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Integrated Reasoning Practice Problem: Multi-Source Reasoning

 

Card #1

Whizzo Chocolate Company in Chicago, IL, makes a wide variety of exceptionally high quality confections.  Each one of their products can be classified into one of 5 groups. (Weights include all necessary packaging for shipping.)

1) 12-piece assortments (1.5 lbs, $14.99), some of which require refrigerated shipping and some of which do not.

2) 20-piece assortments (2.0 lbs, $24.99), some of which require refrigerated shipping and some of which do not.

3) a small chocolate-covered fruit basket (12 lb, $39.99), which requires refrigerated shipping

4) a large chocolate-covered fruit basket (30 lb, $59.99), which requires refrigerated shipping

5) an all-chocolate chessboard with white & dark chocolate chessmen (25 lb, $149.99), which requires refrigerated shipping

 

Card #2

Whizzo Chocolate Company uses only the following shipping methods

Western Food Sender

a) WFS non-refrigerated service: $50 plus $10 times each pound

b) WFS refrigerated service: $80 plus $15 times each pound

 

Card #3

If a single order is a “mixed order”, that is, it contains both items that require refrigerated shipping and items that do not require refrigerated shipping, it does no harm to the latter items to ship them in refrigerated shipping.  If a single order is a mixed order, customer has a choice:

a) only items requiring refrigerated shipping  sent via refrigerated shipping , and all other items sent without refrigeration

b) all items, regardless of type, sentvia refrigerated shipping

When a customer places a mixed order, the Whizzo sales representative will make this choice clear to the customer, and make clear that absolutely no damage will occur by refrigerating those items which don’t require refrigeration.

 

Practice Problems

1) If a person in Pennsylvania has a total of $500 to spend on a Whizzo order, which of the following orders could he afford, including the cost of shipping?

five 12-piece assortments, all requiring refrigerated shipping

Yes

No

two large chocolate-covered fruit basket

Yes

No

the all-chocolate chessboard with white & dark chocolate chessmen

Yes

No

 

 

2) For each of the following “mixed orders”, each containing twenty items total, which shipping option will be less expensive?

Option A) only items requiring refrigerated shipping  sent via refrigerated shipping , and all other items sent without refrigeration

Option B) all items, regardless of type, sent via refrigerated shipping

fifteen 12-piece assortments requiring refrigerated shipping and five 12-piece assortments not requiring refrigerated shipping

A

B

ten 12-piece assortments requiring refrigerated shipping and ten 12-piece assortments not requiring refrigerated shipping

A

B

five 12-piece assortments requiring refrigerated shipping and fifteen 12-piece assortments not requiring refrigerated shipping

A

B

 

 

Answers and Explanations

(1) Yes; No; No; (2) B, A, A;

 

1) Base cost of five 12-piece assortment = 5 x $14.99 = $74.95.

Combined weight = 5 x 1.5 = 7.5 lb.

Refrigeration required.

Shipping cost = 80 + 15*75 = $192.50

Total cost = $74.95 + $192.50 = $267.45 -> affordable

 

Base cost of two large chocolate-covered fruit basket = 2 x $59.99 = $119.98

Combined weight = 2 x 30 = 60 lb

Shipping cost = 80 + 15*60 = $980 -> way over budget

 

Base cost of all-chocolate chessboard = $149.99

Weight = 25 lbs

Shipping cost = 80 + 15*25 = $455 -> over budget

 

2) Suppose you have a mixed order and it is all going to be sent via refrigerated shipping.  That cost $80 + $15*(# of pound).  Suppose some items, not requiring refrigeration, are removed from that shipment, and a non-refrigerated shipment is created.  The additional cost is the $50 base cost of a non-refrigerated shipment.  The savings per pound is the difference in the per pound rates: $15/lb – $10/lb = $5/lb.  When will this saving exceed the additional $50 cost?  When the total weight of the non-refrigerated shipment exceeds 10 lbs.

The first order has five 12-piece assortments not requiring refrigerated shipping:  5 x 1.5 = 7.5 lbs of goods not requiring refrigerated shipping.  That is not enough to justify a separate non-refrigerated order.

The second order has ten 12-piece assortments not requiring refrigerated shipping:  10 x 1.5 = 15 lbs of goods not requiring refrigerated shipping.  That is enough to justify a separate non-refrigerated order.

The third order has even more weight not requiring refrigerated shipping, so this one will also justify a separate non-refrigerated order.

 

BTW, the name “Whizzo Chocolate Company” is my homage to a classic Monty Python skit.  🙂

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8 Responses to Integrated Reasoning Practice Problem: Multi-Source Reasoning

  1. Chinmoy August 1, 2016 at 12:30 am #

    HI Mike,

    Thank you for such a wonderful post.

    I am a bit confused with Q no.2. More specifically, I am stuck with the wordings in Card 2.

    “a) WFS non-refrigerated service: $50 plus $10 times each pound

    b) WFS refrigerated service: $80 plus $15 times each pound”

    – Do we have to consider the $50 and $80 every time for each package?
    I solved the question considering the base price/cost once for the entire shipment and just multiplied the shipping charge with the weight and got it all wrong
    I got 1-A, 2-A, 3-B

    Is my understanding of the statement given in card 2 wrong. As no where it is explicitly mentioned that $50/$80 base price has to be added for each individual package.Could you please clarify?

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert August 15, 2016 at 4:50 am #

      Hi Chinmoy,

      Happy to help 🙂 The descriptions of the shipment methods reflect an individual shipment. So, the $50 or $80 fee applies to a single shipment. The number of packages isn’t important but rather the number of shipments. In the practice problems, we have to evaluate the three shipments separately, since they are three separate orders. For that reason, we consider the cost of shipping in each case.

      Does that clear up your doubts? I hope so, but if not, please let us know 🙂

  2. kalyanramu April 17, 2016 at 8:49 am #

    I think one of the calculations is incorrect

    1. In 1.b, 2*59.99$ = 120$ and not 220$

    It still doesn’t change the final answer

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert April 18, 2016 at 10:34 am #

      Hi Kalyanramu,

      Thanks for your keen eye! I’ve fixed the error. 🙂

  3. manish July 12, 2012 at 5:14 am #

    Thank you so much Mike, Your work is really appreciated.

    • Mike MᶜGarry
      Mike July 12, 2012 at 7:16 pm #

      Manish: You are quite welcome.
      Mike 🙂

  4. Mike MᶜGarry
    Mike July 10, 2012 at 8:52 pm #

    Dear Manish: Let’s look at Q.2(a) —- 15 of the kind that need to be refrigerated and 5 of the kind that don’t. For the all refrigeration option, I calculated $530, and for sending the 15 refrigerated and the 5 not, I calculated $542.50, slightly more. Yes, per item, the refrigerated option is more, but when some items require refrigeration, you automatically have to pay the $80 flat fee. When you move some items to the non-refrigerated method, you also incur the $50 flat fee — the per-item savings for all those non-refrigerated items must add up to more than $50 to cover that fee — otherwise, it would not be worth it to ship some non-refrigerated. Does that make sense?
    Mike 🙂

  5. manish July 10, 2012 at 12:59 pm #

    Please clarify the Q.2
    I believe that if, option B will have a common cost of $830 and since the cost involved is more in refrigeration the option B will be always costlier.
    Please explain.My exam is on next week and i am stuck here with this question.
    Regards,
    Manish


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