USE LOGICAL REASONING

LOGICAL REASONING . . .

• CAN ALSO BE CALLED MATRIX LOGIC OR DEDUCTIVE REASONING

• IS USED WHEN WE ARE GIVEN CLUES TO A SOLUTION THAT WE NEED TO SORT THROUGH, THINK ABOUT, REARRANGE, AND PUT BACK TOGETHER AGAIN IN ORDER TO UNTANGLE A SITUATION

• MOVES FROM GENERIC INFORMATION TO A SPECIFIC SOLUTION

SAMPLE PROBLEM: WHOSE SHOES?

JOHNNY RED, SAMANTHA BLUE, AND JOEY GREEN ARE WEARING RED, BLUE, AND GREEN SHOES,

BUT NO PERSON IS WEARING THE SAME COLOR AS HIS OR HER LAST NAME. IF THE PERSON WEARING THE GREEN SHOES IS JOHNNY’S

COUSIN, TELL WHAT COLOR SHOE EACH PERSON IS WEARING.

LOGICAL MATRIX SOLUTION

X = NO

* = YES

Red Blue Green

JohnnyRed

x * x

Samantha Blue

x x *

JoeyGreen

* x x

USE LOGICAL REASONING TO SOLVE THESE PROBLEMS

1) BRAD, CHAD, AND TAD ARE TAKING MANDY, SANDY, AND CANDY TO THE SUNDAY SUMMER CONCERT. FROM THE CLUES BELOW, DISCOVER WHICH COUPLES WILL BE ATTENDING.

• TAD AND MANDY ARE SIBLINGS AND LIVE ON ELM STREET.

• CHAD IS PICKING UP HIS DATE IN HIS NEW RED SPORTS CAR.

• TAD IS TALLER THAN CANDY’S DATE.

• SANDY AND HER DATE WILL RIDE THEIR BICYCLES TO THE CONCERT.

• BRAD’S DATE LIVES ON OAK DRIVE.

2) THE THOMAS CHILDREN ARE 14, 15, AND 16 YEARS OLD. ONE LIKES CYCLING, ONE LIKES SWIMMING, AND ONE LIKES RUNNING. FROM THE CLUES BELOW, DETERMINE EACH CHILD’S NAME, AGE, AND FAVORITE SPORT.

• THE OLDEST LIKES CYCLING.

• SHANE LIKES SWIMMING.

• BRIDGET IS OLDER THAN KATIE.

• THE 14-YR. OLD DOES NOT LIKE SWIMMING.

USE LOGICAL REASONING TO SOLVE THESE PROBLEMS

3) ADAM, BEN, CAMI, AND DEB ARE FOUR FRIENDS WHO HAVE DIFFERENT FAVORITE COLORS. THEY EITHER LIKE RED, YELLOW, BLUE, OR GREEN. USE THE CLUES TO FIND EACH FRIEND’S FAVORITE COLOR.

• ADAM LIKES EITHER YELLOW OR BLUE.

• BEN LIKES EITHER YELLOW OR RED.

• THE GIRL WHO LIKES RED IS THE SHORTEST OF THE FOUR FRIENDS.

• DEB IS TALLER THAN ADAM.

4) IF TOM CAME JUST BEFORE TIM BUT JUST AFTER TINA, AND IF TESSA CAME JUST BEFORE TINA BUT JUST AFTER TRISTAN, THAN WHAT ORDER DID THEY COME IN?

USE LOGICAL REASONING TO SOLVE THIS PROBLEM

5) BALRAJ, SUKI, JOSUE, AHMED, AND CECILIA ARE ALL RIDING THE BUS TO SCHOOL. FROM THE CLUES BELOW, TELL WHAT EACH PERSON’S HOBBY IS AND WHERE EACH PERSON WORKS ON CAMPUS.

• SUKI GOT ON THE BUS FIRST, FOLLOWED BY THE PERSON WHO LIKES TO RACE CARS AND THEN BY THE MAN WHO WORKS IN THE ENROLLMENT OFFICE.

• CECILIA STRUCK UP A CONVERSATION WITH THE DELI WORKER WHO READS AS A HOBBY. IN THIS CONVERSATION, CECILIA ADMITTED TO PLAYING VIDEO GAMES AS HER HOBBY.

• ALL FIVE PEOPLE ARE LISTED HERE: BALRAJ, THE MAN WHO WORKS AT STUDENT LIFE, THE WOMAN WHO WORKS IN THE GYM, SUKI, AND THE MAN WHO WORKS IN THE BOOKSTORE.

