PRAXIS Core Math MCQ Test

1) Which one of the following is NOT the same as a 3:7 ratio?

6:10

9:21

12:28

15:35

30:70

Reduce each ratio to simplest form (similar to how you would with fractions) and compare:

A) 6:10 reduced by 2 = 3:5, which is not the same as a 3:7 ratio.
B) 9:21 reduced by 3 = 3:7
C) 12:28 reduced by 4 = 3:7
D) 15:35 reduced by 5 = 3:7
E) 30:70 reduced by 10 = 3:7

Thus A) 6:10 is the answer.

Explanation

Reduce each ratio to simplest form (similar to how you would with fractions) and compare:

A) 6:10 reduced by 2 = 3:5, which is not the same as a 3:7 ratio.
B) 9:21 reduced by 3 = 3:7
C) 12:28 reduced by 4 = 3:7
D) 15:35 reduced by 5 = 3:7
E) 30:70 reduced by 10 = 3:7

Thus A) 6:10 is the answer.

2) In which of the following are the two numbers equivalent? I. 1.2 and 1/2 II. 0.8 and 0.800 III. 9 and 3³

I

II

III

I and III

I, II, and III

straight I right parenthesis space 1.2 space and space 1 half space are space not space equivalent comma space since space 1 half space equals space 0.5 space<br /> II right parenthesis space 0.8 space and space 0.800 space are space equivalent. space<br /> III right parenthesis space 9 space and space 3 cubed space are space not space equivalent space since space 3 cubed space equals space 3 space straight x space 3 space straight x space 3 space equals space 27 space space<br /> Therefore comma space only space II space is space true comma space making space left parenthesis straight B right parenthesis space the space correct space answer. space

Explanation

straight I right parenthesis space 1.2 space and space 1 half space are space not space equivalent comma space since space 1 half space equals space 0.5 space<br /> II right parenthesis space 0.8 space and space 0.800 space are space equivalent. space<br /> III right parenthesis space 9 space and space 3 cubed space are space not space equivalent space since space 3 cubed space equals space 3 space straight x space 3 space straight x space 3 space equals space 27 space space<br /> Therefore comma space only space II space is space true comma space making space left parenthesis straight B right parenthesis space the space correct space answer. space

3) Of the five numbers listed below, which is the greatest?

0.00800

0.022

0.00004

0.0197

0.0202

Write the numbers so that they all go to the same place value. Then, compare as regular numbers:

A) 0.00800 = 0.00800 = 800
B) 0.022 = 0.02200 = 2,200
C) 0.00004 = 0.00004 = 4
D) 0.0197 = 0.01970 = 1,970
E) 0.0202 = 0.0202 = 2,020

2,200 has the greatest value, thus B) 0.022 is the answer.

Explanation

Write the numbers so that they all go to the same place value. Then, compare as regular numbers:

A) 0.00800 = 0.00800 = 800
B) 0.022 = 0.02200 = 2,200
C) 0.00004 = 0.00004 = 4
D) 0.0197 = 0.01970 = 1,970
E) 0.0202 = 0.0202 = 2,020

2,200 has the greatest value, thus B) 0.022 is the answer.

4) What digit is in the hundredths place of the number 978.0234?

2

3

4

7

8

Since the hundredths places ends in "ths", this means that its place value is less than one and holds a place to the right of the decimal point.

After the decimal point, going from left to right, the place values are as follows:
. tenths, hundredths, thousandths, ten thousandths...

Therefore, 2 is in the hundredths place and is the correct answer.

Explanation

Since the hundredths places ends in "ths", this means that its place value is less than one and holds a place to the right of the decimal point.

After the decimal point, going from left to right, the place values are as follows:
. tenths, hundredths, thousandths, ten thousandths...

Therefore, 2 is in the hundredths place and is the correct answer.

5) A map is drawn with a scale of 4 inches representing 80 miles. How many inches on the map would represent 280 miles?

7

14

20

28

40

straight A space proportion space can space be space set space up colon<br /> 4 over straight n equals space 80 over 280<br /> Reduce colon<br /> 4 over straight n equals space 2 over 7<br /> Cross space multiply colon<br /> 4 cross times 7 space equals space 2 straight n<br /> space space space space 28 space equals space 2 straight n<br /> Solve space for space straight n colon<br /> space space 28 over 2 equals space fraction numerator 2 straight n over denominator 2 end fraction<br /> space space space space space 14 space equals space straight n<br /> The space answer space is space straight B right parenthesis space 14<br />

Explanation

straight A space proportion space can space be space set space up colon<br /> 4 over straight n equals space 80 over 280<br /> Reduce colon<br /> 4 over straight n equals space 2 over 7<br /> Cross space multiply colon<br /> 4 cross times 7 space equals space 2 straight n<br /> space space space space 28 space equals space 2 straight n<br /> Solve space for space straight n colon<br /> space space 28 over 2 equals space fraction numerator 2 straight n over denominator 2 end fraction<br /> space space space space space 14 space equals space straight n<br /> The space answer space is space straight B right parenthesis space 14<br />

6) Which of the following is greater than 0.674?

