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Investment choices for surplus cash

CAT 2007 Slot 1 · Quantitative Ability · Medium · Maxima and Minima

This is a medium Quantitative Ability question set from the CAT 2007 Slot 1 paper. It tests Maxima and Minima. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Passage / data set

Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.

  • Option A: Invest in a public sector bank. It promises a return of +0.10%+0.10\%.
  • Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%+5\% while a fall will entail a return of −3%-3\%.
  • Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of −2.5%-2.5\%, while a fall will entail a return of +2%+2\%.

Question 1 of 2

The maximum guaranteed return to Shabnam is

  1. A.

    0.25%

  2. B.

    0.10%

  3. C.

    0.20%

  4. D.

    0.15%

  5. E.

    0.30%

Answer

C

Explanation

Let bb be fraction in B and cc be fraction in C. If market rises: return is 5b−2.5c5b - 2.5c. If market falls: return is −3b+2c-3b + 2c. To guarantee maximum return independent of market, set 5b−2.5c=−3b+2c  ⟹  8b=4.5c  ⟹  bc=9165b - 2.5c = -3b + 2c \implies 8b = 4.5c \implies \frac{b}{c} = \frac{9}{16}. So b=36%b = 36\%, c=64%c = 64\%. Return =5(0.36)−2.5(0.64)=1.8−1.6=0.20%= 5(0.36) - 2.5(0.64) = 1.8 - 1.6 = 0.20\%.

Question 2 of 2

What strategy will maximize the guaranteed return to Shabnam?

  1. A.

    100% in option A

  2. B.

    36% in option B and 64% in option C

  3. C.

    64% in option B and 36% in option C

  4. D.

    1/3 in each of the three options

  5. E.

    30% in option A, 32% in option B and 38% in option C

Answer

B

Explanation

The optimal allocation is 36%36\% in B and 64%64\% in C.

Why the other options are wrong

  • A.100% in option A — does not satisfy the condition asked in this question, so it is not the correct answer.
  • B.36% in option B and 64% in option C — does not satisfy the condition asked in this question, so it is not the correct answer.
  • C.64% in option B and 36% in option C — does not satisfy the condition asked in this question, so it is not the correct answer.
  • D.1/3 in each of the three options — does not satisfy the condition asked in this question, so it is not the correct answer.
  • E.30% in option A, 32% in option B and 38% in option C — does not satisfy the condition asked in this question, so it is not the correct answer.

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