• THE PERSON WHO WORKS IN STUDENT LIFE ENJOYS WEIGHT LIFTING.

• THE ROCK CLIMBER, JOSUE, AND THE MAN WHO WORKS IN THE BOOKSTORE SAT ON THE LEFT SIDE OF THE BUS.

1) BRAD, CHAD, AND TAD ARE TAKING MANDY, SANDY, AND CANDY TO THE SUNDAY SUMMER CONCERT. FROM THE CLUES BELOW, DISCOVER WHICH COUPLES WILL BE ATTENDING.

TAD AND MANDY ARE SIBLINGS AND LIVE ON ELM STREET.CHAD IS PICKING UP HIS DATE IN HIS NEW RED SPORTS CAR.

TAD IS TALLER THAN CANDY’S DATE.SANDY AND HER DATE WILL RIDE THEIR BICYCLES TO THE CONCERT.

BRAD’S DATE LIVES ON OAK DRIVE.

FROM THE FIRST CLUE, WE KNOW THAT TAD AND MANDY ARE NOT GOING TOGETHER. FROM THE THIRD CLUE, WE KNOW THAT TAD IS NOT GOING WITH CANDY. SO, TAD IS GOING WITH SANDY. FROM THE FIRST CLUE, WE KNOW THAT MANDY LIVES ON ELM STREET. FROM THE FIFTH CLUE, BRAD’S DATE LIVES ON OAK DRIVE. THIS MEANS THAT BRAD IS GOING WITH CANDY. THIS MEANS THE OTHER COUPLE IS CHAD IS GOING WITH MANDY.

2) THE THOMAS CHILDREN ARE 14, 15, AND 16 YEARS OLD. ONE LIKES CYCLING, ONE LIKES SWIMMING, AND ONE LIKES RUNNING. FROM THE CLUES BELOW, DETERMINE EACH CHILD’S NAME, AGE, AND FAVORITE SPORT.

THE OLDEST LIKES CYCLING.SHANE LIKES SWIMMING.

BRIDGET IS OLDER THAN KATIE.THE 14-YR. OLD DOES NOT LIKE SWIMMING.

THIS PROBLEM IS STILL SIMPLE ENOUGH THAT WE MIGHT BE ABLE TO COMPLETE IT WITHOUT A MATRIX.

FROM CLUES 1 AND 2, WE KNOW THAT SHANE IS NOT THE OLDEST, SO HE IS EITHER 14 OR 15.

FROM CLUE 2 AND 4, WE FIND THAT SHANE IS NOT THE 14-YR. OLD. SO, SHANE IS 15 AND LIKES SWIMMING.

FROM CLUE 3, WE FIND THAT BRIDGET IS 16 AND KATIE IS 14.

FROM CLUE 1, WE FIND THAT BRIDGET LIKES CYCLING. SO, BRIDGET IS 16 AND LIKES CYCLING AND KATIE IS 14 AND LIKES RUNNING. (NOTE: WE HAD TO FIND KATIE’S SPORT IN THE DESCRIPTION OF THE PROBLEM, NOT IN THE LIST OF CLUES.)

3) ADAM, BEN, CAMI, AND DEB ARE FOUR FRIENDS WHO HAVE DIFFERENT FAVORITE COLORS. THEY EITHER LIKE RED, YELLOW, BLUE, OR GREEN. USE THE CLUES TO FIND EACH FRIEND’S FAVORITE COLOR.

ADAM LIKES EITHER YELLOW OR BLUE.BEN LIKES EITHER YELLOW OR RED.

THE GIRL WHO LIKES RED IS THE SHORTEST OF THE FOUR FRIENDS.DEB IS TALLER THAN ADAM.

THIS ONE DOES NOT NEED A MATRIX EITHER. FROM CLUE 3, IT IS A GIRL WHO LIKES RED (EITHER CAMI OR DEB). FROM CLUE 2, BEN LIKES YELLOW. FROM CLUE 1, ADAM LIKES BLUE. FROM CLUES 3 AND 4, DEB LIKES GREEN WHICH ALSO MEANS THAT CAMI LIKES RED.

4) IF TOM CAME JUST BEFORE TIM BUT JUST AFTER TINA, AND IF TESSA CAME JUST BEFORE TINA BUT JUST AFTER TRISTAN, THAN WHAT ORDER DID THEY

COME IN?

