GACE math
The state sales tax is 7.5%. Which number could also represent 7.5%? (Quiz 1)
A- 0.75 B- 0.0075 C- 3/4 D- 3/40 (correct) There is always the option of arriving at the answer by eliminating incorrect answer choices, but it is always a good idea to double-check the final choice. In the case of this question, 3/40=0.075= 75/1000= 7.5/100= 7.5%
Jessica is having 42 friends over for her party. She baked 7 extra-large pizzas with 12 slices each. If everyone shares equally, how much of one pizza will each friend eat? (Quiz 3)
A- 1/6 (correct) B- 1/4 C- 1/3 D- 1/2 To find how much each person eats, we need to split 7 pizzas into 42 portions, so 7/42=1/6, so each person will eat 1/6 of a pizza
Joseph owns a distributing company that repackages cornmeal for bulk quantities into smaller packages. If Joseph wants to fill 100,000 bags that each hold 10 grams of cornmeal, how many kilograms of cornmeal should he buy? (Quiz 1)
A- 10^2 B- 10^3 (correct answer) C- 10^4 D- 10^5 Multiply the quantities 10g/bag and 100,000 bags, and convert grams to kilograms. The arithmetic can be simplified by using powers of 20 as follows: 10g=10^1 g 100,000 bags= 10^5 bags 1000g= 10^3g= 1 kg Therefore: 10^1 g/bag x 10^5 bags x 1 kg/10^3 kg = 10^3 kg
René was selling corn at the local farmer's market. René sold 146 more cobs of corn in the morning than in the afternoon. If he sold a total of 372 cobs of corn, how many cobs did he sell in the afternoon? (Quiz 6)
A- 113 (correct answer) B- 73 C- 186 D- 226 Let x be the number of cobs René sold in the afternoon. In the morning he sold x+146. Add the number of cobs sold in the morning to the number sold in the afternoon, and set the sum equal to 372. Solve for x. x+ 146+ x=372 2x+ 146=372 2x= 372-146=226 x= 226/2=113 cobs
Jack is making cupcakes for the bake sale at his church. Each cupcake needs 1/4 teaspoon of vanilla. How many cupcakes can he make with the 3 3/8 t of vanilla? (Quiz 3)
A- 14 cupcakes B- 13 cupcakes (correct answer) C- 12 cupcakes D- 15 cupcakes The total amount of vanilla is divided by the amount needed for each cupcake: 3 3/8 divided by 1/4 To divide by a fraction, multiply by the reciprocal: 27/8 x 4/1=108/8= 27/2=13 1/2 There can't be half of a cupcake, so 13 cupcakes are the most that can be made.
Jose spends 2 1/3 hours working on homework for math, science, and reading. He spent an equal amount of time on each subject. During his math work, he spent about 1/2 the time on a worksheet and the remaining time reviewing notes. Approximately, how much time did he spend on the worksheet? (Quiz 4)
A- 15 minutes B- 30 minutes C- 20 minutes (correct answer) D- 10 minutes First, determine how much time was spent on each subject. 2 1/3 divided by 3 x 1/3=7/9. So 7/9 hours was spent on math. One half of 7/9 is equal to 7/9x 1/2= 7/18. The problem asks for an approximate amount of time so if 18 was rounded to 20, it would go into 60 3 times (60 divided by 20=3). 3x7=21 so the approximate amount of time is 20 minutes.
The ratio of children to adults in the theatre of a PG-13 movie is 2 to 5. Which of the following is the possible total number of children and adults in the movie? (Quiz 1)
A- 16 B- 45 C- 49 (correct answer) D- 51 Since the ratio of children to adults is 2 to 5, the total number of children is 2 parts while the number of adults is 5 parts. Total there are 7 parts, so the total number of children and adults must be a multiple of 7. Since 49 is a multiple of 7, it is a possible total of the number of children and adults in the theatre. The number of children would be 49x 2/2+5= 14 while the number of adults would be 49 x 5/2+5=35
What is the difference between rounding 57,213 to the thousands place and the ten thousands place? (Quiz 2)
A- 2,000 B- 3,000 (correct answer) C- 40,000 D- 7,000 57,213 rounded to the thousands place is 57,000. 57,213 rounded to the ten thousands place is 60,000. The difference in these numbers is 3,000
Mr. Henry wants to purchase 24 hamburgers and 24 hot dogs for a Bar-B-Q he is having at his house. If hotdogs come in a package of 8 and hamburgers come in a package of 6, how many packages total of hamburgers and hotdogs will Mr. Henry have to buy? (Quiz 1)
A- 24/8+24/6 B-24(1/8+1/6) C-24(7/24) D- all the above (correct answer)
What is the prime factorization of 1,188? (Quiz 3)
A- 2^2x3^3x11 B- 3^3x4x11 C- 2^3x3^2x11 D- 3x6^2x11 The prime factors of 1,188 are 2x2x3x3x3x11. Therefore, 2^3x3^3x11 is the prime factorization of 1,188
Sally walked to her friends's house and then they went for a walk together. According to the graph, how much time of sally's walk was spent a mile or less from home? (Quiz 4)
A- 3/7 (correct answer) B- 1/2 C- 4/7 D- 2/7 She spent 30 minutes within a mile of her home. The graph shows a 70-minute time period. 30/70 simplifies to 3/7
A pool empties at a rate of 12 quarts every 2 minutes. How many hour and minutes will it take to completely empty the pool which contains 12,000 gallons? (1 gallon=4 quarts) (Quiz 1)
A- 33 hours and 20 minutes B- 66 hours and 40 minutes C- 133 hours and 20 minutes (correct answer) D- 16 hours and 40 minutes Both quarts and minutes needs to be converted. 12. quarts= 3 gallons. 12,000/3= 4,000 x 2 minutes= 8,000 minutes/60 minutes= 133 hours and 20 minutes.
