**XLRI Entrance Test XAT 2017 **

**Data Interpretation and Quantitative Ability**

1. The sum of series, (−100) + (−95) + (−95) + ….. + 110 + 115 + 120, is :

(A) 0

(B) 220

(C) 340

(D) 450

(E) None of the above

2. AB is a chord of a circle. The length of AB is 24 cm. P is the midpoint of AB. Perpendiculars from P on either side of the chord meets the circle at M and N respectively. If PM < PN and PM = 8 cm, then what will be the length of PN?

(A) 17 cm

(B) 18 cm

(C) 19 cm

(D) 20 cm

(E) 21 cm

3. If x and y are real numbers, the least possible value of the expression 4(x – 2)^{2} + 4(y – 3)^{2} – 2(x – 3)^{2} is :

(A) –8

(B) –4

(C) –2

(D) 0

(E) 2

4. Four two-way pipes A, B, C, and D can either fill an empty tank or drain the full tank in 4, 10, 12 and 20 minutes respectively. All four pipes were opened simultaneously when the tank is empty. Under which of the following conditions the tank would be half filled after 30 minutes?

(A) Pipe A filled and pipes B, C and D drained

(B) Pipe A drained and pipes B, C and D filled

(C) Pipes A and D drained and pipes B and C filled

(D) Pipes A and D filed and pipes B and C drained

(E) None of the above

5. A shop, which sold same market price shirts, announced on offer-if one buys three shirts then the fourth shirt is sold at a discounted price of Rs 100 only, Patel took the offer. He left the shop with 20 shirts after paying Rs 20,000. What is the marked price of a shirt ?

(A) Rs 1260

(B) Rs 1300

(C) Rs 1350

(D) Rs 1400

(E) Rs 1500

6. The volume of a pyramid with a square base is 200 cm^{3}. The height of pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?

(A) 12 cm

(B) 13 cm

(C) 14 cm

(D) 15 cm

(E) 16 cm

7. A dice is rolled twice. What is the probability that the number in the second roll will be higher than that in the first?

(A) 5/36

(B) 8/36

(C) 15/36

(D) 21/36

(E) None of the above

8. If f(x) = ax + b, a and b are positive real numbers and if

f(__f(x)__) = 9x + 8,

then the value of a + b is

(A) 3

(B) 4

(C) 5

(D) 6

(E) None of the above

9. Arup and Swarup leave point A at 8 AM to point B. To reach B, they have to walk the first 2 km, then travel 4 km by boat and complete the final 20 km by car. Arup and Swarup walk at a constant speed of 4 km/hr and 5 k m/hr respectively. Each rows his boat for 30 minutes. Arup drives his car at a constant speed of 50 km/hr while Swarup drives at 40 km/hr while Swarup drives at 40 km/hr. If no time is wasted in transit, when will they meet again

(A) At 9.15 AM

(B) At 9.18 AM

(C) At 9.21 AM

(D) At 9.24 AM

(E) At 9.30 AM

10. Hari’s family consisted of his younger brother (Chari), younger sister (Gouri) and their father and mother. When Chari was born, the sum of ages of Hari, his father and mother was 70 years. The sum of the ages of four family members, at the time of Gouri’s birth, was twice the sum of the ages of Hari’s father and mother at the time of Hari’s birth. If Chari is 4 years older than Gouri, then find the difference in age between Hari and Chari.

(A) 5 years

(B) 6 years

(C) 7 years

(D) 8 years

(E) 9 years

11. In a True/False quiz, 4 marks are awarded for each correct answer and 1 mark is deducted for each wrong answer. Amit, Benn and Chitra answered the same 10 questions, and their answer are given below in the same sequential order.

AMIT T T __F__ __F__ T T __F__ T T __F__

BENN T T T __F__ __F__ T __F__ T T __F__

CHITRA T T T T __F__ __F__ T __F__ T T

If Amit and Benn both score 35 marks each then Chitra’s score will be:

(A) 10

(B) 15

(C) 20

(D) 25

(E) None of the above

12. In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. Six students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average marks scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average marks in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?

(A) 30

(B) 25

(C) 20

(D) 15

(E) None of the above

13. If 5° ≤ x° ≤ 15°, then the value of sin 30° + cos x° − sin x° will be :

(A) Between –1 and – 0.5 inclusive

(B) Between –0.5 and 0 inclusive

(C) Between 0 and 0.5 exclusive

(D) Between 0.5 and 1 inclusive

(E) None of the above

14. If N = (11^{p +7})(7^{q – 2 }) (5^{r + 1}) (3^{s}) is a perfect cube, where p, q, r and s are positive integers, then the smallest value of p + q + r + s is:

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9

15. An institute has 5 departments and each department has 50 students. If students are picked up randomly from all 5 departments to form a committee, what should be the minimum number of students in the committee so that at least one department should have representation of minimum 5 students?

(A) 11

(B) 15

(C) 21

(D) 41

(E) None of the above

16. AB, CD and EF are three parallel lines, in that order. Let d_{1} and d_{2} be the distances from CD to AB and EF respectively. d_{1} and d_{2} are integers, where d_{1} : d_{2} = 2 : 1. P is a point on AB, Q and S are points on CD and R is a point on EF. If the area of the quadrilateral PQRS is 30 square units, what is the value of QR when value of SR is the least?

