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 7 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 7

1.A computer program was tested 300 times before its release. The testing was done in three stages of 100 tests each. The software failed 15 times in Stage I, 12 times in Stage II, 8 times in Stage III, 6 times in both Stage I and Stage II, 7 times in both Stage II and Stage III, 4 times in both Stage I and Stage III, and 4 times in all the three stages. How many times the software failed in a single stage only?

A.10
B.13
C.15
D.17
E.35

2.Suresh, who runs a bakery, uses a conical shaped equipment to write decorative labels (e., Happy Birthday etc.) using cream. The height of this equipment is 7 cm and the diameter of the base is 5 mm. A full charge of the equipment will write 330 words on an average. How many words can be written using three fifth of a litre of cream?

A.45090
B. 45100
C.46000
D.43200
E. None of the above

Answer question nos. 3-4 based on the following information.

The following pie chart shows the percentage distribution of runs scored by a batsman in a test innings.

3.If the batsman has scored a total of 306 runs, how many 4s and 6s did he hit?

A.31 and 3 respectively
B.32 and 2 respectively
C.32 and 3 respectively
D.33 and 1 respectively
E.33 and 2 respectively

4.If 5 of the dot balls had been hit for 4s, and if two of the shots for which the batsman scored 3 runs each had fetched him one run instead, what would have been the central angle of the sector corresponding to the percentage of runs scored in 4s?

A.160
B.163
C.165
D.167
E.170

5.Carpenter Rajesh has a circular piece of plywood of diameter 30 feet. He has cut out two disks of diameter 20 feet and 10 feet. What is the diameter of the largest disk that can be cut out from the remaining portion of the plywood piece?

A.> 8.00 feet and < 8.20 feet
B.> 8.21 feet and < 8.40 feet
C.> 8.41 feet and < 8.60 feet
D.> 8.61 feet and < 8.80 feet
E.> 8.81 feet and < 9.00 feet

6.Lionel and Ronaldo had a discussion on the ages of Jose’s sons.Ronaldo made following statements about Jose’s sons:

1. Jose has three sons
2. The sum of the ages of Jose’s sons is 13
3. The product of the ages of the sons is the same as the age of Lionel
4. Jose’s eldest son, Zizou weighs 32 kilos
5. The sum of the ages of the younger sons of Jose is 4
6. Jose has fathered a twin
7. Jose is not the father of a triplet
8. The LCM of the ages of Jose’s sons is more than the sum of their ages

Which of the following combination gives information sufficient to determine the ages of Jose’s sons?

A. 1, 2, 3, 4
B. 1, 2, 4, 6
C. 1, 2, 3, 5
D. 1, 2, 5, 7
E. 1, 2, 5, 6

7.Ram and Shyam form a partnership (with Shyam as working partner) and start a business by investing M 4000 and M 6000 respectively. The conditions of partnership were as follows:

-In case of profits till M 200,000 per annum, profits would be shared in the ratio of the invested capital.
-Profits from M 200,001 till M 400,000 Shyam would take 20% out of the profit, before the division of remaining profits, which will then be based on ratio of invested capital.
-Profits in excess of M 400,000, Shyam would take 35% out of the profits beyond M 400,000, before the division of remaining profits, which will then be based on ratio of invested capital.

If Shyam’s share in a particular year was M 367000, which option indicates the total business profit (in M) for that year?

A.520,000
B.530,000
C.540,000
D.550,000
E.None of the above

8.A property dealer bought a rectangular piece of land at M 1000/sq. The length of the plot is less than twice its breadth. Due to its size, there were no buyers for the full plot. Hence he decided to sell it in smaller sized pieces as given below.

The largest square from one end was sold at M 1200/sq. ft. From the remaining rectangle the largest square was sold at M 1150/sq. ft.

Due to crash in the property prices, the dealer found it difficult to make profit from the sale of the remaining part of the land. If the ratio of the perimeter of the remaining land to the perimeter of the original land is 3 : 8, at what price (in M) the remaining part of the land is to be sold such that the dealer makes an overall profit of 10%?

A.500/sq. ft.
B. 550/sq. ft.
C.600/sq. ft.
D.650/sq. ft.
E.None of the above.

9.Prof. Mandal walks to the market and comes back in an auto. It takes him 90 min to make the round trip. If he takes an auto both ways it takes him 30 mins. On Sunday, he decides to walk both ways. How long would it take him?

A.100 minutes
B.120 minutes
C.140 minutes
D.150 minutes
E.None of the above

10.At the centre of a city’s  municipal  park  there  is  a  large  circular  pool.  A  fish  is released  in  the   water   at   the   edge   of   the   pool.   The   fish swims north for 300 feet before it hits the edge of the pool. It then turns east and swims for 400 feet   before   it   hits   the   edge   of   the   pool.   It   then   turns   east   and   swims for 400 feet before hitting the edge again. What is the area of the pool?

A.62500 π
B. 125000 π
C.250000 π
D.500000 π
E.Cannot be answered from the given data

Solutions:

1. Option b. A simple Venn diagram should suffice.

2. One charge of the equipment would be 1/3*22/7*0.0625*7 = 11/24 cu.cm. So, 11/24 cu.cm corresponds to 330 words. So, 1000 cu.cm would correspond to 330*1000*24/11 = 720000. So, 3/5th will correspond to 432000. Option e.

3. 43.14/100*306/4 = 76.5*0.4314 = 33

3.92/100*306/6 = 2

Option e.

4. New total score will be 306 + 20 – 4 = 322.

{43.14/100*306 + 20}/322 = 152/322 which will give us 170 degrees. Option e.

5. Option c.

6. Option e.

7. 120000 + 136000 + 0.35x + 0.39x = 367000

111000 = 0.74x

x = 150000

Total profit is 550000. Option d.

8. Option b. Assume the sides as l and b and proceed as given. No formula required. Simple storytelling.

9. w + a = 90, 2a = 30, w = 75 and so, 2w = 150. Option d.

10. Option a. Using the first two parts, we get the diameter as 50 feet.

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You can follow the entire sprint series here: XAT 2017 Sprint Preparation Series by Learningroots