2/3

0.0698

7/12

6.83%

11/16

Convert all of these to the same form (fraction, decimal, percent) and compare:

Which of the following is greater than .512 = 51.2%?

1/2 = 50%
0.0598 = 5.98%
5/12 = 41.66...%
5.83%
8/15 = 53.33...%

It is clear that 8/15 is the answer.

The quick way would have been to recognize .512 as being just slightly over 1/2, and that the only answer given that is more than 1/2 is 8/15, because 8 is more than half of 15.

Explanation

Convert all of these to the same form (fraction, decimal, percent) and compare:

Which of the following is greater than .512 = 51.2%?

1/2 = 50%
0.0598 = 5.98%
5/12 = 41.66...%
5.83%
8/15 = 53.33...%

It is clear that 8/15 is the answer.

The quick way would have been to recognize .512 as being just slightly over 1/2, and that the only answer given that is more than 1/2 is 8/15, because 8 is more than half of 15.

7) Theodore bought a clock that is 18 centimeters tall. What is the height of the clock in millimeters?

0.18

1.8

180

1,800

18,000

1 centimeter = 10 millimeters

This means that there are 10 times as many millimeters as there are centimeters.

18 x 10 = 180, so the height of the clock is 180 millimeters.

Explanation

1 centimeter = 10 millimeters

This means that there are 10 times as many millimeters as there are centimeters.

18 x 10 = 180, so the height of the clock is 180 millimeters.

8) In a class of 25 students, 15 are boys. What percentage of the students in the class are girls?

10%

15%

25%

40%

60%

Out space of space straight a space total space of space 25 space students comma space if space 15 space are space boys comma space then space 10 space must space be space girls. space<br /> To space determine space the space percentage space of space girls space in space the space class comma space take space the space number space<br /> of space girls space and space divide space it space by space the space total space number space of space students comma space and space then space convert space<br /> to space straight a space percentage space left parenthesis multiply space by space 100 % right parenthesis. space<br /> 10 over 25 space cross times space 100 % space equals space 2 over 5 space cross times space fraction numerator 100 % over denominator 1 end fraction equals space fraction numerator 200 % over denominator 5 end fraction space equals space 40 %<br />

Explanation

Out space of space straight a space total space of space 25 space students comma space if space 15 space are space boys comma space then space 10 space must space be space girls. space<br /> To space determine space the space percentage space of space girls space in space the space class comma space take space the space number space<br /> of space girls space and space divide space it space by space the space total space number space of space students comma space and space then space convert space<br /> to space straight a space percentage space left parenthesis multiply space by space 100 % right parenthesis. space<br /> 10 over 25 space cross times space 100 % space equals space 2 over 5 space cross times space fraction numerator 100 % over denominator 1 end fraction equals space fraction numerator 200 % over denominator 5 end fraction space equals space 40 %<br />

9) Nicole spent $60 on groceries the first week of July. The second week of July she spent $75 on groceries. What was the percent increase in the amount spent by Nicole on groceries?

15%

20%

25%

40%

60%

To space find space the space percent space increase comma space take space the space difference space between space the space new<br /> amount space and space the space original space amount space left parenthesis 75 minus 60 right parenthesis space and space divide space it space by space the space original space<br /> amount space left parenthesis 60 right parenthesis colon<br /> fraction numerator left parenthesis 75 space minus space 60 right parenthesis over denominator 60 end fraction space equals space 15 over 60 equals space 0.25<br /> Convert space to space straight a space percent space by space moving space the space decimal space point space two space places space to space the space right<br /> and space adding space straight a space percent space sign space left parenthesis or space by space multiplying space by space 100 % right parenthesis. space<br /> Thus comma space 0.25 space becomes space 25 %.

Explanation

To space find space the space percent space increase comma space take space the space difference space between space the space new<br /> amount space and space the space original space amount space left parenthesis 75 minus 60 right parenthesis space and space divide space it space by space the space original space<br /> amount space left parenthesis 60 right parenthesis colon<br /> fraction numerator left parenthesis 75 space minus space 60 right parenthesis over denominator 60 end fraction space equals space 15 over 60 equals space 0.25<br /> Convert space to space straight a space percent space by space moving space the space decimal space point space two space places space to space the space right<br /> and space adding space straight a space percent space sign space left parenthesis or space by space multiplying space by space 100 % right parenthesis. space<br /> Thus comma space 0.25 space becomes space 25 %.

10) Natalie did 1/3 of her homework on Saturday and 1/5 more of her homework on Sunday. What is the ratio of the amount of homework she has completed to the amount of homework she has not completed?

3:5

7:8

8:7

7:15

8:15