This is the final set under the CAT 2016 Sprint Preparation Series – LRDI 5. During these last 5 days, we covered around 300 questions that we expect to come across in CAT 2016. The answers to LRDI Sprint CAT 2016 – Day 5 will be posted at the end of the day and will include the solution, possible traps and things to keep in mind come similar question types in CAT 2016. You may go through the entire series here: CAT 2016 Sprint Preparation Series by Learningroots
CAT 2016 Sprint Preparation Series – LRDI 5
Set 1
Table A below provides data about ages of children in a school. For the age given in the first column, the second column gives the number of children not exceeding the age. For example, first entry indicates that there are 9 children aged 4 years or less. Tables B and C provide data on the heights and weights respectively of the same group of children in a similar format. Assuming that an older child is always taller and weighs more than a younger child, answer the following questions.
1. What is the number of children of age 9 years of less whose height does not exceed 135 cm?
a. 48
b. 45
c. 3
d. Cannot be determined
2. How many children of age more than 10 years are taller than 150 cm and do not weigh more than 48 kg?
a. 16
b. 40
c. 9
d. Cannot be determined
3. Among the children older than 6 years but not exceeding 12 years, how many weigh more than 38 kg.?
a. 34
b. 52
c. 44
d. Cannot be determined
Set 2
Rang Barsey Paint Company (RBPC) is in the business of manufacturing paints. RBPC buys RED, YELLOW, WHITE, ORANGE, and PINK paints. ORANGE paint can be also produced by mixing RED and YELLOW paints in equal proportions. Similarly, PINK paint can also be produced by mixing equal amounts of RED and WHITE paints. Among other paints, RBPC sells CREAM paint, (formed by mixing WHITE and YELLOW in the ratio 70:30) AVOCADO paint (formed by mixing equal amounts of ORANGE and PINK paint) and WASHEDORANGE paint (formed by mixing equal amounts of ORANGE and WHITE paint). The following table provides the price at which RBPC buys paints.
4. The cheapest way to manufacture AVOCADO paint would cost
a. Rs. 19.50 per litre.
b. Rs. 19.75 per litre
c. Rs. 20.00 per litre.
d. Rs. 20.25 per litre.
5. WASHEDORANGE can be manufactured by mixing
a. CREAM and RED in the ratio 14:10.
b. CREAM and RED in the ratio 3:1.
c. YELLOW and PINK in the ratio 1:1.
d. RED, YELLOW, and WHITE in the ratio 1:1:2.
6. Assume that AVOCADO, CREAM and WASHEDORANGE each sells for the same price. Which of the three is the most profitable to manufacture?
a. AVOCADO
b. CREAM
c. WASHEDORANGE
d. Sufficient data is not available.
Set 3
Five friends meet every morning at Sree Sagar restaurant for an idli-vada breakfast. Each consumes a different number of idlis and vadas. The number of idlis consumed are 1, 4, 5, 6, and 8, while the number of vadas consumed are 0, 1, 2, 4, and 6. Below are some more facts about who eats what and how much.
i. The number of vadas eaten by Ignesh is three times the number of vadas consumed by the person who eats four idlis.
ii. Three persons, including the one who eats four vadas eat without chutney.
iii. Sandeep does not take any chutney.
iv. The one who eats one idli a day does not eat any vadas or chutney. Further, he is not Mukesh.
v. Daljit eats idli with chutney and also eats vada.
vi. Mukesh, who does not take chutney, eats half as many vadas as the person who eats twice as many idlis as he does.
vii. Bimal eats two more idlis than Ignesh, but Ignesh eats two more vadas than Bimal.
7. Which one of the following statements is true?
a. Daljit eats 5 idlis
b. Ignesh eats 8 idlis
c. Bimal eats 1 idli.
d. Bimal eats 6 idlis.
8. Which of the following statements is true?
a. Sandeep eats 2 vadas.
b. Mukesh eats 4 vadas.
c. Ignesh eats 6 vadas.
d. Bimal eats 2 vadas.
9. Which of the following statements is true?
a. Mukesh eats 8 idlis and 4 vadas but no chutney.
b. The person who eats 5 idlis and 1 vada does not take chutney.
c. The person who eats equal number of vadas and idlis also takes chutney.
d. The person who eats 4 idlis and 2 vadas also takes chutney.
Set 4
Venkat, a stockbroker, invested a part of his money in the stock of four companies — A, B, C and D. Each of these companies belonged to different industries, viz., Cement, Information Technology (IT), Auto, and Steel, in no particular order. At the time of investment, the price of each stock was Rs. 100. Venkat purchased only one stock of each of these companies. He was expecting returns of 20%, 10%, 30% and 40% from the stock of companies A, B, C and D, respectively. Returns are defined as the change in the value of the stock after one year, expressed as a percentage of the initial value. During the year, two of these companies announced extraordinarily good results. One of these two companies belonged to the Cement or the IT industry, while the other one belonged to either the Steel or the Auto industry. As a result, the returns on the stocks of these two companies were higher than the initially expected returns. For the company belonging to the Cement or the IT industry with extraordinarily good results, the returns were twice that of the initially expected returns. For the company belonging to the Steel or the Auto industry, the returns on announcement of extraordinarily good results were only one and a half times that of the initially expected returns. For the remaining two companies which did not announce extraordinarily good results, the returns realized during the year were the same as initially expected.
