Did you take the ATI TEAS 6 Math Practice Test? If so, then it’s time to review your results to see where you went wrong and what areas you need to improve.

## ATI TEAS 6 Mathematical Reasoning Practice Test Answers and Explanations

1- **Choice B is correct**

\(\frac{1}{x} = \frac{\frac{1}{1} }{\frac{7}{13}} = \frac{13}{7}\)

2- **Choice D is correct**

Let a and b be the numbers. Then: \(a + b = x \)

\(a=-6→-6+b=x→b=x+6, 4b = 4(x+6)\)

3- **Choice B is correct**

Circumference \(= 2πr, C=2π×7=14π ,π=3.14 →C=14π=43.98≅44\)

4- **Choice C is correct**

\((5.6+3.4+2.6+1.4)x = x-24, 13x = x-24⇒12x=-24\) Then \(x=-2\)

5- **Choice B is correct**

\(\frac{12}{30} = 0.4\)

6- **Choice D is correct**

Converting mixed numbers to fractions, our initial equation becomes

\(\frac{8}{3} × \frac{68}{9}\), Applying the fractions formula for multiplication, \(\frac{8× 68}{3 × 9} = \frac{544}{27} = 20 \frac{4}{27}\)

7- **Choice A is correct**

\(12÷\frac{3}{8}=32\)

8- **Choice A is correct**

If \(2.4< x ≤5.6\), then \(x\) cannot be equal to 2.4.

9- **Choice A is correct**

\(\frac{36}{52} = \frac{9}{13}\)

10- **Choice B is correct**

Let \(x\) be the average of numbers. Then: \(\frac{180}{12} < x < \frac{288}{12}, 15 < x < 24 \)

From choices provided, only 20 is correct.

11- **Choice C is correct**

yards \(= 12\) feet, \(\frac{(27 feet + 12 yards)}{9} = \frac{(27 feet + 144 feet) }{9} = \frac{(171 feet )}{9} = 19\) feet

12- **Choice C is correct**

Perimeter of a rectangle = 2(width \(+\)length), P \(=\) 108, width\(= 5×\)length

Then: 108=2(5length\(+\)length)\(→108=12\)length\(→\)length\(=9\)

13- **Choice A is correct**

Volume\( =\) length\( ×\) width \(×\) height, \(4500 = 60 × 15 ×\) height \(→\) height \(= 5\)

14- **Choice B is correct**

The distance between Chris and Joe is 16 miles. Chris running at 4.5 miles per hour and Joe is running at the speed of 8.5 miles per hour. Therefore, every hour the distance is 4 miles less.

\(16 ÷ 4 =4\)

15- **Choice A is correct**

\(\frac{5^4}{10} = 62.5\)

16- **Choice D is correct**

\(5 \frac{2}{3} − 2 \frac{3}{4} = \frac{17}{3}-\frac{11}{4}=\frac{68-33}{12}=\frac{35}{12}=2 \frac{11}{12}\)

17- **Choice D is correct**

All angles in a triangle sum up to 180 degrees. \(33 + 52 = 85, 180 – 85 = 95\), The third angle is 95 degrees.

18- **Choice B is correct**

If \(a = 14\) then: \(b = \frac{14^2}{28} + c ⇒ b =\frac{14^2}{28} + c = 7 + c\)

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19- **Choice C is correct**

Circumference \(= 2πr → \)Circumference\( = 2(3.14) (18) = 113.04≅113\)

20- **Choice D is correct**

1 foot \(=\) 12 inches, 14 feet, 30 inches \(=\) 198 inches, 6 feet\(=\) 72 inches, \(198 + 72+8 =278\)

21- **Choice C is correct**

Speed \(= \frac{distance}{time}, 58 =\frac{2,200}{time} →\) time \(=\frac{2,200}{58} = 37.93 ≅ 38\)

22- **Choice D is correct**

Let’s review the choices provided. Put the values of \(x\) and \(y\) in the equation.

