ICAP PRC-2 Quantitative Analysis for Business: mock exams and practice questions

Sample question 1 · A · Basic mathematics

Latifabad Biscuits of Hyderabad models its monthly total cost as C = 240,000 + 175Q, where C is in rupees and Q is the number of biscuit boxes made in the month. Which interpretation of this equation is correct?

1. A Variable costs are Rs 240,000 a month and fixed costs are Rs 175 per box
2. B Average cost is Rs 175 per box at every level of monthly output
3. C Fixed costs are Rs 240,000 a month and each extra box adds Rs 175 to total cost
4. D Total cost doubles whenever monthly output doubles, from any starting level

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Answer: C. For a straight line C = a + bQ, the intercept a is the value of C when Q = 0 and the slope b is the change in C for a one-unit increase in Q.

- a = Rs 240,000: the cost incurred even if no boxes are made, i.e. fixed cost per month.
- b = Rs 175: each additional box adds Rs 175, i.e. variable cost per box.

For example, at Q = 2,000 boxes, C = 240,000 + 175 x 2,000 = Rs 590,000, an average of Rs 295 per box, not Rs 175. At Q = 4,000, C = Rs 940,000, which is less than double Rs 590,000.

Sample question 2 · B · Financial mathematics

Ayesha Rafiq, a Lahore schoolteacher, has Rs 800,000 to place on deposit for 4 years. Her bank offers either 11% a year simple interest or 11% a year compounded annually, with all interest paid at the end of the 4 years. By how much does the interest from the compound option exceed the interest from the simple option (to the nearest rupee)?

1. A Rs 352,000
2. B Rs 414,456
3. C Rs 62,456
4. D Rs 1,214,456

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Answer: C. Simple interest = P x r x t = 800,000 x 0.11 x 4 = Rs 352,000.

Compound amount = 800,000 x (1.11)^4 = 800,000 x 1.51807 = Rs 1,214,456, so compound interest = 1,214,456 - 800,000 = Rs 414,456.

Extra interest from compounding = 414,456 - 352,000 = Rs 62,456. The difference is the interest earned on interest: simple interest is calculated on the original principal only, while compound interest is added to the balance each year and earns interest itself.

Sample question 3 · C · Application of statistics in business

Rehman Pharma wants the views of chemist shops in Punjab on a new delivery schedule. It lists the 120 towns where it has customers, selects 8 of those towns at random and then surveys every chemist shop in the 8 selected towns. Which sampling method is Rehman Pharma using?

1. A Stratified random sampling
2. B Cluster sampling
3. C Quota sampling
4. D Systematic sampling

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Answer: B. The population (chemist shops) falls into natural groups (towns). Choosing some groups at random and examining all members of each chosen group is cluster sampling. It is cheap because fieldwork is concentrated in 8 towns, but the sample may be less representative than a stratified sample if shops in different towns differ.