Practice Problems

Question 1

a > b
c < d

is a + d > b + c

Answer 1

a > b
-(c < d)
—————-
a - c > b - d

a + d > b +c (YES!)

*** When subtracting inequalities you always pick the sign of the equation you are subtracting from.

Question 2

11 and 13 are the only prime factors of x. What are the prime factors of x^4?

Answer 2

11 and 13 – exponentiation does not create new prime factors

Question 3

A table can seat 5 people. In how many ways can 5 people be arranged around the table?

Answer 3

Formula is (n-1)!

(5 - 1)! = 4! = 432*1 = 24 ways

Question 4

How do you translate the following sentences into an equations?

1. p is directly proportional to e
2. p is inversely proportional to e

Answer 4

1. p = k*e (where k is a constant)

2. p = k/e (where k is a constant)

Question 5

How can this be written as an equation?

When x is divided by 100 it has a remainder of 30.

Answer 5

x = 100q +30

***where q is an integer

Question 6

What is true of the prime factors of n and n+1?

Answer 6

They do not share any prime factors

Question 7

Color X ink is created by blending red, blue, green, and yellow inks in the ratio 6:5:2:2. What is the number of liters of green ink that was used to create a certain batch of color X ink?

(1) The amount of red ink used to create the batch is 2 liters more than the amount of blue ink used to create the batch.
(2) The batch consists of 30 liters of color X ink.

Answer 7

(1) 6 * m = x +2 
    5 * m = x
    --------------
   m = 2.      (where m is the multiplier of the ratio)
2*2 = 4 green ink
SUFFICIENT

(2) 6+5+2+2 = 15
15m = 30
m = 2
SUFFICIENT

Question 8

What should you look for when asked “percent greater” or “percent lower” in data sufficiency questions?

Answer 8

You are looking for a ratio:

(final - initial)/initial = final/initial - 1

Question 9

If d is the standard deviation of n, k, and p. What is the standard deviation of n+1, k+1, and p+1?

Answer 9

d

Question 10

For a certain set of numbers, if x is in the set, then x – 3 is also in the set. If the number 1 is in the set, which of the following must also be in the set?

i) 4
ii) -1
iii) -5

Answer 10

iii - Since 1 is in the set, then so must be 1-3=-2. Similarly, since -2 is in the set, then so must be -2-3=-5. Could 4 and -1 be in the set? Certainly, but we don’t know that for sure.