(A) slightly less than 10 units

(B) 10 units

(C) slightly greater than 10 units

(D) slightly less than 20 units

(E) slightly greater than 20 units

17. ABCD is a rectangle. P, Q and R are the midpoint of BC, CD and DA. The point S lies on e the line QR in such a way that SR : QS = 1 : 3. The ratio of the triangle APS and rectangle ABCD is

(A) 36/128

(B) 39/128

(C) 44/128

(D) 48/128

(E) 64/128

**Directions (Q. 18 & 19) : Study the data given in the caselet below and answer these questions :**

** **In an innings of a T20 cricket match (a team an bowl for 20 overs) 6 bowlers bowled allowed maximum of 4 overs. Only the three specialist bowelers bowled their full quota of 4 overs each, and the remaining 8 overs were shared among three non-specialist bowlers. The economy rates of four bowlers were 6, 6, 7 and 9 respectively. (*Economy rate is the total number of runs conceded by a bowler divided by the number of overs bowled by that bowler). *This, however, does not include the data of the best bowler (*lowest economy rate) *and the worst bowler (*highest economy rate*). The number of overs bowled and the economy rate of any bowler are in integers.

18. Read the two statements below:

S1 : The worst bowler did not bowl the minimum number of overs.

S2 : The best bowler is a specialist bowler.

Which of the above statements or their combinations above statements or their combinations can help arrive at the minimum number of overs bowled by a non-specialist bowler?

(A) S1only.

(B) S2 only.

(C) .Either S1 or S2.

(D) S1 and S2 in combination

(E) The minimum number of overs can be determined without using S1 or S2.

19. Read the two statements below:

S1. The economy rates of the specialist bowlers are lower than that of the non-specialist bowlers.

S2. The cumulative runs conceded by the three non-specialist bowlers were 1 more than those conceded by the three specialist bowlers.

Which of the above statements or their combinations can help arrive at the economy rate of the worst bowler?

(A) S1 only.

(B) S2 only.

(C) Either S1 or S2.

(D) S1 and S2 in combination.

(E) The economy rate can be calculated without using S1 or S2.

**Directions (Qs. 20 to 23) : Analyze the graph below and answer these questions :**

The grid below captures relationships among seven personality dimensions: “extraversion”, ‘true_arousal_plac”, “true_arousal_caff”, “arousal_plac”, “arousal_caff”, “performance_plac”, and “performance_caff”. The diagonal represents histograms of the seven dimensions. Left of the diagonal represents scatterplots between the dimensions while the right of the diagonal represents quantitative relationships between the dimensions. The lines in the scatterplots are closest approximation of the points. The value of the relationships to the right of the diagonal can vary from – 1 to +1, with –1 being the extreme linear negative relation and +1 extreme linear positive relation. (Axes of the graph are conventionally drawn).

20. Which of the following is true?

(A) “Extraversion” has two modes.

(B) Median for “arousal_plac” is definitely the same as its average.

(C) Median for “arousal_caff” is definitely higher than its average.

(D) Median for “performance_plac” is definitely lower than its average.

(E) Median for “performance_caff’ is definitely lower than its average.

21. Which of the scatterplots shows the weakest relationships?

(A) Between “extraversion” and “peroformance_caff”.

(B) Between “true_arousal_plac” and “arousal_plac”.

(C) Between “true_arousal_plac” and “performance_plac”.

(D) Between “true_arosual_caff” and “performance_caff’.

(E) Between “arousal_caff” and “performance_caff”.

22. In which of the following scatterplots, the value of one dimension can be used to predict the value of another, as accurately as possible?

(A) “extraversion” and “true_arousal_caff”

(B) “true_arousal_plac” and “arousal_plac”

(C) “true_arousal_plac” and “performance_plac”

(D) “true_arousal_plac” and “performance_caff”

(E) All the above are irrelevant relations.

23. Which of the following options is correct?

(A) 0.93 on the right side of the scatterplot in the fourth row.

(B) 0.94 on the rightside of the diagonal corresponds to the second scatterponds to the second scatterplot in the fourth row.

(C) 0.38 is the relationship between “extraversion” and “true arousal_plac”.

(D) “arousal_caff” and “performance_caff” are positively related.

(E) The line that captures relationship between “arousal_caff” and “arousal_plac” can be denoted b y equation : y = a – bx, where b > 0.

**Directions (Qs. 24 to 27) : Study the paragraph below and answer these questions :**

Abdul has 8 factories, with different capacities, producing boutique kurtas. In the production process, he incurs raw material cost, selling cost (for packaging and transportation) and labour cost. These costs per kurta vary across factories. In all these factories, a worker takes 2 hours to produce a kurta. Profit per kurta is calculated by deducting raw material cost, selling cost and labour cost from the selling price (Profit = selling price – raw materials cost – selling cost – labour cost). Any other cost can be ignored.

24. Which of the following options is in decreasing order of raw materials cost?

(A) Factory 3, Factory, 4, Factory 7, Factory 5

(B) Factory 4, Factory 3, Factory 2, Factory 5

(C) Factory 6, Factory 3, Factory 5, Factory 7

(D) Factory 6, Factory 8, Factory 7, Factory 2

(E) Factory 8, Factory 3, Factory 2, Factory 4

25. Which of the factories listed in the options below has the lowest sales margin (sales margin = profit per kurta divided by selling price per kurta)?

(A) Factory 2

(B) Factory 4

(C) Factory 5

(D) Factory 6

(E) Factory 7

26. Abdul has received an order for 2,000 kurtas from a big retail chain. They will collect the finished pre-packaged kurtas directly from the factories, saving him the selling cost. To deliver this order, he can use multiple factories for production. Which of the following options will ensure maximum profit from this order?

(A) Factory 1

(B) Factories 2 and 3

(C) Factories 4 and 6

(D) Factories 3, 6 and 4

(E) Factory 1 or Factory 7 or Factory 8

27. Abdul has introduced a new technology in all his factories. As a result, a worker needs just 1.5 hours to produce a kurta. If raw materials cost and selling cost remain the same, which of the factories listed in the options below will yield the highest profit per kurta ?

(A) Factory 2

(B) Factory 3

(C) Factor 4

(D) Factory 5

(E) Factory 6

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