## Quantitative Reasoning Questions and Answers Part-6

Data for Questions 1 to 3 : Five women decided to go shopping to M.G. Road, Bangalore.They arrived at the designated meeting place in the following order: 1. Archana, 2. Chellama, 3. Dhenuka, 4. Helen and 5. Sahnaz.
Each woman spent at least ` 1000. Below are some additional facts about how much they spent during their shopping spree.
i. The woman who spent ` 2234 arrive before the lady who spent ` 1193.
ii. One woman spent ` 1340 and she was not Dhenuka.
iii. One woman spent ` 1378 more than Chellamma.
iv. One woman spent ` 2517 and she was not Archana.
v. Helen spent more than Dhenuka.
vi. Shahnaz spent the largest amount and Chellamma the smallest.

1. The woman who spent ` 1193 is:
a) Archana
b) Chellamma
c) Dhenuka
d) Helen

Explanation: From the given information it is clear that four numbers which must have been the values of money spent would be: 2517 (Clue 4), 2234 (Clue 1), 1340 (Clue 2) and 1193 (Clue 1 again).
We need to work out the fifth value.
Also, since Chellamma spent the least and Shahnaz the maximum and since one woman spent` 1378 more than Chellamma, a little bit of introspection will give you the following possibilities for the five numbers:
Possibility 1: If 1193 is the least value
The five numbers are:
1193, 1340, 2234, 2517 and 2571 (since 2571 = 1193 + 1378)
Possibility 2: If 2517 is the maximum value, the five numbers are:
1139 (since 1139 = 2517 – 1378), 1193, 1340, 2234 and 2517
Accordingly, we have the following possible arrangements for the five women and the amount they spent:

Note: The thought structure for placing the 5 values with 5 women in the case of possibility 1, goes as follows:
Step 1:

After placing the least and maximum
Step 2: 2234 should be before 1193 and Dhenuka cannot have spent ` 1340.

A close look at the above table shows that clue 5 (H > D) is not obeyed by this arrangement. Hence, this solution is wrong.
We thus move into possibility 2, i.e.:
1139, 1193, 1340, 2234, 2517, are the five values. The thought structure for placing the five numbers for the five women goes as:
Step 1: Place the maximum and least values for G and C respectively.

This leaves us with 1340, 1193 and 2234 to place.
Step 2: We need to keep 2 constraints in mind while doing this.
(a) 2234 has to come before 1193 (remember not immediately before). At the same time H > D. (Clue 5)
We can arrange 2234 before 1193 in 3 ways as shown below and then 1340 automatically falls into the vacant space.

The answer is Dhenuka. Option (c) is correct

2. What was the amount spent by Helen?
a) ` 1193
b) ` 1340
c) ` 2234
d) ` 2517

Explanation: 1340. Option (b) is correct (Refer explanation of Question 1)

3. Which of the following amounts was spent by one of them?
a) ` 1139
b) ` 1378
c) ` 2571
d) ` 2718

Explanation: 1139. Option (a) is correct (Refer explanation of Question 1)

4. Three travellers are sitting around a fire, and are about to eat a meal. One of them has five small loaves of bread, the second has three small loaves of bread. The third has no food, but has eight coins. He offers to pay for some bread. They agree to share the eight loaves equally among the three travellers, and the third traveller will pay eight coins for his share of the eight loaves. All loaves were of the same size. The second traveller (who had three loaves) suggests that he be paid three coins, and that the first traveller be paid five coins. The first traveller says that he should get more than five coins. How much the first traveler should get?
a) 5
b) 7
c) 1
d) None of these

Explanation: Each loaf of bread is divided into 3 parts. So we have 24 parts and each traveller gets 8 parts.
Ist traveller has 15 parts. He ate 8 parts and gave his 7 parts to the IIIrd traveller.
IInd traveller has 9 parts. He ate 8 parts and gave his1 part to the IIIrd traveller.
So 8 coins should be divided in the ratio 7: 1.
First traveller gets 7 coins.
Option (b) is correct

5. My bag can carry no more than ten books. I must carry at least one book each of management, mathematics, physics and fiction. Also, for every management book I carry I must carry two or more fiction books, and for every mathematics book I carry I must carry two or more physics books. I earn 4, 3, 2, and 1 points for each management, mathematics, physics and fiction book, respectively, I carry in my bag. I want to maximise the points I can earn by carrying the most appropriate combination of books in my bag.
The maximum points that I can earn are:
a) 20
b) 21
c) 22
d) 23

Explanation: Maximum points of 22 can be achieved by taking (1 Management + 2 Fiction + 2 Maths + 5 Physics) books.
4 + 2 + 6 + 10 = 22
Option (c) is correct

6. Eighty kilograms (kg) of store material is to be transported to a location 10 km away. Any number of couriers can be used to transport the material. The material can be packed in any number units of 10, 20 or 40 kg. Courier charges are ` 10 per hour. Couriers travel at the speed of 10 km/hr if they are not carrying any load, at 5 km/hr if carrying 10 kg, at 2 km/hr if carrying 20 kg and at 1 km/hr if carrying 40 kg. A courier cannot carry more than 40 kg of load.
The minimum cost at which 80 kg of store material can be transported to its destination will be:
a) ` 180
b) ` 160
c) ` 140
d) ` 120

Explanation: 160. Option (b) is correct

Data for Questions 7 & 8 : Elle is three times older than Yogesh; Zaheer is half the age of Wahida. Yogesh is older than Zaheer.

7. Which of the following can be inferred?
a) Yogesh is older than Wahida.
b) Elle is older than Wahida.
c) Elle may be younger than Wahida.
d) None of these

Explanation:

From the above table we can infer that Elle must be older than Wahida (as she is thrice a higher value (y) while Wahida’s age is twice a lower value (z)).
Option (b) is correct.

8. Which of the following information will be sufficient to estimate Elle’s age?
a) Zaheer is 10 years old.
b) Both Yogesh and Wahida are older than Zaheer by the same number of years.
c) Both 1 and 2 above.
d) None of these

Explanation: Using both pieces of information we get that if Zaheer = 10, then Wahida and Yogesh = 20 and hence Elle = 60 years
Option (c) is correct (Refer explanation of Question 7)

9. On the walk through the park, Hamsa collected 50 coloured leaves, all either maple or oak. She sorted them by category when she got home, and found the following:
(i) The number of red oak leaves with spots is even and positive.
(ii) The number of red oak leaves without any spot equals the number of red maple leaves without spots.
(iii) All non-red oak leaves have spots, and there are five times as many of them as there are red spotted oak leaves.
(iv) There are no spotted maple leaves that are not red.
(v) There are exactly 6 red spotted maple leaves.
(vi) There are exactly 22 maple leaves that are neither spotted nor red.
How many oak leaves did she collect?
a) 22
b) 17
c) 25
d) 18

Explanation: The answer is 17. Option (b) is correct

10. I have a total of ` 1000. Item A costs ` 110, item B costs ` 90, item C costs ` 70, item D costs ` 40 and item E costs ` 45. For every item D that I purchase, I must also buy only two items of B. For every item A, I must buy one item of C. For every item, E, I must also buy two of item D and one of item B. For every item purchased I earn 1000 points and for every rupee not spent I earn a penalty of 1500 points. My objective is to maximise the points earned. What is the number of items that I must purchase to maximise my points?
a) 13
b) 14
c) 15
d) 16