# If 1/3 of a Number Is 3 More Than of the Number, Then What Is the Number?

Problem Solving

Backsolving

**Start with “___”**

Mike bought a used car and had it repaired. The cost of the repair was one-fifth the purchase price of the car. If the price of the car and the repair was $4800, then what was the purchase price of the car?

A)$800

B)$960

C)$3840

D)$4000

E)$4250

If 1/3 of a number is 3 more than ¼ of the number, then what is the number?

A)18

B)24

C)30

D)36

E)48

Plugging In

**When there are variables in the answer choices**

**Plug in ______when there are fractions, plug in ______when dealing with percents**

Celeste gave Dave n dollars. She gave Karen two dollars more than she gave Dave and she gave Amber three dollars less than she gave Karen. In terms of n, how many dollars did Celeste give Karen, Dave, and Amber altogether?

A)

B)n – 1

C)3n

D)3n – 1

E)3n + 1

If x and y are integers and xy is an even integer, which of the following must be an odd integer?

A)xy + 5

B)x + y

C)x/y

D)4x

E)7xy

At Madison High School each student studies exactly one foreign language. Three-fifths of the students take Spanish, and one-fourth of the remaining students take German. If all of the others take French, what percent of the students take French?

A)10

B)15

C)20

D)25

E)30

Use a chart

In 1980, Judy was 3 times as old as Adam, but in 1984 she was only twice as old as he was. How old was Adam in 1980?

A)4

B)8

C)12

D)14

E)16

Which of the following is the larger of two numbers the product of which is 600 and the sum of which is five times the difference between the two?

A)10

B)15

C)20

D)30

E)50

If t tablets cost c cents, then at this rate how many cents will 5 tablets cost?

A)5ct

B)5c/t

C)c/5t

D)5t/c

E)t/5c

The positive difference between the square of any two consecutive integers is always:

A)the square of an integer

B)a multiple of 5

C)an even integer

D)an odd number

E)a prime number

On the first day after being given an assignment, a student read ½ the number of pages assigned and on the second day 3 more pages. If the student still has 6 more pages to read, how many pages were assigned?

A)15

B)18

C)24

D)30

E)36

A street vendor has just purchased a carton containing 250 hot dogs. If the carton cost x dollars, what is the cost in dollars of 10 of the hot dogs?

A)x/25

B)x/10

C)10x

D)10/x

E)25/x

When both 16 and 9 are divided by n, the remainder is 2. What is n?

A)3

B)4

C)5

D)6

E)7

The units of a 2-digit number is 3 times the tens digit. If the digits are reversed, the resulting number is 36 more than the original number. What is the original number?

A)13

B)26

C)36

D)62

E)93

The sum of x distinct integers greater than zero is less than 75. What is the greatest possible value of x?

A)8

B)9

C)10

## D)11

E)12

The price of a certain stock increased 8 points, then decreased 13 points, and then increased 9 points. If the stock price before the changes was x points, which of the following was the stock price, in points, after the changes?

A)x – 5

B)x – 4

C)x + 4

D)x + 5

E)x + 8

From 1980 to 1990, Lior’s weight increased by 25%. If his weight was k kilograms in 1990, what was it in 1980?

A)1.75k

B)1.25k

C)1.20k

D).80k

E).75k

If x is a positive integer, for which of the following equations must y be a negative integer?

A)xy = 9

B)x + y = 7

C)x + 2y =6

D)y – x = 4

E)–x – y = 3

If a school cafeteria needs c cans of soup each week for each student, and if there are s students in the school, for how many weeks will x cans of soup last?

A)

B)

C)

D)

E)

If the altitude of a triangle increases by 5% and the base of the triangle increases by 7%, by what percent will the area of the triangle increase?

A)3.33%

B)5%

C)6%

D)12%

E)12.35%

If Jim can drive the distance k miles in 50 minutes, how many minutes, in terms of k, will it take him to drive 10 miles at the same speed?

A)

B)

C)60k

D)10k

E)

Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Four years ago Jim was 4 times as old as Sam. How old is Jim now?

A)8

B)12

C)16

D)20

E)24

At the rate of f/3 feet per m minutes, how many feet can a bicycle travel in s seconds?

A)

B)

C)

D)

E)

If Yuriko is now twice as old as Lisa was 10 years ago, how old is Lisa today if Yuriko is now n years old?

A)n/2 + 10

B)n/2 – 10

C)n – 10

D)2n + 10

E)2n – 10

A vending machine dispenses b candy bars, each at a cost of c dollars, every day. During a 30 day period, what is the amount of money in cents taken in by the vending machine from the sale of candy?

A)

B)

C)

D)

E)