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Discount Coupons Optimization

XAT 2024 · Quantitative Ability & Data Interpretation · Medium · Optimization

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Passage / data set

A store offers a choice of five different discount coupons to its customers, described as follows:

  • Coupon A: A flat discount of Rs. 250 on a minimum spend of Rs. 1200 in one transaction.
  • Coupon B: A 15% discount on a minimum spend of Rs. 500 in one transaction, up to a maximum discount of Rs. 300.
  • Coupon C: A flat discount of Rs. 100 on a minimum spend of Rs. 600 in one transaction.
  • Coupon D: A 10% discount on a minimum spend of Rs. 250 in one transaction, up to a maximum discount of Rs. 100.
  • Coupon E: A flat discount of Rs. 50 on a minimum spend of Rs. 200 in one transaction.

The customers are allowed to use at most one coupon in one transaction, i.e., two or more coupons cannot be combined for the same transaction.

Question 1 of 3

Four customers used four different discount coupons for their respective transactions in such a way that they obtained a total discount of Rs. 710. Which discount coupon was not used?

  1. A.

    Coupon A

  2. B.

    Coupon B

  3. C.

    Coupon C

  4. D.

    Coupon D

  5. E.

    Coupon E

Answer

E

Explanation

Maximum discount for each coupon:

  • A: 250
  • B: 300
  • C: 100
  • D: 100
  • E: 50

Sum of max discounts for all 5 coupons =250+300+100+100+50=800= 250 + 300 + 100 + 100 + 50 = 800. If Coupon E is omitted, sum of max discounts of A, B, C, D =250+300+100+100=750≥710= 250 + 300 + 100 + 100 = 750 \ge 710. If any other coupon is omitted, max possible discount would be less than 710 (e.g., omitting C gives 800−100=700<710800 - 100 = 700 < 710). Thus, Coupon E was not used.

Question 2 of 3

Four customers used four different discount coupons for their respective transactions in such a way that nobody used any discount coupon sub-optimally. (A discount coupon is used sub-optimally if using another discount coupon could have resulted in a higher discount for the same transaction.) What was the minimum combined spend (before application of any discount)?

  1. A.

    Rs. 2250

  2. B.

    Rs. 2500

  3. C.

    Rs. 2350

  4. D.

    Rs. 2300

  5. E.

    Rs. 1550

Answer

B

Explanation

To not use a coupon sub-optimally, the transaction amount must yield a discount that no other available coupon could exceed:

  • For Coupon E (flat 50): Min spend =200= 200.
  • For Coupon B (15%): To beat E (50), 15%×X>50  ⟹  X≥33415\% \times X > 50 \implies X \ge 334, min spend to beat E is Rs. 500.
  • For Coupon C (flat 100): Min spend =600= 600.
  • For Coupon A (flat 250): Min spend =1200= 1200. Minimum spends for 4 optimal non-overlapping coupons (E, B, C, A) =200+500+600+1200=2500= 200 + 500 + 600 + 1200 = 2500.

Question 3 of 3

A family wanted to purchase four products worth Rs. 1000 each, and another product worth Rs. 300. They were told that they could: I) pay for the five products through one or more transactions in any way they wanted, as long as the purchase amount of any one product would not get split into different transactions, and II) use the same discount coupon repeatedly for separate transactions, if they opt for more than one transaction.

What was the maximum discount that they could obtain for their purchase?

  1. A.

    Rs. 600

  2. B.

    Rs. 645

  3. C.

    Rs. 650

  4. D.

    Rs. 700

  5. E.

    None of the remaining options is correct.

Answer

D

Explanation

Items: 1000, 1000, 1000, 1000, 300. Total = 4300. Strategy to maximize discount:

  • Transaction 1: 2000 (1000 + 1000) using Coupon B   ⟹  15%×2000=300\implies 15\% \times 2000 = 300 (max limit reached).
  • Transaction 2: 1000 using Coupon B   ⟹  15%×1000=150\implies 15\% \times 1000 = 150.
  • Transaction 3: 1300 (1000 + 300) using Coupon A   ⟹  \implies flat 250 discount. Total discount =300+150+250=700= 300 + 150 + 250 = 700.

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