THIS ONE WILL NOT REQUIRE A MATRIX. FROM THE FIRST PART OF THE SENTENCE (UP UNTIL THE COMMA), WE HAVE THAT TINA CAME FIRST, TOM CAME IN THE MIDDLE, AND TIM CAME LAST. FROM THE FIRST PART OF THE SENTENCE, WE ADD THAT TESSA CAME BEFORE TINA BUT TRISTAN CAME EVEN BEFORE HER. SO, OUR FINAL ORDER IS TRISTAN, TESSA, TINA, TOM, AND TIM.

5) BALRAJ, SUKI, JOSUE, AHMED, AND CECILIA ARE ALL RIDING THE BUS TO SCHOOL. FROM THE CLUES BELOW, TELL WHAT EACH PERSON’S HOBBY IS AND WHERE EACH PERSON WORKS ON CAMPUS.

SUKI GOT ON THE BUS FIRST, FOLLOWED BY THE PERSON WHO LIKES TO RACE CARS AND THEN BY THE MAN WHO WORKS IN THE ENROLLMENT OFFICE.CECILIA STRUCK UP A CONVERSATION WITH THE DELI WORKER WHO READS AS A HOBBY. IN THIS CONVERSATION, CECILIA ADMITTED TO PLAYING

VIDEO GAMES AS HER HOBBY. ALL FIVE PEOPLE ARE LISTED HERE: BALRAJ, THE MAN WHO WORKS AT STUDENT LIFE, THE WOMAN WHO WORKS IN THE GYM, SUKI, AND THE MAN

WHO WORKS IN THE BOOKSTORE.THE PERSON WHO WORKS IN STUDENT LIFE ENJOYS WEIGHT LIFTING.

THE ROCK CLIMBER, JOSUE, AND THE MAN WHO WORKS IN THE BOOKSTORE SAT ON THE LEFT SIDE OF THE BUS.THIS ONE MAY BE COMPLICATED ENOUGH TO REQUIRE A MATRIX. FROM THE CLUES BELOW, HERE IS HOW I WOULD MAKE

MINE:

Race cars

Reading

Video games

Weight lifting

Rock climbing

Enrollment

Deli Student Life

Gym Bookstore

Balraj

Suki

Josue

Ahmed

Cecilia

Enrollemnt

Deli

Student Life

Gym

Bookstore

CLUE 1: SUKI GOT ON THE BUS FIRST, FOLLOWED BY THE PERSON WHO LIKES TO RACE CARS AND THEN BY THE MAN WHO WORKS IN THE ENROLLMENT OFFICE.

THIS TELLS US SEVERAL THINGS: (1) SUKI DOES NOT LIKE TO RACE CARS AND SHE DOES NOT WORK IN ENROLLMENT. (2) THE PERSON WHO LIKES TO RACE CARS DOES NOT WORK IN ENROLLMENT, AND (3) IT IS A MAN WHO WORKS IN

ENROLLMENT. HERE IS WHAT OUR CHART WOULD LOOK LIKE AFTER THIS CLUE: (NOTE: X IS FOR NO AND * IS FOR YES)

Race cars

Reading

Video games

Weight lifting

Rock climbing

Enrollment

Deli Student Life

Gym Bookstore

Balraj

Suki X X

Josue

Ahmed

Cecilia

X

Enrollemnt

X

Deli

Student Life

Gym

Bookstore

CLUE 2: CECILIA STRUCK UP A CONVERSATION WITH THE DELI WORKER WHO READS AS A HOBBY. IN THIS CONVERSATION, CECILIA ADMITTED TO PLAYING VIDEO GAMES AS HER HOBBY.

THIS CLUE TELLS US THREE THINGS: (1) THE READER WORKS IN THE DELI, AND (2) CECILIA LIKES VIDEO GAMES, AND (3) CECILIA DOES NOT WORK IN THE DELI. NOTE THAT WHEN WE CAN FILL IN A YES BOX, WE GO UP AND DOWN AND SIDEWAYS

XING OUT THE OTHER POSSIBILITIES.

Race cars

Reading

Video games

Weight lifting

Rock climbing

Enrollment

Deli Student Life

Gym Bookstore

Balraj

X

Suki X X X

Josue

X

Ahmed

X

Cecilia

X X * X X X X

Enrollemnt

X X

Deli X * X X X

Student Life

X

Gym X

Bookstore

X

CLUE 3: ALL FIVE PEOPLE ARE LISTED HERE: BALRAJ, THE MAN WHO WORKS AT STUDENT LIFE, THE WOMAN WHO WORKS IN THE GYM, SUKI, AND THE MAN WHO WORKS IN THE BOOKSTORE.