10. What is the minimum average return Venkat would have earned during the year?
a. 30%
b. 31.25 %
c. 32.5 %
d. Cannot be determined
11. 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.
a. I and II only
b. II and III only
c. III and IV only
d. II and IV only
12. 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.
a. I and II only
b. II and III only
c. I and IV only
d. II and IV only
13. 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.
a. I and II only
b. II and IV only
c. II and III only
d. III and IV only
Set 5
Two traders, Chetan and Michael, were involved in the buying and selling of MCS shares over five trading days. At the beginning of the first day, the MCS share was priced at Rs 100, while at the end of the fifth day it was priced at Rs 110. At the end of each day, the MCS share price either went up by Rs 10, or else, it came down by Rs 10. Both Chetan and Michael took buying and selling decisions at the end of each trading day. The beginning price of MCS share on a given day was the same as the ending price of the previous day. Chetan and Michael started with the same number of shares and amount of cash, and had enough of both. Below are some additional facts about how Chetan and Michael traded over the five trading days.
I. Each day if the price went up, Chetan sold 10 shares of MCS at the closing price. On the other hand, each day if the price went down, he bought 10 shares at the closing price.
II. If on any day, the closing price was above Rs 110, then Michael sold 10 shares of MCS, while if it was below Rs 90, he bought 10 shares, all at the closing price.
14. 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?
a. Rs 90
b. Rs 100
c. Rs 110
d. Rs 120
e. Rs 130
15. 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?
a. Rs 90
b. Rs 100
c. Rs 110
d. Rs 120
e. Not uniquely determinable
16. 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?
a. Rs 90
b. Rs 100
c. Rs 110
d. Rs 120
e. Rs 130
Solutions
Set 1
1. This is pretty easy if you have understood what is given to you. It is a cumulative table wherein, each row contains its unique elements in addition to the total number of elements above it. If things seem too difficult, it is always better to give ranks and then look for the overlap.
We can see that ranks 1 to 48 are less than or equal to 9 years. Also, ranks 1 to 45 are shorter than or equal to 135 cm. This case is easy but if you get an intermediate range (something that doesn’t start from 1 or doesn’t end on 100), you have to go for the highest value of the lower limit and the lowest value of the upper limit. So, in this case, it will be from 1 to 45.
Option b.
2. Rank 61 to 100 are of age more than 10 years, ranks 76 to 100 are taller than 150 cm and ranks 1 to 91 weigh less than or equal to 48 kg. Now, we can use the overlap rule that I had stated in the earlier case. Highest value of the minima is 76 and lowest value of the maxima is 91. So, total of 16 students. Option a. Looks easier now?
3. Children older than 6 years and less than or equal to 12 years will be ranked from 23 to 77. Ranks 34 to 100 weight more than 38 kg. So, using the overlap rule, we can say that ranks 34 to 77 will satisfy both the criteria. Total of 44 students.
Option c.
Set 2
4. This set is more of trial and error than anything else.
Avocado can be made by mixing orange and white paint. So, the ways in which we can make avocado are:
i. 0.5 * Orange + 0.5 * pink (11 + 9 = 20)
ii. 0.25 * Red + 0.25 * yellow + 0.5 * pink (5 + 6.25 + 9 = 20.25)
iii. 0.5 * Orange + 0.25 * red + 0.25 * white (11 + 5 + 3.75 = 19.75)
iv. 0.25 * Red + 0.25 * yellow + 0.25 * red + 0.25 * white (5 + 6.25 + 5 + 3.75 = 20)
Option b.
5. Washedorange is either 0.5 * orange + 0.5 * white or 0.25 * red + 0.25 * yellow + 0.5 * white. So, option d.
6. As we have seen, avocado can be manufactures at 19.75 per liter. To manufacture cream, it could cost us (10.5 + 7.5 = 18 per liter). Washedorange would cost us (11 + 7.5 = 18.5) or (5 + 6.25 + 7.5 = 18.75). So, cream is the cheapest. Option b.
Set 3
7. The finished table would look like this:
Option a.
8. Option c.
9. Option c.
Set 4
10. This question can be solved without making any table. For the return to be minimum, the companies that would have got extraordinarily good results would be the ones that were supposed to grow by 10% and 20%. So, the growth would be 20% and 30% respectively. The other two rates would remain the same and so, would grow by 30% and 40%. Total growth would be by 120% which would give us an average of 30%.
11. To get a 35% average growth, he should have 140% growth overall. This is possible only when 20% (A – Steel/Auto) increases to one and a half times and 30% (C – Cement/IT) increases to twice OR when 20% (A – Cement/IT) increases to twice and 40% (D – Steel/Auto) increases to one and a half times.
Option d.
12. Average of 38.75% would mean 155% growth overall. This is possible only if 30% (C – Steel/Auto) increases to one and a half times and 40% (D – Cement/IT) increases to twice. Option c.
13. C (30%) belonged to Cement/IT industry and announced extraordinarily good results so, it became 60%. So, the other company that belonged to Steel/Auto would have increased to one and a half times. So, the highest possible earning could be 150% which would be 37.5% on an average. The least earning would be 135% which would be 33.75% on an average. Option b.
Set 5
14. These are the only cases that are possible:
The only case valid for the first question is:
Option c.
15. The four marked scenarios are the only ones possible:
Option b.
16. Only scenario 3 follows the given condition.
Option a.
Hope that the series added a few meters to your final mile. All the best for CAT 2016 and thanks for all the support! 😀
