# XAT 2017 QADI

Paper year paper questions for XAT 2017 LRDI

**1. XAT 2017 QADI | Algebra - Progressions**

The sum of the series, (-100) + (-95) + (-90) + … + 110 + 115 + 120, is

- A.
0

- B.
220

- C.
340

- D.
450

- E.
None of the above

Answer: Option D

**Explanation** :

(–100) + (-95) + ….. + 120

= [(–100) + (-95) + ….. + 95 + 100] + 105 + 110 + 115 + 120

= 105 + 110 + 115 + 120

= 450

Hence, option (d).

Workspace:

**2. XAT 2017 QADI | Arithmetic - Time & Work**

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 filled and pipes B and C drained

- E.
None of the above

Answer: Option A

**Explanation** :

Let the capacity of the tank = LCM(4, 10, 12, 20) = 60 units

∴ Efficiency of A, B, C and D = 15, 6, 5, 3 units/minute respectively.

We need to check options now,

Option 1: Work Done in a minute = 15 – 6 – 5 – 3 = 1 unit

∴ After 30 minutes, the tank will be half filled.

We don’t have to check other options.

Hence, option (a).

Workspace:

**3. XAT 2017 QADI | Arithmetic - Profit & Loss**

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

Answer: Option B

**Explanation** :

Let the marked price of a shirt = M

∴ If a customer buys 3 shirts then the fourth shirt would be given at a discounted price of 100 rupees.

⇒ Total cost of 4 shirts = 3M + 100

Customer bought a total of 20 shirts, hence he bought 15 shirts and marked price and got 5 shirts at the discounted price.

∴ Total amount paid by the customer = 15M + 500

⇒ 15M + 500 = 20,000

⇒ M = 1300

Hence, option (b).

Workspace:

**4. XAT 2017 QADI | Geometry - Circles**

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

Answer: Option B

**Explanation** :

Let us draw the diagram using the given conditions.

AB = 24 cm and P is the mid-point of AB.

∴ AP = PB = 12 cm.

MN is perpendicular to AB and passes through P.

PM < PN.

∴ M should be closer to A and B than N.

MN and AB are 2 perpendicular chords intersecting at P.

Therefore, according to the intersecting chords theorem, AP × PB = PM × PN

⇒ 12 × 12 = 8 × PN

⇒ PN = 18 cm.

Hence, option (b).

Workspace:

**5. XAT 2017 QADI | Algebra - Quadratic Equations**

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

Answer: Option B

**Explanation** :

4(x – 2)^{2} + 4(y – 3)^{2} – 2(x – 3)^{2}

= 4(x^{2} + 4 – 4x) + 4(y – 3)^{2} – 2(x^{2} + 9 – 6x)

= 4(y – 3)^{2} + 2x^{2} – 4x – 2

Now, (y – 3)^{2} least value would be 0.

The least value of 2x^{2} – 4x – 2 would be at x = -(-4)/(2×2) = 1

The least value of 2x^{2} – 4x – 2 = 2(1)^{2} – 4(1) – 2 = -4

The least value of the expression would be = – 4.

Hence, option (b).

Workspace:

**6. XAT 2017 QADI | Algebra - Functions & Graphs**

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 these

Answer: Option C

**Explanation** :

f(x) = ax + b

∴ f(f(x) = a(ax + b) + b

f(f(x) = a^{2}x + ab + b

⇒ a^{2}x + b(a + 1) = 9x + 8

∴ a^{2} = 9 ⇒ a = 3. and

b(a + 1) = 8

⇒ b(3 + 1) = 8

⇒ b = 2

Thus, a + b = 5

Hence, option (c).

Workspace:

**7. XAT 2017 QADI | Arithmetic - Time, Speed & Distance**

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 km/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. 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

Answer: Option D

**Explanation** :

At 4 km/hr, Arup walks 2 km in ½ hour = 30 minutes and at 50 km/hr, he covers 20 km in ⅖ hours = 24 minutes.

At 5 km/hr, Swarup walks 2 km in ⅖ hours = 40 minutes and at 40 km/hr, he covers 20 km in ½ hour = 30 minutes.

Thus, time taken by each of them to reach B is equal.

∴ Initially Swarup will go ahead of Arup and both of them will reach the finish line together.

Time = 30 + 30 + 24 = 84 minutes.

