Let X be the total number of positive factors of 120, and let Y be the total number of pos… — State PSC Exam

Let $X$ be the total number of positive factors of $120$ , and let $Y$ be the total number of positive factors of $150$ . What is the value of the expression $X + Y \div 2 \times 3$ ?

34Cevap
B
42
C
18
D
11

Cevap

The value of the expression is 34.

The correct answer accurately determines the number of factors for 120 (which is 16) and 150 (which is 12). By substituting these values into the expression

16 + 12 \div 2 \times 3

and strictly following the order of operations, division is performed first (

12 \div 2 = 6

), followed by multiplication (

6 \times 3 = 18

), and finally addition (

16 + 18 = 34

Adım Adım Çözüm

Determine the prime factorization of 120 and calculate its total number of positive factors, X.

120 = 2^3 \times 3^1 \times 5^1

. Thus,

X = (3+1)(1+1)(1+1) = 4 \times 2 \times 2 = 16

The total number of factors of an integer is found by adding 1 to each exponent in its prime factorization and multiplying the results.

Determine the prime factorization of 150 and calculate its total number of positive factors, Y.

150 = 2^1 \times 3^1 \times 5^2

. Thus,

Y = (1+1)(1+1)(2+1) = 2 \times 2 \times 3 = 12

Applying the same factor counting formula to the prime factorization of 150.

Substitute the values of X and Y into the expression and evaluate according to the order of operations (BODMAS).

Expression:

16 + 12 \div 2 \times 3

. Step 3a (Division):

12 \div 2 = 6

. Step 3b (Multiplication):

6 \times 3 = 18

. Step 3c (Addition):

16 + 18 = 34

BODMAS dictates that division and multiplication are evaluated from left to right before any addition is performed.

Anahtar Kavram

Calculating total number of factors using prime factorization combined with standard order of operations.

Tahmini Süre:1m 30s

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