[Download PDF] XAT 2011 - QUANT 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 59

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

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 increase in CSR spending 2006 is more than 1.5 times as compared to previous year whereas for none of the other values this is true. Hence, option B is the correct answer.

Question 60

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

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 = $${5/3}{100}\times 100$$ = 1 crore.

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

CSR/ Assets ratio for the year 2004 = $$\dfrac{1}{100}$$ = 0.01

CSR/ Assets ratio for the year 2005 = $$\dfrac{1.15}{110}$$ = 0.01045

CSR/ Assets ratio for the year 2006 = $$\dfrac{2}{125}$$ = 0.016

CSR/ Assets ratio for the year 2007 = $$\dfrac{2}{135}$$ = 0.0148

CSR/ Assets ratio for the year 2008 = $$\dfrac{2.5}{150}$$ = 0.0166

We can see that CSR/Asset ratio is maximum for the year 2008. Hence, option E is the correct answer.

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.

CAT Content

XAT 2011 - QUANT

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

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

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.

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CAT Content

XAT 2011 - QUANT

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

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

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.

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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.