So, they meet again at 9:24 AM.

Hence, option (d).

Workspace:

**8. XAT 2017 QADI | Algebra - Simple Equations**

Hari’s family consisted of his younger brother (Chari), younger sister (Gouri), and their father and mother. When Chari was born, the sum of the 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 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

Answer: Option E

**Explanation** :

Let the ages of Father and Mother at the time of Hari’s birth are F and M respectively.

Let Chari be born x years after Hari’s birth.

∴ Ages of Hari, Father and mother will be x , F + x and M + x at the time of Chari’s birth.

∴ x + (F + x) + (M + x) = 70

⇒ 3x + F + M = 70 … (1)

Gouri was born 4 years after Chari’s birth.

∴ Ages of Chari, Hari, Father and mother will be 4, 4 + x , F + x + 4 and M + x + 4 at the time of Gouri’s birth.

∴ (x + 4) + (F + x + 4) + (M + x + 4) + 4 = 2(F + M)

⇒ 3x + 16 = F + M … (2)

From (1) and (2), x = 9

Hence, option (e).

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**9. XAT 2017 QADI | Miscellaneous**

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 answers 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

Answer: Option A

**Explanation** :

The correct answer fetches 4 marks whereas the wrong answer fetches -1 marks.

Amit scored 35 marks each in these 10 questions.

Let the number of correct answers be ‘c’ and wrong answers be ‘w’

4c – w = 35

c + w = 10

⇒ c = 9, w = 1, which means 9 correct answers and 1 wrong.

∴ Both Amit and Ben gave 1 wrong answer each.

Amit and Ben marked different answers for 3^{rd} and 5^{th} questions.

⇒ Amit and Ben would’ve answered 3^{rd} or 5^{th} question wrong in any order.

∴ They marked all other answers correctly.

⇒ Chitra marked correct answers for 3 questions (i.e., 1^{st}, 2^{nd} and 9^{th})

Out of 3^{rd} and 5^{th} questions marked by Chitra one would be correct and the other wrong.

Hence, Chitra marks 4 answers correctly and remaining 6 were wrong.

∴ Chitra’s score = 4 × 4 – 6 × 1 = 10.

Hence, option (a).

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**10. XAT 2017 QADI | Venn Diagram**

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. 6 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 mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark 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

Answer: Option D

**Explanation** :

Let T_{m} and T_{b} be total scores of the students majoring in Mathematics and Biology respectively.

According to the given conditions,

T_{m} = (M + 6) × 45

T_{b} = (B + 15) × 60

Also, (T_{m} + T_{b}) = (B + P + 21) × 50

45(M + 6) + 60(B + 15) = 50M + 50B + 1050

10B – 5M + 270 + 900 = 1050

10B – 5M = –120

M = 2B + 24

Here, we need to determine the maximum value of P.

∴ We need to minimize the value of B. Minimum value of B can be 0.

∴ M = 24

Again, we know that,

M + B + P + 21 = 60

⇒ 24 + 0 + P + 21 = 60

⇒ P = 15

Hence, option (d).

Workspace:

**11. XAT 2017 QADI | Geometry - Trigonometry**

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 inclusive

- D.
Between 0.5 and 1 inclusive

- E.
None of the above

Answer: Option E

**Explanation** :

sin 30° + cos x° – sin x° where 5° ≤ x° ≤ 15°.

For the given range, cos x > sin x

So, cos x° – sin x° > 0

Also, sin 30° = 0.5

sin 30° + cos x° – sin x° > 0.5

So, first four options are eliminated.

Hence, option (e).

Workspace:

**12. XAT 2017 QADI | Geometry - Mensuration**

The Volume of a pyramid with a square base is 200 cubic cm. The height of the 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

Answer: Option C

**Explanation** :

Let the side of the square base AB = BC = CD = DA = ‘a’.

Height OB = 13.

Volume of a square base pyramid = a^{2} × h/3 = 200 cm^{3}

⇒ a^{2} = 600/13

Diagonal AC = a√2

⇒ AB = a/√2

In right ∆OAB, AO^{2} = AB^{2} + OB^{2}

⇒ AO^{2} = (a/√2)^{2} + 13^{2}

⇒ AO^{2} = a^{2}/2 + 169

⇒ AO^{2} = 300/13 + 169 = 2497/13

⇒ AO ≈ 13.86

Thus, the length of the slant slope (when rounded to the nearest integer) = 14 cm

Hence, option (c).

