Test: Two Part Analysis - GMAT MCQ

The first question is easier to answer. If Marcel drives for 5 hours, then he goes at a constant speed of X for 2 hours and at a constant speed of Y for the remaining 3 hours. Thus, his average speed is 

Now, if Marcel travels a total of 5X miles, then over the first 2 hours he covers 2X miles, so he has 3X miles left to travel at a speed of Y miles per hour:

Therefore, in total his trip lasts 
2 + 3X/Yhours.
You can now find his average speed for the trip:

The probability of the union of events A and B occurring equals the probability of event A occurring, plus the probability of event B occurring, minus the probability of the intersection of events A and B occurring. You know the value of all of these probabilities except the last one. The probability of the intersection of events A and B equals the number of desirable outcomes in the intersection of A and B, which is 4, over the number of total outcomes in the lottery—let’s call that t. Thus, you have:

P (AUB) = P (A) + P (B) - P (A∩B)

So the correct answer in the first column = the total number of lots is 20.
Next, let the number of desirable outcomes in event B be b. In that case, you have:

So the correct answer in the second column is: the number of desirable outcomes in event B is 16.

If Mike accepts the offer from Acme Anvils, his year 20 salary will reflect 19 increases of 5% and will be $50,000 × 1.0519 = $126,347.51. If he takes the job with Retro Rockets, he will have received 19 raises of $3,000 each, and his salary will be $60,000 + 19 × $3,000 = $117,000.

Step 1: Preview the task.
A quick glance at the answer table tells you that this is a quantitative question. Additionally, all answer choices are algebraic expressions in x and y, so you will have to set up some sort of equation and solve for an unknown quantity.

Step 2: Read the prompt.

You have a vendor, a customer, the customer’s budget, and the vendor’s rental prices. Two absolute values are given (the theater’s lighting rental budget and the 4 weeks of the initial rental rate) and two variables for the two rental rates. Circle back to the tasks you have to perform. Note that they are similar but independent of each other. You will have to set up two algebraic expressions, one for each column, and solve the first one for the number of weeks per instrument, and the second one for the number of instruments per week.

Step 3: Proceed to solving, one column at a time.
Column 1: Let W be the maximum number of weeks that 1564 Theatre Group rents each of the 10 instruments. Then W – 4 is the maximum number of weeks per instrument during which 1564 Theatre Group pays $y per instrument (since for the first 4 weeks it pays $x per instrument—and remember, that’s $x in total for each instrument for the first 4 weeks, not $x per week). The total cost per instrument, then, is x + y(W − 4). The theater company is renting 10 instruments, so its total cost is 10[x + y(W − 4)]
Equate this expression to $2,000 and solve for W:

Column 2: Follow the same process you did for column 1. If 1564 Theatre Group is renting each instrument for 10 weeks, then it is paying $x for the first four weeks and $y per week for the remaining 6 weeks. Thus, it is paying 
X + 6y in total for each instrument. Let I be the maximum number of instruments the theater company rents. Then, its total cost is  I(x + 6y)
Equate this expression to $2,000 and solve for I:

The conference organizers need 250 single rooms, and the remaining 1,000 people can be housed in 500 double rooms, so a total of 750 rooms will be needed. For meals, 50 of the 1,250 attendees declined all meals, and 200 more chose only lunches, so 1,250 – 50 – 200 = 1,000 people reserved dinner seating.