[Download PDF] XAT 2011 Paper with Solutions

Instructions

Based on the following information.

The following graphs give annual data of Assets, Sales (as percentage of Assets) and Spending on Corporate Social Responsibility (CSR) (as percentage of Sales), of a company for the period 2004 - 2009.

Question 61

The maximum value of spending on CSR activities in the period 2004-2009 is closest to which of the following options?

Video Solution

Solution

Total value of assets in the year 2004 = 100 crore

Total value of sales in the year 2004 = 0.60*100 = 60 crore

CSR spending in the year 2004 = $$\dfrac{5/3}{100}\times 100$$ = 1 crore.

Similarly, we can calculate for the remaining years. Tabulating the same data, (All the values are in crores)

From the table we can see that maximum spending on CSR activities in the period 2004 - 2009 = 3.16 crore $$\approx$$ 3 crore. Hence, option D is the correct answer.

Question 62

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

Video Solution

Solution

Total value of assets in the year 2004 = 100 crore

Total value of sales in the year 2004 = 0.60*100 = 60 crore

CSR spending in the year 2004 = $$\dfrac{5/3}{100}\times 100$$ = 1 crore.

Similarly, we can calculate for the remaining years. Tabulating the same data, (All the values are in crores)

From the table, we can see that the CSR spending never decreased as compared to previous year. Hence, option E is the correct answer.

Instructions

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.

Question 63

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

Video Solution

Solution

Percentage of Ex-defense serviceman in level 1 = $$\dfrac{6}{52}\times 100$$ = 11.54 percent

Percentage of Ex-defense serviceman in level 2 = $$\dfrac{8}{65}\times 100$$ = 12.31 percent

Percentage of Ex-defense serviceman in level 3 = $$\dfrac{30}{210}\times 100$$ = 14.28 percent

Percentage of Ex-defense serviceman in level 4 = $$\dfrac{25}{130}\times 100$$ = 19.23 percent

Percentage of Ex-defense serviceman in level 5 = $$\dfrac{60}{330}\times 100$$ = 18.18 percent

We can see that in level 4 the Ex-Defence Servicemen are the highest in percentage terms. Hence, option D is the correct answer.

Question 64

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

Video Solution

Solution

From the bar graph we can see that actual staff strength is 130 whereas the staff requirements is 255. So, the company has to abolish 125 vacant seats. we can see that the company has to abolish nearly 50 percent of the total strength which is greater than any other remaining levels. Hence, option D is the correct answer.

Question 65

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

Video Solution

Solution

Percentage representation of Ex- policemen in level 1 = $$\dfrac{4}{52}\times 100$$ = 7.69 percent

Percentage representation of Ex- policemen in level 2 = $$\dfrac{4}{65}\times 100$$ = 6.15 percent

Percentage representation of Ex- policemen in level 3 = $$\dfrac{9}{210}\times 100$$ = 4.29 percent

Percentage representation of Ex- policemen in level 4 = $$\dfrac{7}{130}\times 100$$ = 5.38 percent

Percentage representation of Ex- policemen in level 5 = $$\dfrac{15}{330}\times 100$$ = 4.54 percent

We can see that in level 3 the Ex- policemen are the lowest in percentage terms. Hence, option C is the correct answer.

Instructions

For the following questions answer them individually

Question 66

In a locality, there are ten houses in a row. 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?

Video Solution

Solution

Total number of houses = 10

If first house is robbed, then II is not and if II house is robbed, then III is not and so on.

Thus 2 adjacent houses can never be chosen

So, number of ways in which three houses can be robbed such that no two of them are next to each other.

= $$C^{10 - 2}_3 = C^8_3$$

= $$\frac{8 \times 7 \times 6}{1 \times 2 \times 3}$$

= $$56$$

Question 67

If $$x=(9+4\sqrt{5})^{48} = [x] +f$$, where [x] is defined as integral part of x and f is a fraction, then x (1 - f) equals

Video Solution

Solution

It is given that $$x=(9+4\sqrt{5})^{48}$$ ... (1)

Let us assume that $$y=(9-4\sqrt{5})^{48}$$ ... (2)

We can see that 0 < y < 1.

