract the rates!

IE…Final Rate = the work that the lagging piece needs to do

IE…Distance = distance that the lagging piece needs to make up

Question 5

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled towards each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; train Y, traveling at a constant rate, completed the 100 mile trip in 3 hours. How many miles had train X traveled when it met Train Y?

1) What is the key to work/rate problems?
2) If you’re using “real world” scenarios, what is an easy, organized technique to use?

Answer 5

1) Get something down on your fucking paper!!! Need to draw it out instead of visualizing it in your head!2) Use a DISTANCE CHART (starting at 0 hours, 0 distance, and see how the trains track over the hours) –> example in attachment

Question 6

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled towards each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; train Y, traveling at a constant rate, completed the 100 mile trip in 3 hours. How many miles had train X traveled when it met Train Y?

1) If you’re using Algebra, what should the setup look like?

Answer 6

1) Draw a R/W chart!!!
2) Add these rates since they’re WORKING TOGETHER (moving towards each other)!
- X’s distance = 100 (making Y’s distance = 100 - x)

• ADD the rates (so 53 MPH = combined rate)
• They will travel the SAME TIME (just label this T)
• FINAL EQUATION: 100 = 53T

-Time will be a little under 2 hours…only answer can be A (since B = 40, and 40 would be at 2hours)

Question 7

Car A is 20 miles behind Car B, which is traveling in the same direction along the same route as Car A. Car A is traveling at a constant speed of 58 miles per hour and Car B is traveling at a constant speed of 50 miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?

A) 1.5

B) 2.0

C) 2.5

D) 3.0

E) 3.5

Answer 7

• *Keys here:**
• Set up D = RT chart for both cars!
• Subtract Rates and use X’s Rate and Distance to solve (since this is lagging piece)
• Time is the same for both (so just use T)
• REMEMBER YOU HAVE 2 EQUATIONS (so can plug X = 50T into the equation X+28 = 58T)!!

Question 8

Standard Deviation:

1) (+)(-): What happens to Standard Deviation if you add or subtract the same value to each number in the set?
1) (X)(/): What happens to Standard Deviation if you multiply or divide the same value to each number in the set?

Answer 8

1) If you ADD or SUBTRACT the same number to each number in the set, the SD stays the same
2) MULTIPLY: the SD gets larger (numbers are more spread out)

DIVIDE: the SD gets smaller (numbers are closer together)