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 8 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 8
1.Mr. Mehra is planning for higher education expenses of his two sons aged 15 and 12. He plans to divide Rs 15 lakhs in two equal parts and invest in two different plans such that his sons may have access to Rs. 21 lakhs each when they reach the age of 21. He is looking for plan that will give him a simple interest per annum. The rates of interest of the plans for his younger son and elder son should be
A.5% and 5% respectively
B. 8% and 12% respectively
C.10% and 15% respectively
D.15% and 22.5% respectively
E.20% and 30% respectively
2.Albela, Bob and Chulbul have to read a document of seventy eight pages and make a presentation next day. They realize that the article is difficult to understand and they would require team work to finish the assignment. Albela can read a page in 2 minutes, Bob in 3 minutes, and Chulbul in 4 minutes. If they divide the article into 3 parts so that all three of them spend the equal amount of time on the article, the number of pages that Bob should read is
A. 24
B. 25
C. 26
D. 27
E. 28
3. The taxis plying in Wasseypur have the following fare structure: Rs. 20 for the first two kilometers, Rs. 5 for every km in excess of 2 km and up to 10 km, and Rs. 8 for every km in excess of 10 km. Bullock carts on the other hand charge Rs. 2 per km. Sardar Khan takes a taxi from the Wasseypur railway station to his home. On the way, at a distance of 14 km from the railway station, he meets Faizal Khan, and gets down from the taxi to talk to him. Later he takes a bullock cart to reach his home. He spends a total of Rs. 102 to reach his home from the railway station. How far is his home from the railways station?
A. 17
B. 18
C. 19
D. 20
E. 21
4.The mean of six positive integers is 15. The median is 18, and the only mode of the integers is less than 18. The maximum possible value of the largest of the six integers is
A.26
B.28
C.30
D.32
E.34
5.Ramesh bought a total of 6 fruits (apples and oranges) from the market. He found that he required one orange less to extract the same quantity of juice as extracted from apples. If Ramesh had used the same number of apples and oranges to make the blend, then which of the following correctly represents the percentage of apple juice in the blend?
A.25%
B.33.3%
C.60%
D.60.6%
E.None of the above
6. Sara has just joined Facebook.She has 5 friends. Each of her five friends have twenty five friends. It is found that at least two of Sara’s friends are connected with each other. On her birthday, Sara decides to invite her friends and the friends of her friends. How many people did she invite for her birthday party?
A.> 105
B.> 100 and < 125
C.< 123
D.> 105 and < 123
E.< 125
7. 70% of the students who joined XLRI last year play football, 75% play cricket, 80% play basketball and 85% play carom.The minimum percentage of students who play all four games is
A.5%
B.10%
C.15%
D..20%
E.None of the above
8.p and q are positive numbers such that pq = qp , and q = 9p. The value of p is
A. Root of 9
B. 6th root of 9
C. 9th root of 9
D. 8th root of 9
E. 3rd root of 9
9.Ram, Shyam and Hari went out for a 100 km journey. Ram and Hari started the journey in Ram’s car at the rate of 25 kmph, while Shyam walked at 5 kmph. After sometime. Hari got off and started walking at the rate of 5 kmph and Ram went back to pick up Shyam. All three reached the destination simultaneously. The number of hours required for the trip was:
A.8
B.7
C.6
D.5
E.4
10.The central park of the city is 40 metres long and 30 meters wide. The mayor wants to construct two roads of equal width in the park such that the roads intersect each other at right angles and the diagonals of the park are also the diagonals of the small rectangle formed at the intersection of the two roads. Further, the mayor wants that the area of the two roads to be equal to the remaining area of the park. What should be the width of the roads?
A.10 metres
B.12.5 metres
C.14 metres
D.15 metres
E.16 metres
Solutions:
1. Option e.
2. Let the time taken be x minutes by each of them. They read x/2, x/3 and x/4 pages respectively. So, x = 72 and so, option a is correct.
3. Option c.
4. Sum of the 6 integers is 90. Median is 18 and so, we can have the middle two values as 18. a, b, 18, 18, e, f and f has to be maximized. Only mode is less than 18 and so, a, b can be equal to 1 each with the middle values being 17 and 19. So, e+f will be 52 and e will be 20 at minimum. So, maximum value of f will be 32. Option d.
5. He used 3 apples and 3 oranges. But, juice from 3 apples equals juice from 2 oranges. So, juice from 3 oranges equals juice from 4.5 apples. So, 3/7.5 = 40%. Option e.
6. Best case (for Sara i.e.) will be when all her friends are friends with each other. So, total of 105 invitations have to go out. Worst case, if there are just 2 of her friends who are friends with each other, she will need to send 5+2*23+3*24=123 invitations. Option d.
7. Option b. Check this link to understand maxima-minima questions.
8. plogq = qlogp
logq = log9 + logp
plog9 + plogp = 9plogp
(9p)^p = (p)^9p
9p = p^9
Option d.
9. A typical question based on an easy concept. Shyam and Hari will have to walk the same distance for them to reach together. Let this distance be x. So, Hari covered x km in the same time as Ram covered (100 – x)+(100 – 2x) = 200 – 3x. So,
(200 – 3x)/x = 25/5
x = 25 km. So, total time taken was 25/5+75/25 = 8 hours. Option a.
10. Let the width of the roads be x. So, area of the roads will be 40x + 30x – x^2. As this is equal to 600, we get:
x^2 – 70x + 600 = 0
x = 10. Option a.
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You can follow the entire sprint series here: XAT 2017 Sprint Preparation Series by Learningroots
