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Test: Two Part Analysis - GMAT MCQ


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5 Questions MCQ Test Data Insights for GMAT - Test: Two Part Analysis

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Test: Two Part Analysis - Question 1

Marcel is taking a trip, driving at a constant speed of X miles per hour for the first 2 hours of his trip, and at a constant speed of Y miles per hour after the first 2 hours.

In terms of X and Y, select the expression that represents Marcel’s average speed if he drives for a total of 5 hours, and select the expression that represents Marcel’s average speed if he drives for a total of 5X miles. Make only one selection in each column.

Detailed Solution for Test: Two Part Analysis - Question 1

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:

Test: Two Part Analysis - Question 2

During a lottery, several lots are to be selected. A is the event that a certain subset of these lots is selected, and B is the event that another subset of these lots is selected, such that:

  • the probability of event A occurring is 2/5.
  • the probability of event B occurring is 4/5.
  • the probability of the union of events A and B occurring is 1.
  • the intersection of events A and B is an event with four desirable outcomes.

In the following table, identify the total number of lots and the number of desirable outcomes in event B. Make only one selection in each column.

Detailed Solution for Test: Two Part Analysis - Question 2

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.

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Test: Two Part Analysis - Question 3

Mike is considering job offers from two competing firms. Acme Anvils offers an annual salary of $50,000 with a guaranteed increase of 5% every year. Retro Rockets offers an annual salary of $60,000 with a $3,000 increase each year. Find the salary Mike can expect to earn after 20 years with each company.

Detailed Solution for Test: Two Part Analysis - Question 3

If Mike accepts the offer from Acme Anvils, his year 20 salary will reflect 19 increases of 5% and will be $50,000 × (1.05)19 = $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.
 

Test: Two Part Analysis - Question 4

Light The Stage, a stage lighting equipment rental company, charges $x for the first four weeks that a lighting instrument is rented, and $y per week for each week after that. The company 1564 Theatre Group has budgeted $2,000 to spend on the rental of lighting instruments from Light TheStage for its upcoming production.

In the table, indicate which expression corresponds to the maximum number of weeks per instrument for which 1564 Theatre Group can rent 10 instruments given its budget, as well as which expression corresponds to the maximum number of instruments 1564 Theatre Group can rent for a total of 10 weeks per instrument given its budget. Make only two selections, one in each column.

Detailed Solution for Test: Two Part Analysis - Question 4

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:

Test: Two Part Analysis - Question 5

Registrants for a conference were asked to choose a room for single or double occupancy and to reserve seating for lunches only or for lunches and dinners. A total of 1,250 people registered for the conference, and 250 of those requested single-occupancy rooms. Two hundred people reserved lunch-only seating, and 50 declined all meal service. Find the number of dinners that will be needed and the total number of rooms reserved.

Detailed Solution for Test: Two Part Analysis - Question 5

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.

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