Workspace:

**13. XAT 2017 QADI | Modern Math - Probability**

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

Answer: Option C

**Explanation** :

Total combinations when a die is rolled twice = 6 × 6 = 36

**Case 1:** The first roll = 1

The second roll = (2, 3, 4, 5, 6)

∴ Favourable outcomes = 5

**Case 2**: The first roll = 2

The second roll = (3, 4, 5, 6)

∴ Favourable outcomes = 4

**Case 3**: The first roll = 3

The second roll = (4, 5, 6)

∴ Favourable outcomes = 3

**Case 4**: The first roll = 4

The second roll = (5, 6)

∴ Favourable outcomes = 2

**Case 5**: The first roll = 5

The second roll = (6)

∴ Favourable outcomes = 1

Hence, the number of favourable outcomes = 5 + 4 + 3 + 2 + 1 = 15

Therefore, the probability = 15/36

**Alternately,**

Let us calculate the number of ways a different number comes up both the die = 6 × 5 = 30.

Out of these 30 ways, in half of these first die will have higher number and in other half second die will have higher number.

∴ Probability that second die has higher number = 15/36.

Hence, option (c).

Workspace:

**14. XAT 2017 QADI | Algebra - Number Theory**

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

Answer: Option C

**Explanation** :

The five departments of each department has 50 students.

We have to minimise the number of students in the committee so that at least one department should have representation of minimum 5 students

Let us maximise the number of students in the committee so that no department has representation of 5 students. i.e., any department can have maximum 4 students.

∴ If we select 4 students from each department i.e. a total of 20 students, still no department will have representation of 5 students.

Now if we select one more student, we will have representation of 5 students from at least 1 department.

∴ Minimum number of students in the committee so that at least one department should have representation of minimum 5 students is 21.

Hence, option (c).

Workspace:

**15. XAT 2017 QADI | Algebra - Number Theory**

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

Answer: Option E

**Explanation** :

In order for N to be a perfect cube, every prime number should be a power of multiple of 3 i.e., 0, 3 , 9 …

Also, we need to consider minimum possible values of p, q, r and s. (p, q, r and s > 0)

For 3^{s} to be a perfect cube, minimum value of s = 3.

For 5^{r+1} to be a perfect cube, minimum value of r = 2.

For 7^{q-2} to be a perfect cube, minimum value of q = 2.

For 11^{p+7} to be a perfect cube, minimum value of p = 2.

So, smallest value of p + q + r + s = 2 + 2 + 2 + 3 = 9

Hence, option (e).

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**16. XAT 2017 QADI | Geometry - Quadrilaterals & Polygons**

AB, CD and EF are three parallel lines, in that order. Let d1 and d2 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 more than 20 units

Answer: Option E

**Explanation** :

Let d_{1} = x and d_{2} = 2x.

Now, SR would be shortest when SR = d1 = x

Area of PQRS = 30 square units.

∴ Area of PQRS = ½ × QS × 2x + ½ × QS × x

= (3/2) × QS × x = 30

⇒ QS × x = 20

Smallest value of x = 1 units.

⇒ QS = 20

∴ ∆QSR is right angled at S

⇒ QR^{2} = QS^{2} + SR^{2}

⇒ QR^{2} = 400 + 1

⇒ QR = slightly more than 20.

Hence, option (e).

Workspace:

**Answer the next 2 questions based on the following information:**

In an innings of a T20 cricket match (a team can bowl for 20 overs) 6 bowlers bowled from the fielding side, with a bowler allowed maximum of 4 overs. Only the three specialist bowlers 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.

**17. XAT 2017 QADI | Miscellaneous | Data Sufficiency**

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 can help arrive at the minimum number of overs bowled by a non-specialist bowler?

- A.
S1 only

- 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

Answer: Option E

**Explanation** :

There are 3 specialist bowlers and 3 non- specialists bowlers.

The three specialist bowlers bowled 4 overs each and 3 non-specialist bowlers would have bowled 8 overs.

8 overs can be bowled by 3 non-specialist bowlers when they bowl 3, 3 and overs.

This is the only possibility since maximum overs a non-specialist can bowl is 3 overs.

