# Full-Length ISEE Lower Level Math Practice Test-Answers and Explanations

Did you take the ISEE Lower Level 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.

## ISEE Lower Level Math Practice Test Answers and Explanations

1- **Choice D is correct**

The ratio of lions to tigers is 14 to 4 or 7 to 2 at the zoo. Therefore, a total number of lions and tigers must be divisible by \(5. 7+2=9,\) From the numbers provided, only 142 is not divisible by 9.

2- **Choice D is correct**

If \(\frac{1}{4}\) of a number is greater than 5, the number must be greater than 20.

\(\frac{1}{4}\) \(x>5\)→multiply both sides of the inequality by 4,then: \(x>20\)

3- **Choice D is correct**

\(6×(M+N)=42\), then \(M+N=7. M>0→N\) could not be \(7\)

4- **Choice D is correct**

The closest to 6.02 is 6 in the choices provided.

5- **Choice D is correct**

\(\frac{16}{6}=\frac{8}{3}=2.66\), the only choice that is greater than \(2.66\) is \(\frac{7}{2}\). ( \(\frac{7}{8}=0.875 ,\frac{9}{5}=1.8 ,\frac{5}{3}=1.6\)) \(\frac{7}{2}=3.5 ,3.5>2.66\)

6- **Choice D is correct**

Let \(x\) be the number. Then: \(6+x=24→x=18→18+30=48\)

7- **Choice D is correct**

N is even. Let’s choose 2 and 4 for N. Now, let’s review the choices provided.

A. \(\frac{N}{2}=\frac{2}{2}=1, \frac{N}{2}=\frac{4}{2}=2\), One result is odd and the other one is even.

B. \(N+4=2+4=6, 4+4=8\) Both results are even.

C. \(2N=2×2=4, 4×2=8\) Both results are even.

D. \(N+1=2+1=3, 4+1=5\) Both results are odd.

8- **Choice C is correct**

\(7.2-3.56=3.64\), which is closest to \(3.7\)

9- **Choice C is correct**

The value of digit 2 in both numbers and are in the hundreds place. Therefore, they have the same value.

10- **Choice C is correct**

A represents digit 2 in the multiplication. \(15×462=6,930\)

11- **Choice C is correct**

\(\frac{6}{3}×\frac{8}{9}=\frac{48}{27}=\frac{16}{9}\), Choice B is equal to \(\frac{16}{9}\). \(\frac{6×8}{27}=\frac{16}{9}\)

12- **Choice C is correct**

\(6×7×6×11\) is equal to the product of \(42\) and \(66\). \((6×7)×(6×11)=42×66\)

13- **Choice C is correct**

\(42=x×7→x=42÷7=6\) , \(x\) equals to \(6\). Let’s review the options provided:

A. \(x+3→6+3=9\) →\(42\) is not divisible by \(9\).

B. \(3x+1→3×6+1=19\) →\(42\) is not divisible by \(19\).

C. \(x×7→6×7=42\) →\(42\) is divisible by \(42\).

D. \(2x-7→2×6-7=5\) →\(42\) is not divisible by \(5\).

14- **Choice B is correct**

\(x+3=17→x=14 , 2y-6=14→y=10, x-y=14-10=4\)

15- **Choice D is correct**

\(\frac{3+4+5×2-6}{4+2}=\frac{11}{6}\)

16- **Choice B is correct**

First, find the pattern, \(1+2=3→3+3=6→6+4=10→10+5=15\)

The difference between two consecutive numbers increases by 1. The difference of 10 and 15 is So 5, the next number should be \(21. 15+6=21\)

17- **Choice B is correct**

\(14-21=-7\), The temperature at midnight was \(7\) degrees below zero.

18- **Choice B is correct**

Area of a triangle \(=\frac{1}{2}×(base)×(height)=\frac{1}{2}×8×4=16\)

19- **Choice D is correct**

area of a square=side\(×\)sid

20- **Choice C is correct**

\(7+4N=43→4N=43-7=36→N=9\)

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21- **Choice D is correct**

Let’s review the options provided:

A. \(5×3=15\) →This is true!

B. \((4+3)×5=35\) → This is true!

C. \(18×(3-1)=36\)→ This is true!

D. \(27÷(5-2)=7\)→ This is NOT true!

22- **Choice C is correct**

There is 6 red ball and 15 are a total number of balls. Therefore, the probability that John will pick out a red ball from the basket is 6 out of 15 or \(\frac{6}{6+9}=\frac{6}{15}=\frac{2}{5}\).

