tsia2 math practice test

A placement test used in Texas to assess a student's readiness for college-level coursework in math, reading, and writing.

The sum of n and the product 3 times n is 12. What is the value of n?
  • A. 2
  • B. 3
  • C. 4
  • D. 4 ½
Correct Answer & Rationale
Correct Answer: B

To solve the equation formed by the problem statement, we express it as \( n + 3n = 12 \), which simplifies to \( 4n = 12 \). Dividing both sides by 4 gives \( n = 3 \). Option A (2) does not satisfy the equation, as substituting it results in \( 2 + 6 = 8 \), which is incorrect. Option C (4) leads to \( 4 + 12 = 16 \), also incorrect. Option D (4 ½) results in \( 4.5 + 13.5 = 18 \), which is too high. Thus, only \( n = 3 \) fulfills the original equation, confirming its validity.

Other Related Questions

If an item regularly costs d dollars and is discounted 12 percent, which of the following represents the discounted price in dollars?
  • A. 0.12d
  • B. 0.88d
  • C. 1.12d
  • D. d-0.12
Correct Answer & Rationale
Correct Answer: B

To find the discounted price after a 12 percent discount on an item that costs d dollars, we first calculate the amount of the discount, which is 12% of d, or 0.12d. To determine the final price, we subtract this discount from the original price: d - 0.12d = 0.88d. Option A (0.12d) represents only the discount amount, not the final price. Option C (1.12d) incorrectly suggests an increase in price. Option D (d - 0.12) does not account for the percentage; it inaccurately represents the discount as a flat dollar amount rather than a percentage of the original price. Thus, 0.88d correctly reflects the discounted price.
If the values of x and y are negative, which of the following values must be positive?
  • A. x²-y²
  • B. x/y
  • C. x+y
  • D. x-y
Correct Answer & Rationale
Correct Answer: B

When both x and y are negative, the quotient \( x/y \) results in a positive value. This is because dividing a negative number by another negative number yields a positive outcome. Option A, \( x^2 - y^2 \), can be either positive or negative depending on the magnitudes of x and y; thus, it is not guaranteed to be positive. Option C, \( x + y \), is the sum of two negative numbers, which will always be negative. Option D, \( x - y \), involves subtracting a negative (y) from another negative (x), which can also yield a negative or zero result, depending on their values. Only \( x/y \) is assuredly positive.
During a sale, the regular price of a pair of running shoes is reduced by 20 percent. $64.00, what is the regular price of the running shoes?
  • A. $48.00
  • B. $51.20
  • C. $76.80
  • D. $80.00
Correct Answer & Rationale
Correct Answer: D

To find the regular price of the running shoes, we need to determine what amount, when reduced by 20%, equals $64.00. This can be calculated using the formula: Sale Price = Regular Price × (1 - Discount Rate). Here, the discount rate is 20%, or 0.20. Therefore, the equation becomes $64.00 = Regular Price × 0.80. Solving for Regular Price gives us $64.00 / 0.80 = $80.00. Option A ($48.00) is incorrect because it suggests a much larger discount than 20%. Option B ($51.20) miscalculates the reduction, indicating a 36% discount. Option C ($76.80) inaccurately reflects a smaller discount, resulting in an incorrect sale price. Thus, only option D correctly represents the regular price before the 20% reduction.
The average of 4 numbers is 9. If one of the numbers is 7, what is the sum of the other 3 numbers?
  • A. 2
  • B. 12
  • C. 29
  • D. 36
Correct Answer & Rationale
Correct Answer: C

To find the sum of the other three numbers, start by calculating the total sum of all four numbers. Since the average is 9, multiply this by 4, yielding a total of 36. Given that one of the numbers is 7, subtract this from the total: 36 - 7 = 29. Therefore, the sum of the other three numbers is 29. Option A (2) is too low, as it does not account for the total sum needed. Option B (12) underestimates the remaining numbers. Option D (36) mistakenly includes the known number, rather than calculating the sum of the others.