After successfully completing the CAT 2016 sprint series and the SNAP 2016 sprint series, we are back with the XAT 2017 sprint preparation series – Quant 6 to boost your prep. This series will consist of 10 sets of questions from past year XAT papers, leading to XAT 2017 and covered almost all the question types that you needed to know come the 8th of January.
XAT 2017 sprint preparation series – Quant 6
1.Nikhil’s mother asks him to buy 100 pieces of sweets worth 100/-. The sweet shop has 3 kinds of sweets, kajubarfi, gulabjamun and sandesh. Kajubarfi costs Rs. 10/- per piece, gulabjamun costs Rs. 3/- per piece and sandesh costs 50 paise per piece. If Nikhil decides to buy at least one sweet of each type, how many gulabjamuns should he buy?
A.1
B.2
C.3
D.4
E.5
2.A potter asked his two sons to sell some pots in the market. The amount received for each pot was same as the number of pots sold. The two brothers spent the entire amount on some packets of potato chips and one packet of banana chips. One brother had the packet of banana chips along with some packets of potato chips, while the other brother just had potato chips. Each packet of potato chips costs Rs. 10/- and the packet of banana chips costs less than Rs. 10/-. The packets of chips were divided between the two brothers so each brother received equal number of packets.
How much money should one brother give to the other to make the division financially equitable?
A.1
B.2
C.4
D.5
E.7
3.A city has a park shaped as a right angled triangle. The length of the longest side of this park is 80 m. The Mayor of the city wants to construct three paths from the corner point opposite to the longest side such that these three paths divide the longest side into four equal segments. Determine the sum of the squares of the lengths of the three paths.
A.4000 m
B.4800 m
C.5600 m
D.6400 m
E.7200 m
Answer question nos. 4- 5 based on the following information.
Ramya, based in Shanpur, took her car for a 400 km trip to Rampur. She maintained a log of the odometer readings and the amount of petrol she purchased at different petrol pumps at different prices (given below). Her car already had 10 litres of petrol at the start of the journey, and she first purchased petrol at the start of the journey, as given in table below, and she had 5 litres remaining at the end of the journey.
| Odometer Reading (Km) | Petrol Purchased (Litre) | Rate of Petrol (M/Litre) | |
| Start of Journey | 400 | 20 | 30 |
| 600 | 15 | 35 | |
| 650 | 10 | 40 | |
| End of Journey | 800 |
4.What has been the mileage (in kilometers per litre) of her car over the entire trip?
A.8.00
B.8.50
C.9.00
D.9.50
E.None of the above
5.Her car’s tank-capacity is 35 Petrol costs Rs. 45/- litre in Rampur. What is the minimum amount of money she would need for purchasing petrol for the return trip from Rampur to Shanpur, using the same route? Assume that the mileage of the car remains unchanged throughout the route, and she did not use her car to travel around in Rampur.
A.1714
B.1724
C.1734
D.1744
E.Data insufficient to answer.
6.A medical practitioner has created different potencies of a commonly used medicine by dissolving tables in water and using the resultant solution
Potency 1 solution: When 1 tablet is dissolved in 50 ml, the entire 50 ml is equivalent to one dose.
Potency 2 solution: When 2 tablets are dissolved in 50 ml, the entire 50 ml of this solution is equivalent to 2 doses, … and so on.
This way he can give fractions of tablets based on the intensity of infection and the age of the patient.
For particular patient, he administers 10 ml of potency 1, 15 ml of potency 2 and 30 ml of potency 4. The dosage administered to the patient is equivalent to
A.> 2 and < 3 tablets
B. > 3 and < 3.25 tablets
C. > 3.25 and < 3.5 tablets
D.> 3.5 and < 3.75 tablets
E. > 3.75 and < 4 tablets
7.Ram prepares solutions of alcohol in water according to customers’ This morning Ram has prepared 27 litres of a 12% alcohol solution and kept it ready in a 27 litre delivery container to be shipped to the customer. Just before delivery, he finds out that the customer had asked for 27 litres of 21% alcohol solution. To prepare what the customer wants, Ram replaces a portion of 12% solution by 39% solution. How many litres of 12% solution are replaced?
