Lesson 11.2 Perform - SHSAT Math

1. 1. What is the prime factorization of 144

Mathematical Equivalence

OFF

What is the prime factorization of 60?

Mathematical Equivalence

OFF

|6 − (−1.3) + 2| + |4 − 2.8 − 3| =

Mathematical Equivalence

ON

In the set of consecutive integers from 15 to 30 inclusive, two integers are multiples of both 3 and 5. How many integers in this set are multiples of neither 3 nor 5?

____

|(−5.6) + 2| + |1 − (−2.7)| = ?

• 0.1

• 5.3

• 7.3

• 11.3

Answer explanation

First, calculate |(-5.6) + 2| = |-3.6| = 3.6. Then, |1 - (-2.7)| = |1 + 2.7| = |3.7| = 3.7. Finally, add them: 3.6 + 3.7 = 7.3. Thus, the answer is 7.3.

The intervals between the tick marks on the number line above are equal. What is the value of point K?

• 1/20

• 1/4

• 7/20

• 3/4

Answer explanation

The number line is divided into equal intervals. Point K is located at the second tick mark, which corresponds to 1/4 of the total distance from 0 to 1. Therefore, the value of point K is 1/4.

How many positive even factors of 52 are greater than 5 and less than 50?

(a)  

• 1
• 2

• 3

• 4

Answer explanation

The positive even factors of 52 are 2, 4, 6, 8, 10, 12, 26, and 52. Among these, only 6, 8, 10, 12, and 26 are greater than 5 and less than 50. Thus, there are 5 such factors, but only 1 (26) is even. Therefore, the answer is 1.

The greatest common factor of 720 and 756 is (a)  

• 12
• 24
• 36
• 42

Answer explanation

To find the greatest common factor (GCF) of 720 and 756, we can use prime factorization. The GCF is 36, as it is the highest number that divides both 720 and 756 without a remainder.

What is the least common multiple of 8, 9, and 12?

• A. 18

• B. 32

• C. 60

• D. 72

Answer explanation

To find the least common multiple (LCM) of 8, 9, and 12, we can use their prime factorizations: 8 = 2^3, 9 = 3^2, 12 = 2^2 * 3. The LCM takes the highest powers: 2^3 and 3^2, resulting in 2^3 * 3^2 = 72. Thus, the answer is D. 72.

A 10-gallon water cooler is one-third full. Approximately how many 1-gallon jugs of water are needed to completely fill the cooler?

• 2

• 3

• 6

• 7

Answer explanation

The cooler holds 10 gallons and is one-third full, meaning it has about 3.33 gallons of water. To fill it, you need 10 - 3.33 = 6.67 gallons. Rounding up, you need 7 one-gallon jugs to completely fill the cooler.