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DIRECTIONS for the questions 1 to 2:

Five horses, Red, White, Grey, Black and Spotted participated in a race. As per the rules of the race, the persons betting on the winning horse get four times the bet amount and those betting on the horse that came in second get thrice the bet amount. Moreover, the bet amount is returned to those betting on the horse that came in third, and the rest lose the bet amount. Raju bets Rs. 3000, Rs. 2000 Rs. 1000 on Red, White and Black horses respectively and ends up with no profit and no loss.

Q1) Which of the following cannot be true?
1) At least two horses finished before Spotted
2) Red finished last
3) There were three horses between Black and Spotted
4) There were three horses between White and Red

Q2) Suppose, in addition, it is known that Grey came in fourth. Then which of the following cannot be true?
1) Spotted came in first
2) Red finished last
3) White came in second
4) Black came in second

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DIRECTIONS for the questions 3 to 7:

Abdul, Bikram and Chetan are three professional traders who trade in shares of a company XYZ Ltd. Abdul follows the strategy of buying at the opening of the day at 10 am and selling the whole lot at the close of the day at 3 pm. Bikram follows the strategy of buying at hourly intervals: 10 am , 11 am, 12 noon, 1 pm and 2 pm, and selling the whole lot at the close of the day. Further, he buys an equal number of shares in each purchase. Chetan follows a similar pattern as Bikram but his strategy is somewhat different. Chetan’s total investment amount is divided equally among his purchases. The profit or loss made by each investor is the difference between the sale value at the close of the day less the investment in purchase. The “return” for each investor is defined as the ratio of the profit or loss to the investment amount expressed as a percentage.

Q3) On a “boom” day the price of XYZ Ltd. keeps rising throughout the day and peaks at the close of the day. Which trader got the minimum return on that day?
1) Bikram
2) Chetan
3) Abdul
4) Abdul or Chetan

Q4) On a day of fluctuating market prices, the share price of XYZ Ltd. ends with a gain, i.e., it is higher at the close of the day compared to the opening value. Which trader got the maximum return on that day?
1) Bikram
2) Chetan
3) Abdul
4) cannot be determined

Q5) Which one of the following statements is always true?
1) Abdul will not be the one with the minimum return
2) Return for Chetan will be higher than that of Bikram
3) Return for Chetan cannot be higher than that of Abdul
4) None of the above

One day, two other traders, Dane and Emily joined Abdul , Bikram and Chetan for trading in the shares of XYZ Ltd. Dane followed a strategy of buying equal numbers of shares at 10 am, 11 am and 12 noon, and selling the same numbers at 1 pm, 2 pm and 3 pm. Emily, on the other hand, followed the strategy of buying shares using all her money at 10 am and selling all of them at 12 noon and again buying the shares for all the money at 1 pm and again selling all of them at the close of the day at 3 pm. At the close of the day the following was observed:

i. Abdul lost money in the transactions.
ii. Both Dane and Emily made profits.
iii. There was an increase in share price during the closing hour compared to the price at 2 pm.
iv. Share price at 12 noon was lower than the opening price.

Q6) Which of the following is necessarily false?
1) Share price was at its lowest at 2 pm
2) Share price was at its lowest at 11 am
3) Share price at 1 pm was higher than the share price at 2 pm
4) None of these

Q7) Share price was at its highest at
1) 10 AM
2) 11 AM
3) 12 Noon
4) 1 PM

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DIRECTIONS for the questions 8 to 9:

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%
Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of –3%
Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of –2.5%, while a fall will entail a return of +2%

1) 0.25%
2) 0.1%
3) 0.2%
4) 0.15%

1) 100% in option A
2) 36% in option B and 64% in option C
3) 64% in option B and 36% in option C
4) 1/3 in each of the three options

DIRECTIONS for the questions 10 to 11:

Mr. David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is Rs. 30. On the other hand, the cost, in rupees, of producing x units is 240 + bx + cx2, where b and c are some constants. Mr. David noticed that doubling the daily production from 20 to 40 units increases the daily production cost by 66.66%. However, an increase in daily production from 40 to 60 units results in an increase of only 50% in the daily production cost. Assume that demand is unlimited and that Mr. David can sell as much as he can produce. His objective is to maximize the profit.

Q10) How many units should Mr. David produce daily?

1) 130
2) 100
3) 70
4) 150

Q11) What is the maximum daily profit, in rupees, that Mr. David can realize from his business?

1) 620
2) 920
3) 840
4) 760

### Solutions and Explanations

1. We solve this question by options.
If we consider option 4 to be true, then either the White or Red horse will finish first. It means that the amount Raju receives at the end of the race will be at least Rs. 8000 or Rs. 12000 (depending on which of the two horses finish first). However, his investment at the start of the race was only Rs. 6000. So, his profit could never be zero; in the worst scenario he will at least make Rs. 2000.
Option (4) cannot be true.
Hence, option 4.

2. We solve this question by options.
If we consider option 3 to be true, then White finishes second and one of the Red or Black horses will come in the first or third positions. With White at the second position, the amount Raju receives at the end of the race will be at least Rs. 6000, and from Red or Black he will earn some money. Therefore, the total money Raju receives will be more than Rs. 6000. Since his investment at the start of the race was only Rs. 6000, his profit could never be zero.
Option (3) cannot be true.
Hence, option 3.

