Venkat Stock Returns Analysis

CAT 2005 Slot 1 · DILR · Hard · DILR

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Passage / data set

Venkat invested in 4 companies (A, B, C, D), belonging to Cement, IT, Auto, and Steel in no particular order. Initial price =100= 100 per stock. Expected returns: A = 20%, B = 10%, C = 30%, D = 40%. Two companies announced extraordinary results:

  • One from Cement/IT (return doubled =2×= 2 \times expected)
  • One from Steel/Auto (return =1.5×= 1.5 \times expected) The other two had actual returns equal to initial expected returns.

Question 1 of 4

What is the minimum average return Venkat would have earned during the year?

  1. A.

    30%

  2. B.

    3114%31\frac{1}{4}\%

  3. C.

    3212%32\frac{1}{2}\%

  4. D.

    Cannot be determined

Answer

A

Explanation

To minimize total return, assign doubling (2×2\times) and 1.5×1.5\times to the stocks with lowest expected returns (10% and 20%). Case 1: 10%×2+20%×1.5+30%+40%=20%+30%+30%+40%=120%10\% \times 2 + 20\% \times 1.5 + 30\% + 40\% = 20\% + 30\% + 30\% + 40\% = 120\%. Average return =120%/4=30%= 120\% / 4 = 30\%.

Question 2 of 4

If Venkat earned a 35% return on average during the year, then which of these statements would necessarily be true? I. Company A belonged either to Auto or to Steel Industry. II. Company B did not announce extraordinarily good results. III. Company A announced extraordinarily good results. IV. Company D did not announce extraordinarily good results.

  1. A.

    I and II only

  2. B.

    II and III only

  3. C.

    III and IV only

  4. D.

    II and IV only

Answer

B

Explanation

Total return =35%×4=140%= 35\% \times 4 = 140\%. Initial sum =20+10+30+40=100%= 20 + 10 + 30 + 40 = 100\%. Extra needed =40%= 40\%. Extra return possibilities: 20×1=2020 \times 1 = 20 (if A doubles) and 40×0.5=2040 \times 0.5 = 20 (if D gets 1.5×1.5\times). So A doubled (20→40%20 \to 40\%), D got 1.5×1.5\times (40→60%40 \to 60\%). Thus, A announced extraordinary results (Cement/IT) and B did not announce extraordinary results. Statements II and III are necessarily true.

Question 3 of 4

If Venkat earned a 38.75% return on average during the year, then which of these statement(s) would necessarily be true? I. Company C belonged either to Auto or to Steel Industry. II. Company D belonged either to Auto or to Steel Industry. III. Company A announced extraordinarily good results. IV. Company B did not announce extraordinarily good results.

  1. A.

    I and II only

  2. B.

    II and III only

  3. C.

    I and IV only

  4. D.

    II and IV only

Answer

C

Explanation

Total return =38.75%×4=155%= 38.75\% \times 4 = 155\%. Extra needed =55%= 55\%. To get 55% extra: 40%×1=4040\% \times 1 = 40 (D doubled) and 30%×0.5=1530\% \times 0.5 = 15 (C got 1.5×1.5\times). So C belongs to Auto/Steel (since it got 1.5×1.5\times), and B did not announce extraordinary results. Statements I and IV are necessarily true.

Question 4 of 4

If Company C belonged to the Cement or the IT industry and did announce extraordinarily good results, then which of these statement(s) would necessarily be true? I. Venkat earned not more than 36.25% return on average. II. Venkat earned not less than 33.75% return on average. III. If Venkat earned 33.75% return on average, Company A announced extraordinarily good results. IV. If Venkat earned 33.75% return on average, Company B belonged either to Auto or to Steel Industry.

  1. A.

    I and II only

  2. B.

    II and IV only

  3. C.

    II and III only

  4. D.

    III and IV only

Answer

B

Explanation

Company C (30%) doubled to 60% (extra 30%). For the other company (Auto/Steel, gets 1.5×1.5\times):

  • If B (10%10\%) gets 1.5×1.5\times: extra =5%= 5\%, total =135%= 135\%, avg =33.75%= 33.75\%.
  • If A (20%20\%) gets 1.5×1.5\times: extra =10%= 10\%, total =140%= 140\%, avg =35%= 35\%.
  • If D (40%40\%) gets 1.5×1.5\times: extra =20%= 20\%, total =150%= 150\%, avg =37.5%= 37.5\%. Thus average return is between 33.75% and 37.5%. So II is true. If avg is 33.75%, B got 1.5×1.5\times, so B belongs to Auto/Steel (Statement IV is true). Statements II and IV are necessarily true.

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