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Test Prep GMAT Test Exam Practice Questions (P. 3)

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Question #21
A drawer holds 4 red hats and 4 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and immediately returning every hat to the drawer before taking out the next?
  1. A
    1/8
  2. B
    1/4
  3. C
    1/2
  4. D
    3/8
  5. E
    7/12

Correct Answer:
C
Getting three red out of 4 that are taken out has 4 options (4! / (3! ֳ— 1!)), each option has a probability of (1/2) since drawing a red or blue has a 50% chance. 4 ֳ—
1/16 = 1/4 to get three red hats. The same goes for three blue hats so 1/4+1/4 = 1/2.

Question #22
If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression (2X + Y)(2Z + W)?
  1. A
    9
  2. B
    12
  3. C
    15
  4. D
    16
  5. E
    18

Correct Answer:
C
(2X + Y)(2Z + W) = 4XZ + 2XW + 2ZY + WY.
Now, plug in this data to get: 3 + 2(6) = 15.

Question #23
X is an even number and Y is a positive odd number. Which of the following expressions cannot be even?
  1. A
    (XY) Y
  2. B
    X Y
  3. C
    X
  4. D
    XY
  5. E
    Y

Correct Answer:
E
The fastest way to solve this problem is by plugging in some numbers.
Let's say: X = 2, Y = 1.
According to answer e: 1 ֳ— 1 = 1 and that must be an odd number.

Question #24
How much interest will $2,400 earn at an annual rate of 8% in one year if the interest is compounded every 4 months?
  1. A
    $141
  2. B
    $150
  3. C
    $197
  4. D
    $234
  5. E
    $312

Correct Answer:
C
Here, it is enough to calculate the simple interest of 8% per year.
$2,400 ֳ— 8/100 ֳ— 1 = $192. Since we are calculating as a compounded rate, the interest should be a bit higher or choice $197 as the correct answer.

Question #25
X is a prime number bigger than 10. Also, Y = X + X
+ X
+ X
.
What is definitely true about Y?
  1. A
    Y is a prime number.
  2. B
    Y is odd.
  3. C
    Y is even.
  4. D
    Y is divisible by 3.
  5. E
    Y is divisible by 7.

Correct Answer:
C
Because X is a prime number bigger than 10, it must be odd. Ignoring the powers of X in the expression of Y, you'll see that Y is a sum of 4 odd numbers therefore it must be even.

Question #26
What is the least integer that is a sum of four different primes each greater than 20?
  1. A
    79
  2. B
    83
  3. C
    120
  4. D
    133
  5. E
    169

Correct Answer:
C
Find the sum of the first 4 primes larger than 20: 23 + 29 + 31 + 37 = 120.

Question #27
One quarter of the workers at the factory is clerical, one fifth is technical, half are administrative and the other 25 are managerial. How many workers total are there in the factory?
  1. A
    250
  2. B
    366
  3. C
    400
  4. D
    500
  5. E
    2500

Correct Answer:
D
First, calculate the fraction of the 25 managerial workers out of the total number of workers by subtracting the fractions given from 1. The 25 managerial workers are 201 of the workers, therefore, a total number of 500 workers.

Question #28
The price of a product is $a. Bill bought s products and then sold 80 percent of them $b. Which of the following represents the whole deal if Bill's profit was three times the cost?
  1. A
    0.8sb = 4sa
  2. B
    (1 גˆ’ 0.8)s גˆ’ ab = 3s
  3. C
    3(0.8a גˆ’ sb) = sa
  4. D
    (s גˆ’ 0.8s) (b גˆ’ a) = 3
  5. E
    (s0.8s) / (b גˆ’ a) = 3

Correct Answer:
A
This statement is equivalent to 0.8sb גˆ’ sa = 3sa. The income is 0.8sb, the cost is sa, so the profit is three times the cost.
0.8sb גˆ’ sa = 3sa,
0.8sb = 4sa

Question #29
A grocer bought 24 kg of coffee beans at price X. After a while one third of the stock got spoiled so he sold the rest for 200$ per kilo and made a total profit of twice the cost. What must be price X?
  1. A
    66 / $
  2. B
    50 / $
  3. C
    44 / $
  4. D
    33 / $
  5. E
    24 / $

Correct Answer:
C
The total income is 16 ֳ— 200. The cost is 24X, and the total profit is 3200 גˆ’ 24X = 48X.

Question #30
Kenny is three times older than Bob. In P years he will be twice older than Bob will be Q years later. Which of the following represents Kenny's age comparing to
Bob's? (If X = Kenny's age)
  1. A
    X + P = 6X(P + Q)
  2. B
    2(X + P) = 3X + Q
  3. C
    (X + P) / 2 = X/3 + P + Q
  4. D
    3(X + P + Q) = 2X
  5. E
    3X = 2(P + Q)

Correct Answer:
C
X is Kenny's age. X/3 is Bob's age. Answer ג€(X + P) / 2 = X/3 + P + Qג€ is equivalent to (X + P) = 2(X/3 + P + Q), which means that in P years, X + P is 2 times (X/3
+ P) plus Q years.

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