A. \((1, 4) ⇒ y = -3(1)+7=4\) This is true!

B. \((3, -2) ⇒ y = -3(3)+7=-2\) This is true!

C. \((-4, 19) ⇒ y = -3(-4)+7=19 \)This is true!

D. \((-3, 15) ⇒ y = -3(-3)+7=16\) This is not true!

Only choice D does not work in the equation.

23- **Choice D is correct**

Since Julie gives 13 pieces of candy to each of her friends, then, then number of pieces of candies must be divisible by 13.

A. \(187 ÷ 13 = 14.38 \)

B. \(216 ÷ 13 = 16.615 \)

C. \(343 ÷ 13 = 26.38 \)

D. \(377 ÷ 13 = 29 \)

Only choice D gives a whole number.

24- **Choice D is correct**

Jason spent \(34\%\) of his total time (25 hours) on History. Then: \(\frac{34}{100} × 25 = 8.5\)

25- **Choice A is correct**

Jason spent \(24\%\) of his time on Writing and Physics. Then: \(\frac{24}{100} × 25 =6\)

26- **Choice A is correct**

Plug in 100 for F in the equation: \(C = \frac{5}{9} (F – 32) = \frac{5}{9} (100 – 32) = \frac{5}{9} (68) = 37.7\)

27- **Choice C is correct**

\(17\%\) of \(x = 25.5, x = \frac{100 × 25.5}{17} =150\)

28- **Choice A is correct**

\(\frac{4}{5} x+\frac{4}{7}= \frac{8}{14} → \frac{4}{5} x = \frac{8}{14} – \frac{4}{7} → \frac{4}{5} x = \frac{8-8}{14} → \frac{4}{5} x = \frac{0}{14}, x =0\)

29- **Choice B is correct**

\(\frac{1}{16}=0.0625→C=5\)

\(\frac{1}{25}=0.04→D=4→C×D=5×4=20\)

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30- **Choice D is correct**

To find the discount, multiply the number by (\(100\% –\) rate of discount).

Therefore, for the first discount we get: \((D) (100\% – 12\%) = (D) (0.88) = 0.88 D \)

For increase of \(15 \%: (0.88 D) (100\% + 15\%) = (0.84 D) (1.15) = 0.966 D = 96.6\%\) of D or 0.966D

31- **Choice C is correct**

Let \(x\) be the number. Then: \(6x+8=44\)

Solve for \(x: 6x+8=44→6x=44-8=36→x=36÷6=6\)

32- **Choice A is correct**

Use simple interest formula: I=prt (I = interest, p = principal, r = rate, t = time)

I\(=(14000)(0.038)(3)=1596\)

33- **Choice D is correct**

\(\frac{1}{5} + \frac{3}{4} + \frac{1}{3} =\frac{12+45+20}{60} = \frac{77}{60} = 1.283\)

34- **Choice C is correct**

Let \(x\) be the number of new shoes the team can purchase. Therefore, the team can purchase 160 \(x\). The team had $32,000 and spent $18,000. Now the team can spend on new shoes $14,000 at most. Now, write the inequality: \(160x+18,000 ≤32,000\)

35- **Choice B is correct**

To get a sum of 8 for two dice, we can get 5 different options: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) To get a sum of 5 for two dice, we can get 4 different options: (1, 4), (2, 3), (3, 2), (4, 1) Therefore, there are 9 options to get the sum of 8 or 5. Since, we have \(6 × 6 = 36\) total options, the probability of getting a sum of 8 and 5 is 9 out of 36 or \(\frac{1}{4}\).

36- **Choice D is correct**

Solve for \(x. 8≤-2x+4<16 ⇒\) (subtract 4 all sides) \(8-4≤-2x-4+4<16-4 ⇒ 4≤-2x<-12 ⇒\) (divide all sides by \(-2)-2≥x>-6 x \)is between \(-2\) and \(-6\). Choice D represent this inequality.