Share Trading by Chetan and Michael

CAT 2006 Slot 1 · DILR · Hard · Data Interpretation

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Passage / data set

Two traders, Chetan and Michael, traded MCS shares over five trading days. At the start of Day 1, MCS share price was Rs 100; at the end of Day 5, it was Rs 110. Each day, the closing price went up by Rs 10 or down by Rs 10.

Rules:

  1. Chetan: If price went UP, he sold 10 shares at closing price. If price went DOWN, he bought 10 shares at closing price.
  2. Michael: If closing price was ABOVE Rs 110, he sold 10 shares. If closing price was BELOW Rs 90, he bought 10 shares.

Question 1 of 5

If Chetan sold 10 shares of MCS on three consecutive days, while Michael sold 10 shares only once during the five days, what was the price of MCS at the end of day 3?

  1. A.

    Rs 90

  2. B.

    Rs 100

  3. C.

    Rs 110

  4. D.

    Rs 120

  5. E.

    Rs 130

Answer

Rs 110

Explanation

Chetan sold on 3 consecutive days   ⟹  \implies price went up on 3 consecutive days. Michael sold 10 shares only once   ⟹  \implies closing price was above Rs 110 on exactly one day (i.e. Rs 120 or 130). Price path: Day 1 (110), Day 2 (120), Day 3 (110), Day 4 (120), Day 5 (110) or similar. For price to go up 3 consecutive days: Day 1: 110, Day 2: 120, Day 3: 110, etc. Checking Case 3: 90 -> 100 -> 110 -> 120 -> 110. Here, price went up on Day 2, Day 3, Day 4 (3 consecutive days). On Day 4, price is 120 (>110), so Michael sold once. Day 3 price = Rs 110.

Question 2 of 5

If Chetan ended up with Rs 1300 more cash than Michael at the end of day 5, what was the price of MCS share at the end of day 4?

  1. A.

    Rs 90

  2. B.

    Rs 100

  3. C.

    Rs 110

  4. D.

    Rs 120

  5. E.

    Not uniquely determinable

Answer

Rs 100

Explanation

Analyzing possible price paths where Chetan's net cash change minus Michael's net cash change equals Rs 1300: Cases 1, 2, 4, 5, 6 give Day 4 price = Rs 100.

Question 3 of 5

If Michael ended up with 20 more shares than Chetan at the end of day 5, what was the price of the share at the end of day 3?

  1. A.

    Rs 90

  2. B.

    Rs 100

  3. C.

    Rs 110

  4. D.

    Rs 120

  5. E.

    Rs 130

Answer

Rs 90

Explanation

For Michael to have 20 more shares than Chetan, Michael must have bought shares when price went below Rs 90, or Chetan sold more net shares. Case 1: 90 -> 80 -> 90 -> 100 -> 110. Chetan shares change: -10 + 10 - 10 - 10 - 10 = -30. Michael shares change: Day 2 (price 80 < 90) bought 10 shares   ⟹  +10\implies +10. Difference = +10−(−30)=+40+10 - (-30) = +40 or similar. In Case 1, Day 3 price is Rs 90.

Question 4 of 5

If Michael ended up with Rs 100 less cash than Chetan at the end of day 5, what was the difference in the number of shares possessed by Michael and Chetan (at the end of day 5)?

  1. A.

    Michael had 10 less shares than Chetan.

  2. B.

    Michael had 10 more shares than Chetan.

  3. C.

    Chetan had 10 more shares than Michael.

  4. D.

    Chetan had 20 more shares than Michael.

  5. E.

    Both had the same number of shares.

Answer

Both had the same number of shares.

Explanation

Cases satisfying Michael having Rs 100 less cash than Chetan are Case 3 and Case 7. In both cases, Michael's net share change and Chetan's net share change are identical (x−10x - 10 for both). Therefore, both had the same number of shares.

Question 5 of 5

What could have been the maximum possible increase in combined cash balance of Chetan and Michael at the end of the fifth day?

  1. A.

    Rs 3700

  2. B.

    Rs 4000

  3. C.

    Rs 4700

  4. D.

    Rs 5000

  5. E.

    Rs 6000

Answer

Rs 5000

Explanation

To maximize combined cash increase, we need price paths reaching Rs 120/130 to generate maximum cash from selling. In Case 9 (110 -> 120 -> 130 -> 120 -> 110): Chetan cash gain = 1100 + 1200 + 1300 - 1200 - 1100 = Rs 1300. Michael cash gain = 1200 + 1300 + 1200 = Rs 3700. Combined cash gain = 1300+3700=50001300 + 3700 = 5000.

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