6th GRADE EOG MATH PRACTICE PROBLEMS

Problem 1 :

Joe will go to the swimming pool on 20 different days this month.

  • A one-day pass to the pool is $2.25.
  • A monthly pass to the pool is $30.00.

How much money will Joe save by buying a monthly pass?

A) $20     B)  $18     C)  $15       D) $12

Solution :

Cost of one day pass = $2.25

Cost for 20 days = 20(2.25)

= 45

Cost of monthly pass = $30

The amount that Jill will save = 45 - 30

= $15

So, option C is correct.

Problem 2 :

A rectangular parking lot has an area of 2/3 of a square kilometer. The width is 1/2 of a kilometer. What is the length, in kilometers, of the parking lot?

A) 1/3    B) 2/3     C) 1 1/3     D) 1   2/3

Solution :

Area of rectangular parking = 2/3 square kilometer

Width = 1/2 kilometer

Length = L

Length x width = 2/3

(1/2) x L = 2/3

L = (2/3) / (1/2)

L = 4/3

Converting into mixed fraction, we get

L = 1   1/3

So, option C is correct.

Problem 3 :

The price of a theater ticket increased from $7.50 to $7.75. The theater sold 315 tickets at the higher price. With the price increase, how much more did the theater earn on the tickets?

A) $78.00      B) $78.25    C) $78.50   D) $78.75

Solution :

Difference in cost = 7.75 - 7.50

= 0.25

Cost of 315 tickets with difference amount = 0.25 (35)

= 78.75

So, answer option D is correct.

Problem 4 :

Hannah babysits to earn money.

  • She charges $6.50 to babysit for the first hour.
  • She charges $5.75 for each additional hour.
  • Let n equal the number of hours after the first hour.

Which expression represents how much Hannah charges?

A)  12.25n     B) 6.50 + 5.75n   

C) 6.50n + 5.75     D) 6.50n + 5.75n

Solution :

Charges for first hour of babysit = $6.50

Hourly charges for the next hours = 5.75 n

So, total charge = 6.50 + 5.75n

Option B is correct.

Problem 5 :

What is the value of (1/7)3 ?

A)  3/7     B) 1/7      C) 3/343     D) 1/343

Solution :

(1/7)3 = (1/7) x (1/7) x (1/7)

= 1/343

So, option D is correct.

Problem 6 :

Which choice shows a set of data that could be represented by the box plot shown below?

6th-grade-eog-q6

A) 1, 3, 5, 6, 7, 7, 8, 13, 19, 20

B) 1, 3, 5, 6, 6, 8, 13, 14, 19, 20

C) 1, 2, 3, 5, 7, 8, 8, 13, 19, 20

D) 1, 5, 5, 6, 6, 6, 8, 13, 19, 20

Solution :

6th-grade-eog-q6p1.png

Option A :

1, 3, 5, 6, 7, 7, 8, 13, 19, 20

Minimum = 1

1, 3, 5, 6

Q1 = (3 + 5)/2 ==> 4

8, 13, 19, 20

Q3 = (13 + 19)/2 ==> 16

Median = 7

So, option A is correct.

Problem 8 :

A rectangular room has an area of 131  1/4 square feet. The length of the room is 12  1/2 feet. What is the width, in feet, of the room?

Solution :

Problem 9 :

Allen is building birdhouses that require 1/2 -ft-long boards. How many pieces that are exactly 1/2 ft long can be made from a board that is 8  1/4 ft long?

Solution :

Number of pieces=8 14 ÷12=334 ÷12=334×21=332= 16.5

So, 16 pieces.

Problem 10 :

How much money should John get back when he uses $10.00 to pay for purchases totaling $5.25?

Express the answer as dollars. cents.

Solution :

Amount John pays = 10

Value of purchasing = 5.25

= 10 - 5.25

= 4.75

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