THIS TELLS US THE FOLLOWING: (1) BALRAJ DOEN NOT WORK IN STUDENT LIFE, THE GYM OF THE BOOKSTORE, (2) A MAN WORKS AT STUDENT LIFE, (3) A MAN WORKS IN THE BOOKSTORE. AFTER WE FILL IN ALL OF THIS, WE SEE THAT CECILIA MUST

WORK IN THE GYM.

Race cars

Reading

Video games

Weight lifting

Rock climbing

Enrollment

Deli Student Life

Gym Bookstore

Balraj

X X X X

Suki X X X X X

Josue

X X

Ahmed

X X

Cecilia

X X * X X X X X * X

Enrollemnt

X X

Deli X * X X X

Student Life

X

Gym X

Bookstore

X

CLUE 4: THE PERSON WHO WORKS IN STUDENT LIFE ENJOYS WEIGHT LIFTING.AFTER WE FILL THIS IN, WE CAN ALSO DEDUCE THAT BALRAJ AND SUKI ARE NOT THE WEIGHT LIFTERS. WE CAN SEE THAT

FROM THE CHART. WE CAN ALSO GO BACK TO CLUE TWO TO SEE THAT SUKI LIKES READING. NOW ON THE CHART, WE CAN SEE THAT BALRAJ WORKS IN ENROLLMENT.

Race cars

Reading

Video games

Weight lifting

Rock climbing

Enrollment

Deli Student Life

Gym Bookstore

Balraj

X X X * X X X X

Suki X * X X X X * X X X

Josue

X X X X X

Ahmed

X X X X X

Cecilia

X X * X X X X X * X

Enrollemnt

X X X

Deli X * X X X

Student Life

X X X * X

Gym X X

Bookstore

X X

CLUE 5: THE ROCK CLIMBER, JOSUE, AND THE MAN WHO WORKS IN THE BOOKSTORE SAT ON THE LEFT SIDE OF THE BUS.FROM THIS CLUE, WE FIND THAT JOSUE IS NOT THE ROCK CLIMBER AND DOES NOT WORK IN THE BOOKSTORE. SO, HE

WORKS IN STUDENT LIFE AND AHMED WORKS IN THE BOOKSTORE. WE ALSO KNOW THAT AHMED IS NOT THE ROCK CLIMBER. NOW WE LOOK AT THE CHART TO SEE THAT THE MAN WHO WORKS IN STUDENT LIFE IS ALSO THE WEIGHT LIFTER, HENCE JOSUE. THIS LEAVE ONLY RACING CARS FOR AHMED WHICH IN TURN LEAVES ONLY ROCK CLIMBING FOR BALRAJ. IT IS NOT

NECESSARY TO COMPLETE THE BOTTOM PART OF THE CHART BECAUSE NOW WE CAN ANSWER THE QUESTION:BALRAJ IS THE ROCK CLIMPBE AND WORKS IN ENROLLMENT. SUKI IS THE READER AND WORKS IN THE DELI.

JOSUE IS THE WEIGHT LIFTER AND WORKS AT STUDENT LIFE. AHMED RACES CARS AND WORKS AT THE BOOKSTORE. CECILIA PLAYS VIDEO GAMES AND WORKS AT THE GYM.

Race cars

Reading

Video games

Weight lifting

Rock climbing

Enrollment

Deli Student Life

Gym Bookstore

Balraj

X X X X * * X X X X

Suki X * X X X X * X X X

Josue

X X X * X X X * X X

Ahmed

* X X X X X X X X *

Cecilia

X X * X X X X X * X

Enrollemnt

X X X

Deli X * X X X

Student Life

X X X * X

Gym X X

Bookstore

X X

MORE LOGICAL REASONING PROBLEMS AND RESOURCES ONLINE

• HTTP://WWW.MRMYERS.ORG/BRAIN_BUSTERS/MATRIX_LOGIC/INSTRUCTIONS.HTML

• HTTP://WWW.MRMYERS.ORG/BRAIN_BUSTERS/MATRIX_LOGIC/RACE.HTML

• HTTP://WWW.IXL.COM/MATH/GRADE-6/USE-LOGICAL-REASONING-TO-FIND-THE-ORDER

• HTTP://WWW.PROPROFS.COM/QUIZ-SCHOOL/STORY.PHP?TITLE=MATH-LOGIC-REASONING-SKILLS

• HTTPS://WWW.YOUTUBE.COM/WATCH?V=N_DWOSFVT3W

• HTTPS://WWW.YOUTUBE.COM/WATCH?V=7FN_LHX07IW