So, the least number of overs bowled by a non-specialist bowler would be 2 only.

So, none of the S1 and S2 required to answer the question.

Hence, option (e).

Workspace:

**18. XAT 2017 QADI | Miscellaneous | Data Sufficiency**

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.

Answer: Option D

**Explanation** :

S1: The given economy rates of 4 bowlers are 6, 6, 7 and 9. So, the non-specialist bowlers would have 7, 9, x as their economy rates and specialist bowlers would have y, 6, 6 as their economy rates.

S2: The overs bowled by specialist bowlers would be 4, 4 and 4 each. The number of overs bowled by non-specialist bowlers would in any combination of 3, 3 and 2 each.

The runs given by specialist bowlers would be 6 × 4 + 6 × 4 + 4y = 48 + 4y …(1)

**Case 1**: For non-specialist bowlers, overs bowled are 3, 3, 2 and economy rate is 7, 9 and x respectively.

∴ The runs given by non-specialist bowlers = (7 × 3 + 9 × 3 + x × 2) = 48 + 2x ...(2)

According to the question: (2) – (1) = 1

∴ 2x – 4y = 1

Now, 2x – 4y cannot give an odd value.

**Case 2**: For non-specialist bowlers, overs bowled are 3, 3, 2 and economy rate is x, 7 and 9 respectively.

The runs given by non-specialist bowlers would be (9 × 2 + 7 × 3 + 3x) = 39 + 3x

According to the question: (2) – (1) = 1

∴ 39 + 3x = 48 + 4y + 1

This is satisfied for x =10 and y = 5

Thus, we need both the statements to get to worst economy rate of the bowler.

Hence, option (d).

Workspace:

**Answer the next 4 questions based on the following information:**

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.

Exhibit: Business Details of Abdul’s 8 Factories

**19. XAT 2017 QADI | DI - Tables & Graphs**

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

Answer: Option A

**Explanation** :

We know, Selling price = Raw material cost + Labour cost + Selling cost + Profit

∴ Raw material cost = Selling price – Labour cost – Selling cost - Profit

Here, a worker takes 2 hours to produce a kurta.

∴ Raw material cost for F1 = 4800 – 775 – 60 – 2 × 450 = 3065

Similarly, we can make the following table.

Now, check the option for the decreasing order.

Hence, option (a).

Workspace:

**20. XAT 2017 QADI | DI - Tables & Graphs**

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

Answer: Option E

**Explanation** :

Sales margin = profit per kurta / Selling price per kurta

Factory 2 = 800/5300 = 0.15

Factory 4 = 800/5500 = 0.145

Factory 5 = 600/5400 = 0.111

Factory 6 = 875 /6000 = 0.145

Factory 7 = 500 /4900 = 0.10

Thus, Factory 7 has the lowest sales margin.

Hence, option (e).

Workspace:

**21. XAT 2017 QADI | DI - Tables & Graphs**

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

Answer: Option D

**Explanation** :

Here, selling cost would be added to the profit.

F1: Profit = 775 + 60 = 835

F2: Profit = 800 + 45 = 845

F2: Profit = 900+60 = 960

F4: Profit = 800 + 68 = 868

F5: Profit = 600 + 75 = 675

F6: Profit = 875 + 65 = 940

F7: Profit = 500 + 85 = 585

F8: Profit = 600 + 70 = 670

Maximum profit margin is from factory 3. But it can only produce 800 kurtas.

Next best profit margin is from factory 6. It can produce additional 1100 kurtas.

∴ 1900 kurtas can be produced by factory 3 and 6 together.

Remaining 100 kurtas should be produced by factory 4 since it has the third highest profit margin.

Hence option (d).

Workspace:

**22. XAT 2017 QADI | DI - Tables & Graphs**

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.
Factory 4

- D.
Factory 5

- E.
Factory 6

Answer: Option B

**Explanation** :

Here, a worker takes 1.5 hours to produce a kurta.

Hence for factory 2 new labour cost would be 1.5 × 400 = 600 instead of 2 × 400 = 800

⇒ Profit of factory 2 will increase by 0.5 × 400 = 200.

New profit for factory 2 = 500 + 200 = 700.

Similarly, we can make the following table for new profit of each of the companies mentioned in the options.

Thus, the maximum profit is obtained from Factory 3.

Hence, option (b).