Jeremy is building a tower with all red, green, and blue blocks in his collection. He has three more green blocks than blue blocks. He has ten more red blocks than green blocks. If he has six blue blocks, how many blocks will there be in is final tower?
A- 34 (correct answer) B- 9 C- 19 D- 25 He has 6 blue blocks, 9 (6+3) green blocks, and 19 (9+10) red blocks. Therefore, he has 6+9+19=34 total blocks.
Hailey's mom wants to help her practice using fractions. They decide to make their famous chocolate chip cookie recipe, but it will need to be tripled so that she will have enough for all of the third-grade students. The original recipe calls for 2 ½ cups of flour and ¾ cup of sugar. How much more flour than sugar does she need to make enough cookies for her grade? (Quiz 1)
A- 4 1/4 cups B-3 1/2 cups C- 1 3/4 cups D- 5 1/4 cups (correct answer) 2 1/2 x 3=7 1/2 which is the total amount of flour needed. 3/4 x 3=2 1/2 which is the amount of sugar needed. 7 1/2-2 1/4= 5 1/4
If the number 888 is written as a product of its prime factors in the form a^3bc, what is the numerical value of a +b +c? (Quiz 2)
A- 42 (correct answer) B- 37 C-8 D-222 The prime factorization of 888 is 2^3x3x37. 42 is the correct answer because 2+3+37 is 42
At the end of the school year, Mrs. Rose is giving her students the leftover pencils. She wants to give each student the same number and then keep the remaining for the next year. If Mrs. Rose has 23 students and 150 pencils, how many will each student receive? (Quiz 5)
A- 5 B- 12 C- 6 (correct answer) D- 7 Since there are 23 students, divide 150 by 23. 150 divided by 23=6 R12. Each student will receive 6 pencils and Mrs. Rose will have 12 left over for the next year.
The legend on a map says 1 cm= 10 km. What is the actual distance, in km, between two points if the map distance is 546 mm? (Quiz 1)
A- 5460 km B- 546 km (correct answer) C- 54.6 km D- 5.46 km Convert the map distance in mm to cm: 546 x 1cm/10mm =54.6 cm. Form a ratio from the map legend, and multiply by the map distance: 10km/1cm x 54.6= 546 km
Michal is riding at a constant 12 miles per hour. At noon he sees a road sign stating that Longtown is 14 miles away and Lyons is 16 miles away. How far will he be from Lyons at 12:45 p.m.?
A- 6 miles B- 9 miles C- 7 miles (correct answer) D- 8 miles At a rate of 12 miles per hour, Michal will travel 9 mi in 45 min: 12 mi/hr x 3/4 hr= 9mi. Subtract 9 miles from the initial distance of 16 miles to find the remaining distance to Lyons of 7 miles.
An average person takes 15 breaths per minute. how many breaths will an average person take in 4 minutes and 40 seconds? (Quiz 2)
A- 68 B- 60 C- 65 D- 70 (correct answer) Each breath takes 4 seconds. In 4 minutes, a person breathes 60 times. In 40 seconds, a person breathes 10 times, because 40 seconds is 2/3 of a minute and 2/3 of 15 is 10. 60+10=70
Which of the following provides a counterexample to the statement given? Two complementary angles are not congruent. (Quiz 4)
A- 90°+90°=180° B- 50°+40°=90° C- 100°+80°=180° D- 45°+45°=90° (correct answer) Two 45 degree angles are congruent and also sum to 90°
A student claims that the largest area a rectangle can have is 99cm^2 if the perimeter is 40 cm. Which of the following rectangle disproves this claim? (Quiz 6)
A- a square with a 20 cm side length B- a square with a 10 cm side length (correct) C- a rectangle with side lengths of 11 cm and 9 cm D- a rectangle with side lengths of 12 cm and 8 cm The area of this square is 100 cm^2 and the perimeter is 40 cm. All squares are rectangles, but not all rectangles are squares.
