8 x = 50
x =^508 = 6.25- C Let b = the number of boys and g = the number of girls.
Relationship 1: b + g = 300
Relationship 2: b > 2g
Substitution with inequalities can be difficult. Think of what would be the
case if b = 2g. Substitute 2g for b in the first equation and arrive at 2g + g
= 300 → 3 g = 300 → g = 100. Since 2g < b instead of 2g = b, the number of
girls must be less than 100. The greatest integer less than 100 is 99 (you only
consider integers since the number of girls must be a whole number). - 7 Let j = Jack’s current age and b = Bob’s current age.
Relationship 1: j + 6 = 2b
Relationship 2: j = b + 1
To solve for b, substitute b + 1 for j in the first equation:
(b +1) + 6 = 2b
b + 7 = 2b
7 = b- A Rows × columns = total marbles. Thus xy = 343. You also know that y = 7x.
To solve for x, substitute 7x for y in the first equation:
x(7x) = 343
7 x^2 = 343
x^2 = 49
x = 7
Quantitative Comparison Questions
- C Let k = Kate’s current age, and let s = Sara’s current age. Based on the
prompt, you can create the following relationship: k = s + 3. Since the
quantities compare Kate’s age and Sara’s age, make them comparable by
substituting (s + 3) for k in Quantity A. The value for Quantity A will be
(s + 3) – 4 = s – 1. The value for Quantity B will be s – 1. Thus the two
quantities are equal. - B Since the columns ask you to compare the number of chairs in the
auditorium to x^2 , you should attempt to express the number of chairs in terms
of x. To determine the total number of chairs, do chairsrow × number of rows. Thus
the number of chairs = x(x–1) = x^2 – x. Quantity A is thus x^2 – x and Quantity
B is x^2. Since x must be positive (there can’t be a negative number of chairs or
rows), x^2 must be greater than x^2 – x.
CHAPTER 12 ■ FROM WORDS TO ALGEBRA 32504-GRE-Test-2018_313-462.indd 325 12/05/17 12:03 pm