Workspace:

**Answer the next 4 questions based on the following information:**

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).

**23. XAT 2017 QADI | DI - Tables & Graphs**

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.

Answer: Option A

**Explanation** :

We need to look at histogram to interpret the answer.

The histogram for performance_caff and performance_plac is left skewed which will shift median to right side compared to the mean.

The situation is opposite in case of arousal_caff.

Furthermore, arousal_plac‘s histogram is not symmetric and hence, there is no guarantee of its mean and median being equal.

Hence, options 2, 3, 4 and 5 are incorrect.

Hence, option (a).

Workspace:

**24. XAT 2017 QADI | DI - Tables & Graphs**

Which of the scatterplots shows the weakest relationship?

- A.
Between "extraversion" and "performance_caff".

- B.
Between "true_arousal_plac" and "arousal_plac".

- C.
Between "true_arousal_plac" and "performance_plac".

- D.
Between "true_arousal_caff" and "performance_caff".

- E.
Between "arousal_caff" and "performance_caff".

Answer: Option A

**Explanation** :

The weakest relationship should have relationship value close to zero.

The closest relationship to zero, among the five options, is 0.16, which is between extraverion and performance_caff.

Hence, option (a).

Workspace:

**25. XAT 2017 QADI | DI - Tables & Graphs**

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 "performancc_caff"

- E.
All the above are irrelevant relations.

Answer: Option C

**Explanation** :

The question can be answered by looking at the scatterplot, which is on the left hand side of the diagonal.

Option (a) is weak as the scatter is dispersed all over.

Option (b) is very close, but some dispersion can be seen away from the trend line.

The scatterplot in the option (d) is dispersed as well and hence it cannot be right answer.

The scatterplot in the option (c) is indeed the closest to the trend line and hence it should be the answer, though the relationship is weaker as compared to that in the option (b) (This is because it is curvilinear in shape, while relationship value assumes linearity)

Hence, option (c).

Workspace:

**26. XAT 2017 QADI | DI - Tables & Graphs**

Which of the following options is correct?

- A.
0.93 on the right side of the diagonal corresponds to the third scatterplot in the fourth row.

- B.
0.94 on the right side of the diagonal corresponds to the second scatterplot in the fourth row.

- C.
0.38 is the relationship between "extraversion" and "true_arousal_plac".

- D.
"arousal_catr” and "performance_caff" arc positively related.

- E.
The line that captures relationship between "arousal_caff" and "arousal_plac" can be denoted by equation: y = a - bx, where b > 0.

Answer: Option B

**Explanation** :

Comparison between the visual pattern in the left side and the numbers in the right hand side .

Hence, option (b).

Workspace:

**27. XAT 2017 QADI | Geometry - Quadrilaterals & Polygons | Geometry - Mensuration**

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

- A.
36/128

- B.
39/128

- C.
44/128

- D.
48/128

- E.
64/128

Answer: Option A

**Explanation** :

Let the length of the rectangle be ‘l’ and breadth be ‘b’.

The given figure is.

Let us draw a line MS parallel to DC

∆RMS ~ ∆RDQ

∴ RM : MD = RS : SQ = 1 : 3

Let the length of the rectangle (i.e., AB = CD) ABCD be 8l and width be 8b (i.e., AD = BC).

∴ AR = 4b and RM = b

Also, MS = l and SL = 7l.

Also, PL : LC = 1 : 3 [∵ RS : SQ = 1 : 3]

Area (∆ARS) = ½ × AR × SM = 2lb

Area (∆RDQ) = ½ × RD × DQ = 8lb

Area (∆ABP) = ½ × AB × BP = 16lb

Area (PSQC) = Area (∆PSL) + Area(∆SLQC)

= ½ × SL × PL + ½ × (SL + QC) × LC

= 3.5lb + 16.5lb

= 20lb

Area of ∆ASP = Area of rectangle ABCD – [Area (∆ARS) + Area (∆RDQ) + Area (∆ABP) + Area (PSQC)]

= 64lb – [2lb + 8lb + 16lb + 20lb]

= 64lb - 46lb = 18lb

∴ $\frac{Area(\u2206ASP)}{Area\left(ABCD\right)}$ = $\frac{18lb}{64lb}$ = $\frac{36}{128}$

Hence, option (a).

Workspace:

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