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 2 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 2

Answer question numbers 1 and 2 based on the following information.

Total income tax payable is obtained by adding two additional surcharges on calculated income tax.

-Education Cess: An additional surcharge called ‘Education Cess’ is levied at the late of 2% on the amount of income tax

-Secondary and Higher Education Cess: An additional surcharge called ‘Secondary and Higher Education Cess’ is levied at the rate of 1% on the amount of income tax

Income-Tax Rates for Financial Year 2009-10 |
||

Individual & HUF below age of 65 years |
Women below age of 65 years |
Tax Rates |

Income up to (Rs.) | Income up to (Rs.) | |

160000 | 190000 | Nil |

160001-300000 | 190001-300000 | 10% |

300001-500000 | 300001-500000 | 20% |

Above 500001 | Above 500001 | 30% |

1. Sangeeta is a young working lady. Towards the end of the financial year 2009-10, she found her total annual income to be Rs.3,37,425/-. What % of her income is payable as income tax?

A.5.64

B.6.82

C.7.38

D.8.10

E.None of the above

2. Madan observed his tax deduction at source, done by his employer, as Rs. 3,17,910/-. What was his total income (in Rs.) if he neither has to pay any additional tax nor is eligible for any refund?

A.13,48,835/-

B.14,45,522/-

C.14,47,169/-

D.15,70,718/-

E.None of the above

3. A straight line through point P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. lf S is not the centre of the circumcircle, then which of the following is true?

A.(1/PS) + (1/ST) < 2/√ (QS)(QR)

B.(1/PS) + (1/ST) < 4/ QR

C.(1/PS) + (1/ST) > 1√ (QS)(QR)

D.(1/PS) + (1/ST) > 4/ QR

E.None of the above

4. What is the maximum possible value of (21 Sin X + 72 Cos X)?

A.21

B.57

C.63

D.75

E.None of the above

5. The scheduling officer for a local police department is trying to schedule additional patrol units in each of two neighbourhoods – southern and northern. She knows that on any given day, the probabilities of major crimes and minor crimes being committed in the northern neighbourhood were 0.418 and 0.612, respectively, and that the corresponding probabilities in the southern neighbourhood were 0.355 and 0.520. Assuming that all crime occur independent of each other and likewise that crime in the two neighbourhoods are independent of each other, what is the probability that no crime of either type is committed in either neighbourhood on any given day?

A.0.069

B.0.225

C.0.69

D.0.775

E.None of the above

Answer question numbers 6 and 7 based on the following information.

A man standing on a boat south of a light house observes his shadow to be 24 meters long, as measured at the sea level. On sailing 300 meters eastwards, he finds his shadow as 30 meters long, measured in a similar manner. The height of the man is 6 meters above sea level.

6. The height of the light house above the sea level is:

A.90 meters

B.94 meters

C.96 meters

D.100 meters

E.l06 meters

7. What is the horizontal distance of the man from the lighthouse in the second position?

A.300 meters

B.400 meters

C.500 meters

D.600 meters

E.None of the above

8. A 25 ft long ladder is placed against the wall with its base 7 ft from the The base of the ladder is drawn out so that the top comes down by half the distance that the base is drawn out. This distance is in the range:

A.(2, 7)

B.(5, 8)

C.(9, 10)

D.(3, 7)

E.None of the above.

9. The domain of the function f(x) = log_{7}{log_{3}(log5(20x – x^{2} – 91 ))} is:

A.(7, 13)

B.(8, 12)

C.(7, 12)

D.(12, 13)

E.None of the above

10. There are four machines in a factory. At exactly 8 pm, when the mechanic is about to leave the factory, he is informed that two of the four machines are not working. The mechanic is in a hurry, and decides that he will identify the two faulty machines before going home, and repair them next morning. It takes him twenty minutes to walk to the bus stop. The last bus leaves at 8:32 pm. If it takes six minutes to identify whether a machine is defective or not, and if he decides to check the machines at random, what is the probability that the mechanic will be able to catch the last bus?

A.0

B.1/6

C.1/4

D.1/3

E.1

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Solutions:

1. Tax paid is 10% of 110000 and 20% of 37425 = 11000 + 7485 = 18485 on 337425 which is less than 6% and so, option a is the only one that could fit. In case you are not sure whether it is a or none of these, you can multiply 5.64 and 3374.25 and cross check if it gives something around 18485.

2. Assuming that Madan is less than 65 years old, we get 1.03*(14000 + 40000 + 0.3x) = 317910

0.3x = 255000 approximately

x = 850000 and so, total salary will be approximately Rs. 13,50,000. Option a.

3. Let the triangle be a right angled triangle with sides 6, 8 and 10. The radius of the circumcircle will be 5 units. Also, let P-S-T be perpendicular to QR. As nothing has been specified with regard to nature of the figure and the answers talk about a general property, we can make these assumptions. So, we get PR = 6, PQ = 8, QR = 10, PS = ST = 4.8, RS = 3.6 and QS = 6.4. Also, understand that b and d are opposite to each other and one of them has to be true. So, you can check for just one inequality using the values that we have got and we should be done. Option d it is.

4. 21sinX + 72cosX

75(21/75*sinX + 72/75*cosX)

If sinY = 72/75, cosY = 21/75 (as 21-72-75 are in the ratio 7-24-25 which is a right angled triangle)

75*sin(X+Y)

Maximum value will be 75.

5. 0.582*0.388*0.645*0.480=0.6*0.4*0.6*0.5=0.0720 approximately. So, we can go with option a.

6. We get two sets of figures:

Side view before

Side view after

Top view

From the first two figures, we get 4y = 5x

From the third figure, we get x^2 + y^2 = 90000

So, y = 500 and h = 106. Option e.

7. Option c

8. Let the base of the ladder move by 2x. The top of the ladder will slide down by x.

(7 + 2x)^2 + (24 – x)^2 = 625

5x^2 + 625 – 20x = 625

x = 4. So, the distance is 8. Option b. The options were a bit shady and few sources say it should be none of these but 8 was there in just one option.

9. log_{3}(log_{5}(20x – x^{2}– 91 )) > 0

log_{5}(20x – x^{2} – 91) > 1

(20x – x^{2} – 91) > 5

(20x – x^{2} – 96) > 0

(12 – x)(x – 8) > 0

So, option b.

10. The mechanic has to leave by 8.12. So, he can check for 2 machines. There are 4!/2!2! arrangements possible i.e. 6. The mechanic will be fine if he gets both the machines he has checked as defective or not. So, 2/6 is the required probability. Option d.

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