Section 5. Quantitative Reasoning
- C The simplest way to simplify the comparison is to rewrite the value of
Quantity B using a base of 2: 8 = 2^3 , so 8^20 = (2^3 )^20 = 2^60. - A When working with quadratic equations, you should manipulate them to
be in the form: x^2 + bx + c = 0. The first quadratic equation will thus read:
x^2 – 5x – 6 = 0, and the second equation will read: y^2 + 6 y + 9 = 0. Next, factor
both equations. The first equation factors to: (x – 6)(x + 1) = 0, so x = 6 or
x = –1. The second equation factors to (y + 3)^2 = 0, so y = –3. When x = 6,
quantity A is greater. When x = –1, quantity A is greater. - C Using the R = WT formula, you know that Bob’s rate is: x 3 /8 = 24 x , and Jack’s
rate is^240 x = 20 x. To arrive at an expression for Quantity A, use R × T = W.
x
24 t = 5x. Solve for t:
t =
5 x
x
24
t = 5x ×^24 x
t = 120
To arrive at an expression for Quantity B, use R × T = W. ( 20 x)t = 6x.
Solve for t:
t =6 x
x
20
t = 6x ×^20 x
t = 120
The values in the quantities are equal.- B Since the fractions in the two columns have the same numerator, the
fraction with the smaller denominator will yield the larger quantity. Thus the
comparison is:
1 + 23 t versus 1 + 33 t
Subtract 1 from both sides:
3
2 t versus3
3 tSince t > 1, 33 t will be smaller than 23 t , which means that the denominator in
Quantity B is smaller than the denominator in Quantity A. Therefore, the
value of Quantity B is greater than the value of Quantity A. If one were to
plug in a value of 2 for t then one would see that Quantity A is 0.5714 while
Quantity B is 0.7518.- A It might be tempting to choose C here since the percent increase and
decrease are the same. However, note that since the price of the home is greater
in 1993 than in 1992, the percent decrease will be taken from a bigger whole
than will the percent increase. This means that the decrease from 1993 to 1994
will be greater than the increase from 1992 to 1993. Thus the price of the home
in 1994 will be less than the price of the home in 1992.
64 PART 1 ■ GETTING STARTED01-GRE-Test-2018_001-106.indd 64 12/05/17 11:38 am