Full-Length ATI TEAS 7 Math Practice Test-Answers and Explanations

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ATI TEAS 7 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 the 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 is 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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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 represents this inequality.

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