Also, x + y = 2($$48C0*(9)^{48}$$+$$48C2*(9)^{46}*(4\sqrt{5})^2$$+$$48C4(9)^{44}*(4\sqrt{5})^4$$+...+$$48C48*(4\sqrt{5})^{48}$$)

We can see that x + y is an integer therefore we can say that y + f = 1. Hence, y = (1 - f)

We can see that = x(1 - f) = x*y

$$\Rightarrow$$ $$(9+4\sqrt{5})^{48}(9-4\sqrt{5})^{48}$$

$$\Rightarrow$$ $$(9^2-(4\sqrt{5})^2)^{48}$$

$$\Rightarrow$$ $$(81-80)^{48}$$ = 1

Hence, option A is the correct answer.

Question 68

Let $$a_{n} = 1 1 1 1 1 1 1..... 1$$, where 1 occurs n number of times. Then,
i. $$a_{741}$$ is not a prime.
ii. $$a_{534}$$ is not a prime.
iii. $$a_{123}$$ is not a prime.
iv. $$a_{77}$$ is not a prime.

Video Solution

Solution

i. $$a_{741}$$ has 741 ones, it will be divisible by 3

ii. $$a_{534}$$ has 534 ones, it will be divisible by 3

iii. $$a_{123}$$ has 123 ones, it will be divisible by 3

iv. $$a_{77}$$ has 77 ones and each pair of 11 ones is divisible by 13.

Therefore, i,ii,iii and iv are not prime.

Ans -(D) All are correct.

Instructions

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 rate 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.

Question 69

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?

Video Solution

Solution

Income tax payable by Sangeeta according to her salary band = 0.2*(337425-300000) + 0.1(300000-190000) = Rs. 18485

Total education cess levied on income tax = 2 + 1 = 3% of income tax

Therefore, the total income tax payable by Sangeeta = 1.03*18485 = 19039.55.

Hence, the required percentage = $$\dfrac{19039.55}{337425}\times 100$$ = 5.64 percent

Therefore, we can say that option A is the correct answer.

Question 70

Mr. 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?

Video Solution

Solution

Madan's tax deduction at source = Rs. 3,17,910

From the table we can see that one can pay this much amount of tax if he earns more than 5 lakh.

Let say Madan's is Rs. x more than 5 lakhs. Therefore, Madan's total income = Rs. 500000+x.

Total income tax paid by Madan = 1.03{0.3*(x) + 0.2*(200000) + 0.1(140000)}

$$\Rightarrow$$ $$\dfrac{317910}{1.03} = 0.3x + 54000$$

$$\Rightarrow$$ x = 848835.

Therefore, Madan's total income = 500000+848835 = Rs. 1348835. Hence, option A is the correct answer.

CAT Content

XAT 2011

The maximum value of spending on CSR activities in the period 2004-2009 is closest to which of the following options?

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

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

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

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

In a locality, there are ten houses in a row. 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?

If $$x=(9+4\sqrt{5})^{48} = [x] +f$$, where [x] is defined as integral part of x and f is a fraction, then x (1 - f) equals

Let $$a_{n} = 1 1 1 1 1 1 1..... 1$$, where 1 occurs n number of times. Then,
i. $$a_{741}$$ is not a prime.
ii. $$a_{534}$$ is not a prime.
iii. $$a_{123}$$ is not a prime.
iv. $$a_{77}$$ is not a prime.

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?

Mr. 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?

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CAT Content

XAT 2011

The maximum value of spending on CSR activities in the period 2004-2009 is closest to which of the following options?

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

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

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

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

In a locality, there are ten houses in a row. 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?

If $$x=(9+4\sqrt{5})^{48} = [x] +f$$, where [x] is defined as integral part of x and f is a fraction, then x (1 - f) equals

Let $$a_{n} = 1 1 1 1 1 1 1..... 1$$, where 1 occurs n number of times. Then, i. $$a_{741}$$ is not a prime.ii. $$a_{534}$$ is not a prime.iii. $$a_{123}$$ is not a prime.iv. $$a_{77}$$ is not a prime.

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?

Mr. 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?

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Let $$a_{n} = 1 1 1 1 1 1 1..... 1$$, where 1 occurs n number of times. Then,
i. $$a_{741}$$ is not a prime.
ii. $$a_{534}$$ is not a prime.
iii. $$a_{123}$$ is not a prime.
iv. $$a_{77}$$ is not a prime.