Word Problems

Sets

- Breaks up people or groups of things up into their component parts and answer questions accordingly. - Venn Diagrams, and when that fails use formulas

Work Problems

- Complete job to several parts - Figure out how long it would take with both parts together or individually

Motion Problems Formula

- Distance traveled, speed or time elapsed given motion parameters d = r-t

Consecutive Integer Problems

- How numbers relate to each other - Try and work backwards, if possible

Key with Sets

- Just knowing someones preference does not tell you anything about that persons other preferences - Can belong to 1, >1, or niether

Word Problems - How to Solve

- Learn and recognize common patterns - You dont have to immediately see how it all unfolds. - Unlock chain of recognition >> Driving Fog through headlights

How to Solve 2 Group Sets

- Use Formula Group A + Group B - Both + Neither

Defined Operations

- how GMAT tests functions - strange symbols - methodically work through problem, symbol is an instruction book telling you what to do

Shortcuts

1) Answer choices are numbers - work backwards 2) Answer choices are variables - make up numbers! Don't work in the abstract

Three Types of Motion Problems

1) Opposite Directions d1 + d2 = Total Distance 2) Same Direction/Catch Up d1 = d2 3) Round Trip d1 = d2 Each one has its own equation

If the operation && is defined for all a and b by the equation a && b = (a2 b2) / 3. Then 2&&(3 && -1) = A 4 B 2 C -4/3 D -2 E -4

3 && - 1= 3^2 * -1 /3 = -3 2 && -3 = 2^2 * -3 / 3 = -4 E

In an increasing sequence of 10 consecutive integers, the sum of the first 5 is 560. What is the sum of the last 5? A 585 B 580 C 575 D 570 E 565

Numbers here are too large to plug in answers 1 2 3 4 5 6 7 8 9 10 --------- ---------- 560 x a + a+1 + a+2 + a+3 + a+ 4+ a+ 5 = 560 Solve a = 110 But this involves a lot of addition and too much equation. Here is how to do this properly. Go directly to defining what you need to solve for. 1 2 3 4 5 6 7 8 9 10 --------- ---------- 560 x sum 6-10 = a+5+a+6+a+7+a+8+a+9 = 5a + 35 Solve for a = 110 Plug into 5a+35 = 585 A

Age Problems

Asking how two peoples age's relate, Past, Present, Future Work Backwards, Make Up Ages Draw a timeline to kick off recognition - w/ Past, Present and Future

Matrix Problems

Cross between sets and probability Lots of moving problems and contingencies Contingency Outcomes Use a probability Tree!

In the race, the tortise leaves the starting line walking at 5mph the hare waits 30 minutes before starting, then crossing the starting line and runs at 30 mph . How far must the hare travel before overcoming the tortise? A 1/2 B 3/5 C 1 D 3 E 5

Overtake d1 =d2 T d1 = 5(t1) H d2 = 30(t1-30) BUT 30 mins = .5hrs d2 = 30(t1-.5) 5(t1) = 10(t1-30) t1 = 3/5 d2 = 30(3/5-1/2) d2 = 3 D

John is now 14 years older than Sam. If in 10 years John will be twice as old as Sam, How old will John be in 5 years? A 9 B 19 C 21 D 23 E 33

PAST PRES FUT Translate age problems, then plug in values now s = j - 14 +5 +10 s = j/2 plug in numbers C - 21 now s = j - 14 j = 16, s = 2 +5 j = 21 s = 5 +10 s = j/2 j=26, s = 12 No Try D now s = j - 14 j = 18, s=4 +5 j= 23 +10 s = j/2 j = 28 s = 14 yes!

Three times the first of three consecutive odd integers is 3 more than twice the third. Find the third integer. A 7 B 9 C 11 D 13 E 15

Plug in numbers from answer choices - if 3a = 2+ 2c start w C 1. 2. 3 7 9 11 21 24 We need a bigger number to cancel out D 1. 2. 3 9 11. 13 27 29 E 1. 2. 3 11. 13. 15 33 33 Don't use algebra - you don't know what kind of mistakes you could make. doing it this way - ENSURES the correct answers

Three Group Sets

Use Venn Diagrams Key - work from the middle out

All but 4 of the 120 seniors are members of the chess club, pep club or both. If 90 seniors are in the pep club, and 70 seniors are in chess club how many seniors are in both clubs? A 20 B 24 C 40 D 44 E 160 Data Sufficiency

none - 4 total - 120 pep - 90 chess - 70 both - x 120 = 90+70+4-x x = 44

Hose A can fill a swimming pool in 3 days. Hose B can fill the same pool in 4 days. How long will it take for both hoses working together to fill the pool if hose A stops when the pool is half full?

rA = 1/3 rB = 1/4 w = 1/2 r = rA = rB = 7/12 w = rt .5 = 7/12(t1) t1 = 6/7 w = 1/2 r = rB = 1/4 w = rt .5 = 1/4(t2) t2 = 2 total = 2 6/7 D

Hoses A and B always operate independently and at their respective constant rates. When working alone, Hose A can fill a swimming pool in 5 hrs and Hose B can fill the same pool in X hrs. When the two hoses operate simultaneously to fill the swimming pool, it takes them 2 hours to complete this job. What is the value of x?

rA = 1/5 rB = 1/X rA + rB = 1/2 Rates are additive 1/5 + 1/x = 1/2 x = 3 1/3 A

Key Work Problem Formula

time together/time for 1 part alone + time together/time for 1 part alone = 1 (one job)

Advanced Work Problems

w = rt Always Convert times to rates and express in per unit time. Rate is inverse of time. 5 hrs/job = 1/5 rate 1/5 job per hr (This only works if you are talking about the ENTIRE job) Use w = rt to solve for unknown Rates are additive Rc = R1 + R2 + ... Reset equations when conditions change. Machines added, taken away. Solve with multiple equations. Solve new equations

When working backwards does not work for an Age Problem...how to represent algebraically

x, x+1, x+2 Odd/Even = x+2, x+4, x+6

The water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hrs. The water from a second outlet, flowing at a constant rate can fill the same pool in 5 hrs. If both at the same time, how long to fill pool? A 0.22 B 0.31 C 2.50 D 3.21 E 4.56

x/5 + x/9 = 1 x = 45/14 3.21 D