Test: Algebra - GMAT MCQ

The fixed costs per month are $1,000, and the variable costs per pen are $1.25. Let's denote the number of pens sold as "x."

The total cost is the sum of fixed costs and variable costs:

Total Cost = Fixed Costs + (Variable Cost per Pen * Number of Pens)
Total Cost = $1,000 + ($1.25 * x)

The total revenue is the price per pen multiplied by the number of pens sold:

Total Revenue = Price per Pen * Number of Pens
Total Revenue = $2.50 * x

To break even, the total revenue must equal the total cost:

$2.50 * x = $1,000 + ($1.25 * x)

Now, we can solve for x:

$2.50 * x - $1.25 * x = $1,000
$1.25 * x = $1,000
x = $1,000 / $1.25
x = 800

Therefore, the company must sell a minimum of 800 pens each month to break even.

Hence, the correct answer is D: 800 pens.

Given that both x and y are integers, we need to find the minimum value of x that satisfies the condition where the cube root of 1800x is an integer.

To determine this, we perform prime factorization on 1800, resulting in 2³ * 3² * 5².

We express y as (1800x)^(1/3), which simplifies to (2³ * 3² * 5² * x)^(1/3).

While we can easily extract 2³ from the cube root, we cannot extract 3² * 5² as they require an additional power to be extracted from the cube root.

Therefore, in order to satisfy the condition, x must be equal to 5 * 3, resulting in x = 15.

Hence, the correct rephrased answer is: Among the given options, the minimum acceptable value of x is 15, corresponding to Answer C.

First off, we can minimize the sum of a, b and c by maximizing the value of a.
(36)(5) = 180, so 5 is too big
(36)(4) = 144
So, a = 4

173 - 144 = 29.
So, we now have 6b + c = 29
We can minimize the sum of b and c by maximizing the value of b.
(6)(5) = 30, so 5 is too big
(6)(4) = 24
So, b = 4

If a = 4 and b = 4, then 36a + 6b + c = 144 + 24 + c = 173
So, c = 5

So, the minimum value of a + b + c is 4 + 4 + 5 = 13

On Monday and Thursday, she spent $5.43 TOTAL
So, our running total = $5.43

On Tuesday and Wednesday, she spent $3.54 on each day
Running total = $5.43 + $3.54 + $3.54

On Friday, she spent $7.89 on lunch.
Running total = $5.43 + $3.54 + $3.54 + $7.89 = $20.40

What was her average daily cost?
The average cost over the 5 days = (total amount spent)/5
= $20.40/5
= $4.08

The equation states that "1/2 the square root of x is the cube root of x." Mathematically, we can express this as:

(1/2) * √x = ∛x

To simplify the equation, let's raise both sides to the power of 6 (the least common multiple of 2 and 3):

[(1/2) * √x]^6 = (∛x)^6

Simplifying further:

[(1/2)^6] * (√x)^6 = x

(1/64) * x^3 = x

Now, let's multiply both sides by 64 to eliminate the fraction:

x^3 = 64x

Dividing both sides by x (assuming x ≠ 0):

x^2 = 64

Taking the square root of both sides:

x = ±8

Since x is defined as a positive number, we take the positive value:

x = 8

Therefore, the correct answer is option A: 64.

Let's assume the numerator of the original fraction is 'x', and the denominator is 'y'.

According to the given information, the original fraction is 2/5, so we have:

x/y = 2/5 ---(1)

Now, let's consider the second condition: "If the numerator is decreased by 2 and the denominator increased by 1, the resulting fraction is equivalent to 1/4."

If we decrease the numerator by 2, we get (x - 2), and if we increase the denominator by 1, we get (y + 1). So the resulting fraction is:

(x - 2)/(y + 1) = 1/4 ---(2)

Now, we can solve equations (1) and (2) simultaneously to find the values of x and y.

From equation (1), we have:

x/y = 2/5

Cross-multiplying:

5x = 2y

Simplifying:

y = (5x/2) ---(3)

Now, let's substitute equation (3) into equation (2):

(x - 2)/[(5x/2) + 1] = 1/4

Cross-multiplying:

4(x - 2) = (5x/2) + 1

Simplifying:

4x - 8 = (5x/2) + 1

Multiplying through by 2 to eliminate the fraction:

8x - 16 = 5x + 2

Subtracting 5x from both sides:

3x - 16 = 2

Adding 16 to both sides:

3x = 18

Dividing both sides by 3:

x = 6

Therefore, the numerator of the original fraction is 6.

The correct answer is option C: 6.