23- **Choice C is correct**

An equilateral triangle has 3 lines of symmetry.

24- **Choice B is correct**

\(20\) percent of \(280 = 20\% \)of\( 280 =\frac{20}{100}×280=56\)

25- **Choice D is correct**

average\(=\frac{sum \space of \space all \space numbers}{number \space of \space numbers}=\frac{7+9+11+21+38}{5}=17.2\)

26- **Choice B is correct**

The shape has 6 equal sides. And its side is 5. Then, the perimeter of the shape is:

27- **Choice B is correct**

Write the numbers in order: 1,3,5,6,11,12,19, Median is the number in the middle. Therefore, the median is 6.

28- **Choice B is correct**

\(N=3\), then: \(\frac{48}{3}+12=16+12=28\)

29- **Choice C is correct**

Four people can paint 6 houses in 12 days. It means that for painting 12 houses in 12 days we need 10 people. To paint 12 houses in 6 days, 20 people are needed.

30- **Choice B is correct**

\(\frac{5}{9}-\frac{3}{9}=\frac{2}{9}=0.22\)

31- **Choice B is correct**

The biggest city is city C and the smallest city is city B.

The number of men in city A is 662 and the number of men in city C is 281. Then: \(662-281=381\)

32- **Choice C is correct**

There are equal From the choice provided, only choice C is not equal to \(\frac{3}{8}\). \(\frac{12}{56}=\frac{9}{112}\)

33- **Choice C is correct**

\(25a-15=30, 25a=30+15 , 25a=45, a=1.8\)

34- **Choice C is correct**

All angles in a triangle sum up to 180 degrees. Two angles of a triangle measure 35 and 80.

\(35+80=115\) Then, the third angle is: \(180 –115=65\)

35- **Choice C is correct**

\(115+12+6=133\)

36- **Choice D is correct**

There are equal numbers of four types of cards. Therefore, the total number of cards must be divisible by 4. Only choice D (56) is divisible by 4.

37- **Choice D is correct**

30 seconds is one-half of a minute. One-fourth of 110 is 55. \(110 ÷ 2 = 55 \)

Jim types 55 words in 30 seconds.

38- **Choice C is correct**

39- **Choice A is correct**

8,903.3795 rounded to the nearest tenth is 8,903.4

40- **Choice B is correct**

least common multiple (LCM) of 6 and 15 is the smallest number that is divisible by both 6 and 15. LCM = 30

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41- **Choice D is correct**

The factors of 32 are: {1, 2, 4, 8, 16, 32} 18 is not a factor of 32.

42- **Choice B is correct**

5 hours =300 minutes. Write a proportion and solve. \(\frac{50}{1} = \frac{300}{x} → x = \frac{300}{50} = 6\)

43- **Choice D is correct**

Find common denominator and solve. \(\frac{4}{5}-\frac{3}{7}=\frac{28}{35}-\frac{15}{35}=\frac{13}{35}\)

44- **Choice B is correct**

All angles in a triangle add up to 180 degrees. \(36+58=94, 180–94=86\)

45- **Choice B is correct**

If 28 balls are removed from the bag at random, there will be one ball in the bag.

The probability of choosing a brown ball is 1 out of 28. Therefore, the probability of not choosing a brown ball is 25 out of 28 and the probability of having not a brown ball after removing 25 balls is the same.

46- **Choice D is correct**

The question is this: 2.5 is what percent of 1.25? Use percent formula: part \(=\frac{percent}{100} × whole ⇒\space part= \frac{percent}{100} × 1.25 ⇒ 2.5 = \frac{percent ×1.25}{100} ⇒250 = percent ×1.25 ⇒ percent =\frac{250}{1.25} = 200\)

47- **Choice C is correct**

The question is this: 650.55 is what percent of 867.4?

Use percent formula: \(part = \frac{percent}{100} × whole\)

\(650.55 = \frac{percent}{100}× 867.4 ⇒ 650.55 = \frac{percent ×867.4}{100}⇒65055 = percent ×867.4 ⇒\)

\(percent = \frac{65055}{867.4}= 75\), \(650.55\) is \(75\%\) of \(867.4\). Therefore, the discount is: \(100\% – 75\% = 25\%\)

48- **Choice C is correct**

Area of a triangle = \( \frac{1}{2} (base)(height)\) , \(A = \frac{1}{2} (14)(7) = 49\)

49- **Choice A is correct**

One method to compare fractions is to convert them to decimals.

