MAT 2012 Question Paper

Let's check option A, i.e check whether Science and Engineering streams has ratio 4:5

Total number of graduates in science = (22 + 28 + 34 + 32 + 40 + 12) x 1000 = 168 x 1000

Total number of graduates in Engineering = (24 + 28 + 62 + 58 + 12 + 26) x 1000 = 210 x 1000

Ratio = 168 x 1000 : 210 x 1000

= 4 : 5 

Hence, option A is the correct answer.

Percentage of IT graduates in state A,

= $$\frac{31}{46 + 31 + 23 + 22} \times 100 = \frac{3100}{122} = 25.4$$%

Percentage of IT graduates in state B,

= $$\frac{38}{41 + 38 + 28 + 28} \times 100 = \frac{38}{135} = 28.14$$%

Percentage of IT graduates in state C,

= $$\frac{22}{62 + 34 + 26 + 23} \times 100 = \frac{22}{145} = 15.17$$%

Percentage of IT graduates in state D,

= $$\frac{18}{59 + 45 + 31 + 18} \times 100 = \frac{18}{153} = 11.76$$%

Percentage of IT graduates in state E,

= $$\frac{27}{38 + 28 + 24 + 12} \times 100 = \frac{27}{102} = 26.47$$%

Percentage of IT graduates in state F,

= $$\frac{16}{54 + 25 + 16 + 11} \times 100 = \frac{16}{106} = 15.09$$%

$$\therefore$$ Percentage of IT graduates in C and F is mostly same.

Hence, option A is the correct answer.

Total number of Engineering graduates in B, C, F taken together = 28 + 62 + 26 = 116 x 1000

Total number of Arts graduates in D and E taken together = 45 + 24 = 69 x 1000

Required percentage = $$\frac{116 - 69}{69} \times 100 = \frac{47}{69} \times 100 = 68$$%

Hence, option B is the correct answer.

Total number of science graduates in all states = 164 x 1000

Total number of graduates of all other streams taken together = (155 + 235 + 210) = 600 x 1000

$$\therefore$$ Required percentage = $$\frac{164}{600} \times 100 = 27.9$$%(approx)

Hence, option B is the correct answer.

Difference between Engineering graduates and IT graduates and Science and arts graduates from all the states (in thousands) is given by,

In state A - |31 - 24| = 7 and |22 - 26| = 4

In state B - |38 - 28| = 10 and |28 - 42| = 14

In state C - |24 - 62| = 38 and |35 - 28| = 7

In state D - |18 - 58| = 40 and |32 - 45| = 13

In state E - |28 - 12| = 16 and |39 - 24| = 15

In state F - |18 - 26| = 8 and |12 - 52| = 40

Thus in states C, D, E Difference between Engineering graduates and IT graduates is higher than difference between Science graduates and

Arts graduates.

Hence, option D is the correct answer.

Sales of red colour refrigerator in all the given years in thousands = (20 + 30 + 45) = 95

Sales of Blue colour refrigerator in all the given years in thousands = (25 + 32 + 48) = 105

Sales of Lemon colour refrigerator in all the given years in thousands = (47 + 23 + 32) = 102

Sales of Grey colour refrigerator in all the given years in thousands = (2 + 27 + 34) = 63

Sales of White colour refrigerator in all the given years in thousands = (32 + 45 + 43) = 120

Highest selling colour is white. Percentage of volume it accounted for, is given by,

Required percentage = $$\frac{120}{95 + 105 + 102 + 63 + 120} \times 100$$

= $$\frac{12000}{485} = 25$$% (approx)

Hence, option B is the correct answer.

Percentage increase in red colour from 2010 to 2011 = $$\frac{45 - 30}{30} \times 100 = \frac{15}{30} \times 100 = 50$$%

Percentage increase in blue colour from 2010 to 2011 = $$\frac{48 - 32}{32} \times 100 = \frac{16}{32} \times 100 = 50$$%

Percentage increase in Lemon colour from 2010 to 2011 = $$\frac{32 - 23}{23} \times 100 = \frac{9}{23} \times 100 = 39.13$$%

Percentage increase in Grey colour from 2010 to 2011 = $$\frac{34 - 27}{27} \times 100 = \frac{7}{27} \times 100 = 25.92$$%

There is no increase from 2010 to 2011 in white colour.

Sales in red and blue colour registered highest percentage increase.

Hence, option C is the correct answer.

Sales in 2011 = 45 + 48 + 32 + 34 + 43 = 202

Sales of all the refrigrator's in all the years 

= (20 + 30 + 45) + (25 + 32 + 48) + (47 + 23 + 32) + (2 + 27 + 34) + (32 + 45 + 43) = 485

Share of sales volume accounted for by the year 2011 is given by,

= $$\frac{202}{485} \times 100 = 41.64$$

Hence, option D is the correct answer.

Total sales of Red, Lemon and White refrigrator taken together in 2010 = (30 + 23 + 45) = 98

Total sales of Blue and Grey ones in 2009 and 2011 taken together = (25 + 2 + 48 + 34) = 109

Ratio between them = 98 : 109 $$\cong$$ 9 : 10

Hence, option A is the correct answer.

Percentage in sale of refrigrator,

For red = $$\frac{15 - 10}{10} \times 100 = 50$$%

For Blue = $$\frac{16 - 7}{7} \times 100 = 128.5$$%

For Lemon = $$\frac{9 - 24}{24} \times 100 = -62.5$$%

For Grey = $$\frac{7 - 25}{25} \times 100 = -72.5$$%

For White = $$\frac{2 - 13}{13} \times 100 = -84.6$$%

There are 5 instances where the difference in sale of refrigrator was greater or lesser than 35% or more as compared to the previous year.

Hence, option B is the correct answer.