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EXPLANATIONS for the questions 3 to 7:

Firstly, let us try to understand the way the investments of the three traders behave.
Abdul buys shares at 10 am everyday and sells them at a particular price at 3 pm. So his return is determined by the difference in the share price at these two times. Bikram and Chetan buy shares at equal intervals. But since Chetan buys them in equal amount he would end up buying more when the price is less and less when the price is more. Whether the prices are continuously rising or continuously falling down or in a fluctuating market, Chetan always has a higher proportion of lower priced shares as compared to Bikram. This increases his profit in a rising market and reduces his loss in a falling market. Therefore Chetan never has return lower than that of Bikram.
We have explained this concept by taking examples. For more depth we have also provided the theoretical explanation. The theoretical explanation is only for better understanding and may not be suitable in a test environment.
Consider the scenario when the share price keeps rising throughout the day.
Let the share price at 10 am be Rs. 100, 11 am be Rs. 110, 12 noon be Rs. 140, 1 pm be Rs. 150, 2 pm be Rs. 180, and finally at 3 pm be Rs. 200.

Abdul buys shares at Rs. 100 at 10 am and sells them at Rs. 200 at 3 pm. Abdul’s return is 100%.

Let Bikram buy one share at each interval. So, at 10 am, he buys a share for Rs. 100; at 11 am, he buys a share for Rs. 110; at 12 noon, he buys a share for Rs. 140; at 1 pm, he buys a share for Rs. 150; and at 2 pm, he buys a share for 180 × 1 = Rs. 180.
Thus, he buys a total of 5 shares for 100 + 110 + 140 + 150 + 180 = Rs. 680
3 pm, he sells all 5 shares for 200 × 5 = Rs. 1,000.
Thus, his profit will be 1,000 − 680 = Rs. 320
Hence, Bikram's return is 320/680 = .47 or 47%

Let Chetan invest Rs. 415,800 at each interval. So, at 10 am, he buys 415800/100 = 4158 shares; at 11 am, he buys 415800/110 = 3780 shares; at 12 noon, he buys 415800/140 = 2970 shares; at 1 pm, he buys 415800/150 = 2772 shares; at 2 pm, he buys 415800/180 = 2310 shares.
Thus, he buys 4158 + 3780 + 2970 + 2772 + 2310 = 15990 shares for 415800 × 5 = Rs. 20,79,000.
He sells these shares for 200 × 15990 = Rs. 31,98,000. His profit will be 3198000 − 2079000 = Rs. 11,19,000.
Hence, Chetan's return is 11,19,000/20,79,000 = 373/693 = .53 or 53%
From the above example, we see that in case of continuously rising share prices,
Abdul’s return > Chetan’s return > Bikram’s return
Thus, Bikram gets the minimum return on a “boom” day.
Hence, option 1.

Note: Theoretical Explanation:
Let x1, x2, … , x6 be the share prices at 10 am, 11 am, 12 noon, 1 pm, 2 pm and 3 pm respectively.
For Abdul:
Abdul buys shares at Rs. x1 and sells them at Rs. x6.
Abdul's return = (x6 - x1)/x1

For Bikram:
Let Bikram have bought n shares at each hourly interval.
Hence, Bikram’s returns

For Chetan:
Let Chetan invest Rs. P at each hourly interval.
His investment amount = 5P
Since he invests Rs. P at each interval, he buys:
Chetan’s returns =

Now, let’s compare Bikram’s and Chetan’s returns. Since Arithmetic Mean is always greater than or equal to the Harmonic Mean, Chetan’s returns will be greater than or equal to Bikram’s.

3. Hence, option 1.

4. Since Chetan’s return is always higher than or equal to that of Bikram, the trader with the maximum return would be either Abdul or Chetan.
If it is a continuously rising market then Abdul would end up having the highest gain.
But there might be a scenario when the share price of XYZ would go down after 10 AM and rise in the end at 3 PM to a higher value.
In such a case, if Chetan gets the shares at lower prices than what the price was at 10 AM he would end up making more profit and hence higher return.
Here, Abdul’s returns remain unaltered as 100%.
Let Chetan always buy shares worth Rs. 100.
So he would end up buying 1 + 10 + 10 + 10 + 10 = 41 shares.
When he sells the same at Rs. 200 he gets Rs. 8,200 for the same.
Chetan’s profit = 8200 − 500 = 7700
Chetan's return = 7700/500 = 15.4 = 1540%
Hence, option 4.

5. We have seen that Chetan’s return would be higher than or equal to that of Bikram. It would be equal to Bikram’s return in the scenario when the share price remains at a constant value throughout the day.
Hence, option 4.

6. Hence, option 1.

7. x1 > x6 > x5 > x2, x4 < x6 and x1 > x3 > x4
x1, i.e. the share price at 10 am, is the highest.
Hence, option 1.

8. Option 3.

9. Check options. Option 2.

10. The cost function is C(x) = 240 + bx + cx2
C(20) = 240 + 20b + 400c
C(40) = 240 + 40b + 1600c
C(60) = 240 + 60b + 3600c
On solving, c = 1/10, b = 10
Profit for x units is 30x – C(x)
P(x) = 30x – 240 – 10x - x2/10 = –240 + 20x – x2/10
Option 2.

11. Option 4.