A. \(\frac{5}{6} = 0.833\)

B. \(\frac{1}{4} = 0.25\)

C. \(\frac{7}{9} = 0.77\)

D. \(\frac{5}{8}= 0.625\)

0.833 or \(\frac{5}{6}\) is the largest number.

50- **Choice B is correct**

\(\frac{16}{100} = 0.16\)

51- **Choice C is correct**

Since Julia running at 4.5 miles per hour and Julia is running at the speed of 7 miles per hour, each hour their distance decreases by 2.5 miles. So, it takes 3.2 hours to cover the distance of 7.5 miles. \(8÷2.5=3.2\)

52- **Choice D is correct**

Since Julie gives 7 pieces of candy to each of her friends, then, the number of pieces of candies must be divisible by 7.

A. \(78 ÷ 7 = 11.14\)

B. \(129 ÷ 7 = 18.42\)

C. \(167 ÷ 7 = 23.85\)

D. \(189 ÷ 7 = 27\)

Only choice D gives a whole number.

53- **Choice C is correct**

\($11×12=$132\), Petrol use: \(12×3=36\) liters, Petrol cost: \(36×$1=$36\)

Money earned: \($132-$36=$96\)

54- **Choice C is correct**

\(0.45×100=45\%\)

55- **Choice B is correct**

Perimeter=2(width\(+\)length), A= width\(×\)length

First, find the length of the rectangle.

Perimeter=2(width\(+\)length) → 156=2(19\(+\) length) →156 = 38+2(length)→ 118=2(length) → length=59

A\(=19×59=1121\)

56- **Choice C is correct**

An obtuse angle is an angle of greater than 90 degrees and less than 180 degrees. Only choice C is an obtuse angle.

57- **Choice D is correct**

The failing rate is 46 out of \(184 = \frac{46}{184}\), Change the fraction to percent: \(\frac{46}{184} ×100\%=25\%\)

25 percent of students failed. Therefore, 75 percent of students passed the exam.

58- **Choice D is correct**

\(\space \)\(\space \)\(49 \space hr. \space 17 \space min.\)

\(-\) \(31 \space hr. \space 29 \space min.\)

\(\space \)\(\space \)\(17\space hr. \space 48 \space min.\)

59- **Choice D is correct**

If the length of the box is 36, then the width of the box is one-fourth of it, 9, and the height of the box is 3 (one-third of the width). The volume of the box is:

\(V=(length)(width)(height)=(36)(9)(3)=972 m^3\)

60- **Choice B is correct**

Let x be the number of raptors Daniel saw on Monday. Then:

Mean\(=\frac{x+7+12+9+8}{5} = 9 → x+36=45 → x = 45-36 = 9\)

61- **Choice B is correct**

There are 12 squares and 8 of them are shaded. Therefore, 8 out of 12 or \(\frac{8}{12}=\frac{2}{3}\) are shaded.

62- **Choice B is correct**

1 pizza has 6 slices. 14 pizzas contain (\(14 × 6\)) 84 slices.

63- **Choice D is correct**

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

Therefore, for the first discount we get: (\(450\))(\(100\%\)\(–\)\(10\%\))=(\(450\))(\(0.90\))

For the next \(25 \%\) discount: \((450)(0.90)(0.75)\)

64- **Choice D is correct**

A quadrilateral with one pair of parallel sides is a trapezoid.

65- **Choice C is correct**

Plugin 20 for A in the equation. Only choice A works. \(A×10=350 , A=35\)

66- **Choice D is correct**

\(1\) hour: \($5.45\) , \(12\) hours: \(12×$5.45=$65.4\)

67- **Choice B is correct**

There are 68 students in the class. 24 of them are male and 44 of them are female.

44 out of 68 are female. Then: \(\frac{44}{68}=\frac{x}{100}→4,400=68x→x=4400÷68=64.7\%≈65\)

68- **Choice D is correct**

Write a proportion and solve. \(\frac{3}{5}=\frac{x}{120}\) , Use cross multiplication: \(5x=360→x=72\)

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