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 1 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 1

Answer question numbers 1 to 4 based on the following information.

The following graphs give annual data of *Assets, Sales* ( as percentage of Assets) and *Spending on **C**orporate **Soci**al Responsibility **(CSR) *(as percentage of Sales) ,of a company for the period 2004 – 2009 .

1.In which year was the increase in spending on CSR, vis-a-vis the previous year, the maximum?

A.2005

B.2006

C.2007

D.2008

E.2009

2.Of the years indicated below, in which year was the ratio of CSR/Assets the maximum?

A.2004

B.2005

C.2006

D.2007

E.2008

3.What was the maximum value of spending on CSR activities in the period 2004-2009?

A.Rs. 0.5 Crore

B.Rs 1.0 Crore

C.Rs. 2.0 Crore

D.Rs. 3.0 Crore

E.Rs. 4.0 Crore

4.In which year, did the spending on CSR (measured in Rs) decline, as compared to previous year?

A.2006

B. 2007

C. 2008

D.2009

E. None of above

Answer question numbers 5 to 7 based on the following information.

Five years ago Maxam Glass Co. had estimated its staff requirements in the five levels in their organization as: Level-1: 55; Level-2: 65; Level-3: 225; Level-4: 255 & Level-5: 300. Over the years the company had recruited people based on ad-hoc requirements, in the process also selecting ex-defence service men and ex-policemen. The following graph shows actual staff strength at various levels as on date

5.The level in which the Ex-Defence Servicemen are highest in percentage terms is:

A.1

B.2

C.3

D.4

E.5

6.If the company decides to abolish all vacant posts at all levels, which level would incur the highest reduction in percentage terms?

A.1

B.2

C.3

D.4

E.5

7.Among all levels, which level has the lowest representation of Ex-policemen?

A.1

B.2

C.3

D.4

E.5

8.In a locality, there are ten houses. On a particular night a thief planned to steal from three houses of the locality. In how many ways can he plan such that no two of them are next to each other?

A.56

B.73

C.80

D.120

E.None of the above

9.If x = (9 + 4√5)^{48} = [x] + f, where [x] is defined as integral part of x and f is a fraction, then x(1 – f) equals:

A.1

B.Less than 1

C.More than 1

D.Between 1 and 2

E.None of the above

10.Let a_{n} = 1 1 1 1 1 1 1……… 1, where 1 occurs n number of Then,

1.a_{741} is not a prime

2.a_{534} is not a prime

3.a_{123} is not a prime

4.a_{77} is not a prime

A.(1) is correct

B.(1) and (2) are correct.

C.(2) and (3) are correct.

D.All of them are correct.

E. None of them is correct.

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1. It can be observed that the CSR spend was the highest in the year 2006. Option b.

2. Option e.

3. It was almost Rs. 3 crores in 2009. Option d.

4. It never shows a decline. So, option e.

5. Level 1 is 600/52

Level 2 is 800/65

Level 3 is 3000/210

Level 4 is 2500/130

Level 5 is 6000/330

Level 4 is the highest. Option d.

6. Level 4. Option d.

7. Level 1 is 400/52

Level 2 is 400/65

Level 3 is 900/210

Level 4 is 700/130

Level 5 is 1500/330

Level 3 is the least. Option c.

8. 10c3 – 8 – (7*2+6*7) = 56 ways. Option a.

9. x = (9 + 4√5)^{48}

y = (9 – 4√5)^{48} which is the conjugate of x.

(9 + 4√5)^{48} * (9 – 4√5)^{48} = 1

(9 + 4√5)^{48} + (9 – 4√5)^{48} will give us an integer as the odd powers of root 5 will cancel themselves out.

x + y = 2m

Also, xy = 1

x + 1/x = 2m

As x is greater than 1, y has to be less than 1.

So, x + y = 2m

[x] + f + y = 2m

f + y is an integer less than 2. So, f + y = 1

x(1 – f) = xy = 1.

Option 1.

10. Statements 1, 2, 3 are correct as the number of 1s is divisible by 3. Option d is the only one that satisfies this.

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