- C Set up the given information algebraically. Let j = Jack’s current age and
l = Linda’s current age. 8 years ago, Jack’s age was thus j – 8, and Linda’s age
was l – 8. Now, use this information to create an algebraic relationship:
j – 8 = 2(l – 8). The second relationship concerns their ages in 4 years. At that
point, Jack’s age will be j + 4, and Linda’s age will be l + 4. We can create the
relationship: j + 4 = 1.5(l + 4).
Now, we have a system of equations:
j – 8 = 2(l – 8)
j + 4 = 1.5(l + 4)
Simplify the first equation to arrive at: j – 8 = 2 l – 16 →j = 2 l – 8. Now,
substitute 2l – 8 for j in the second equation and simplify:
(2l – 8) + 4 = 1.5(l + 4) → 2 l – 4 = 1.5l + 6 →.5l = 10 →l = 20. Now we can
use l = 20 to solve for Jack’s age. j = 2 l – 8 = 2(20) – 8 = 32.
So Jack’s current age is 32, and Linda’s current age is 20. Therefore, 8 years ago,
Jack’s age was 24, and, in 4 years, Linda’s age will be 24. The quantities are
equal. - A A property of a triangle with sides of length a, b, and c, where c is the longest
side, is that, if a^2 + b^2 < c^2 , then the triangle is obtuse, meaning one angle has
a measurement greater than 90 degrees. Since the above inequality applies to
triangle RST, we can infer that it is obtuse. Therefore, Quantity A is greater. - A First, simplify the comparison by subtracting 2b from both quantities to
arrive at:
Quantity A: 2a + b
Quantity B: c
Now, we can use the rule: the length of any given side of a triangle must be
greater than the difference of the other two sides and less than the sum of
those two sides. From this rule, we can conclude that c < a + b. Since c < a + b
and 2a + b > a + b, we can conclude that 2a + b > c. - D We know that the slope of line l is 2, but knowing the point of intersection
is not enough to learn anything about the slope of line m. Therefore, a
relationship between the two quantities cannot be determined. - E When any number is divided by 10, the remainder is determined by the
units digit of that number, so our real goal is to determine the units digit of
34 x +^2. To do so, let’s choose a simple value for x: x = 1.
Thus, 3^4 x +^2 = 36 = 729.
In this case, the units digit is 9. Since there’s only one answer to this question,
the fact that the units digit now is 9 means that the units digit will always be 9.
The answer is thus E. - 45 Since this question has only fractions and no actual values, we should
choose smart numbers. Let the number of directors = 5. In that case, the
number of managers = 3. Let the amount earned per week by each director = 3.
In that case, the amount earned per week by each manager is 4. The total
CHAPTER 2 ■ GRE DIAGNOSTIC TEST 6901-GRE-Test-2018_001-106.indd 69 12/05/17 11:38 am