A.5
B. 9
C.10
D.2
E.15
8.City Bus Corporation runs two buses from terminus A to terminus B, each bus making 5 round trips in a day. There are no stops in between A and B. These buses ply back and forth on the same route at different but uniform speeds. Each morning the buses start at 7 AM from the respective terminuses. They meet for the first time at a distance of 7 km from terminus A. Their next meeting is at a distance of 4 km from terminus B, while travelling in opposite directions. Assuming that the time taken by the buses at the terminuses is negligibly small, and the cost of running a bus is M 20 per km, find the daily cost of running the buses (in M ).
A.3200
B.4000
C.6400
D.6800
E.None of the above
9.Shyam, a fertilizer salesman, sells directly to farmers. He visits two villages A and B. Shyam starts from A, and travels 50 meters to the East, then 50 meters North-East at exactly 45° to his earlier direction, and then another 50 meters East to reach village B. If the shortest distance between villages A and B is in the form of
meters, find the value of a + b + c
A.52
B.4
C.58
D.59
E.None of the above
10.Three truck drivers, Amar, Akbar and Anthony stop at a road side eating Amar orders 10 rotis, 4 plates of tadka, and a cup of tea. Akbar orders 7 rotis, 3 plates of tadka, and a cup of tea. Amar pays M 80 for the meal and Akbar pays M 60. Meanwhile, Anthony orders 5 rotis, 5 plates of tadka and 5 cups of tea. How much (in rupees) will Anthony pay?
A.75
B. 80
C.95
D.100
E. None of the above.
Solutions:
1. k + g + s = 100
10k + 3g + 0.5s = 100
20k + 6g + s = 200
k, g, s >= 1
19k + 5g = 100
k can be equal to 5 only and so, we get g = 1. Option a.
2. Let amount of each pot be x. So, total amount spent is x^2.
If there are say 2a packets of potato chips, the second brother will get a + 0.5 packets and the first brother will get a – 0.5 packets of potato chips.
The money with the second brother is 10a + 5.
The money with the first brother will be 10a – 5 + b where b is an integer less than 10.
Total money will be 20a + b
Now, 20a + b has to be in the form of x^2
Also, 2a has to be an odd number as otherwise, we will not be able to distribute the packets equally. So,
So, a = 0.5 and b = 6 or a = 1.5 and b = 6 or a = 9.5, b = 6 and so on. So, the value of b is 6. So, the money with the first brother is 10a + 5 and that with the second brother is 10a + 1. So, the first brother will have to give 2 Rs. to the second brother. Option b.
3. Option c. Use Apollonius’ theorem and you should be done.
4. 400 km on 50 liters. Option a.
5. 150 km with 5 liters already present at the rate of 8 kmpl. So, 13.75 liters fresh petrol required at Rampur. Next, 50 km to be traveled at the rate of 8 kmpl at Rs. 40 per liter. So, Rs. 250 spent. And finally, to cover 200 km, she would need to spend another Rs. 875. Total of 1743.75. Option d.
6. For potency 1, 50 ml has 1 tablet. So, 10 ml will have 1/5 tablet. For potency 2, 50 ml has 2 tablets. So, 15 ml will have 3/5 tablets. For potency 4, 50 ml has 4 tablets. So, 30 ml will have 12/5. Total of 16/5 or 3.2 tablets. Option b.
7. Option b.
8. Let the distance between terminal A & terminal B be x km.
Bus 1 covers 7 km and Bus 2 covers (x – 7) km at first meet.
Bus 1 and Bus 2 cover a total distance of x before first meet and a total distance of 2x between the first meeting point and the second meeting point.
Bus 1 covers a distance of 14 km between 1st and 2nd meet
Distance covered by bus 1 before 2nd meet = 7 + 14 = 21 km.
But distance covered by bus 1 = x + 4 and so, x = 17 km
Total distance covered by the buses = 34 × 5 × 2 = 340 km. Option d.
9. Option e.
10. 10a + 4b + c = 80
7a + 3b + c = 60
5a + 5b + 5c = ?
3a + b = 20. So, (6, 2) or (5, 5) or (4, 8) or (3, 11) and so on… in any case, a + b + c will be 20 and so, the answer is option d.
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You can follow the entire sprint series here: XAT 2017 Sprint Preparation Series by Learningroots
