amount earned last week by all the managers is thus: amount per manager ∗
number of managers = 3 ∗ 4 = 12. The total amount earned last week by all the
directors is thus: amount per director ∗ number of directors = 3 ∗ 5 = 15. The
resulting ratio is thus^1215 , which reduces to^45.- B When dealing with exponential terms, it’s usually a good idea to express the
bases in their prime form, after which we can employ any relevant exponent rules.
Start with the first equation: 2a is already in prime form, so let’s express 8b
in its prime factorization: 8 = 23 , so 8b = (2^3 )b = 23 b. Let’s also express 64 in its
prime factorization. 64 = 26. Now, the equation reads:
2 a 23 b = 26
Simplify: 2a 23 b = 2 a+^3 b = 26. Since both sides are expressed in base 2, the exponents
must be equal. Thus, a + 3 b = 6.
Now, let’s do the same thing for the second equation: 9a = (3^2 )a = 32 a, and 27 = 33.
So the second equation reads: 3^2 a ∗ 3 b = 33. Since both sides are expressed in
base 3, the exponents must be equal. Thus, 2a + b = 3.
We now have a system of equations:
a + 3b = 6
2 a + b = 3
Since we want to solve for a, let’s isolate b in the second equation: b = 3 – 2a.
Now substitute 3 – 2a for b in the first equation:
a + 3(3 – 2a) = 6 →a + 9 – 6a = 6 →–5a = –3→a = (^35)
- A and C
Choice A: From the given information, we know that x/y is a positive
proper fraction. If you multiply a positive proper fraction by itself, the
result will be smaller than the original fraction. Thus, choice A must be
true.
Choice B: Choose values: If x = 3 and y = 4, then x^2 /y = 32 /4 = 94 , which is
greater than^34. However, if x = 12 and y = 2, then x^2 /y = 14 /2 = 18 , which is not
greater than^14. Thus, choice B doesn’t have to be true.
Choice C: Choose values: If x = 1 and y = 2, then x +^5 y + 5 = 67 , which is less
than 1. Now try fractions: if x = 12 , and y = 23 , then x +^5 y + 5 = 12 + 5/^23 + 5 =^112 /^173 ,
which is less than 1. Choice C must be true. - B The fastest way to answer this question is to think about the job in terms
of the unit machine-hours. If 9 machines need 20 hours to do the job, then
the job requires 9 machines ∗ 20 hours = 180 machine-hours. This is a fixed
amount, so, to do the same job, any change in the number of machines will
cause an inverse change in the number of hours, and vice versa. So, to solve
for the number of machines, n, needed to do the job in 45 hours, we can
create the equation: n machines ∗ 45 hours = 180 machine-hours. Solve for n:
n = 18045 = 4.
70 PART 1 ■ GETTING STARTED01-GRE-Test-2018_001-106.indd 70 12/05/17 11:38 am