MAT 2004 Question Paper

Since the act has been repeated despite various warnings, so course I would only be another warning and would not help. Severe punishment to set example for him and others is inevitable. Thus, course II shall follow.

=> Ans - (B)

Such kind of products should be encouraged because they form important assets and will bring lot of profit in the country. So, India should use financial assistance. 

Thus only action I follows.

=> Ans - (A)

Quarter which has the highest revenue will also have the highest average revenue. Revenue of Quarter :

First = 4+5+10 = 19

Second = 6+6+10 = 22

Third = 8+5+12 = 25 

Fourth = 10+6+11 = 27     [MAX]

=> Ans - (D)

Total revenue for all the companies in all the quarters

= $$(4+5+10)+(6+6+10)+(8+5+12)+(10+6+11)=93$$

=> Ans - (D)

Statement A alone is insufficient, as there is no time given and statement B alone is sufficient, as the number of teachers and students are missing.

All the teachers can complete 1/5 of work in 1 hour and all students can complete 1/3 of work in 1 hour. Therefore in 1 hr they can complete 8/15 of work in 1 hour and total work will be completed in 15/8 hours.

$$\therefore$$ Statement B alone is sufficient.

=> Ans - (B)

A : When N is divided by 5, the remainder is 3.

=> $$N=5k+3$$, where $$k$$ is an whole number.

Let $$k=0$$, => $$N=3$$

Thus, when $$N^2=9$$ is divided by 5, remainder = 4

=> Statement A alone is sufficient.

Clearly, second statement is insufficient, as there can be multiple solutions.

=> Ans - (A)

Let the digits of the number be $$x$$ and $$y$$

Clearly, each statement alone is not sufficient as there can be many possibilities. By combining the above statements, we get :

=> $$x+y=4$$ and $$x-y=4$$

By solving above equations, we get : $$x=4$$ and $$y=0$$, thus number = 40

$$\therefore$$ Both statements together are sufficient.

=> Ans - (C)

If $$abc$$ is a multiple of 3, then $$(a+b+c)$$ will also be multiple of 3.

(A) : $$a=3$$ and $$b=4$$

=> $$3+4+c=3k$$, where $$k$$ is a natural number.

=> Possible values of $$c=2,5,8$$

Thus, statement A alone is not sufficient.

(B) : If C is odd, there can be multiple values of the number, thus statement B alone is insufficient.

By combining above statements together, we get the number as 345

$$\therefore$$ Both statements together are sufficient.

=> Ans - (C)

(A) : Perfect squares between 1 and 93 = 1,4,9,16,25,36,49,64,81

Perfect cubes between 1 and 93 = 1,8,27,64

=> Possible values of N = 1, 64

Thus, first statement alone is not sufficient.

(B) : Number of square roots between 1 and 93 = 1,2,3,4,5,6,7,8

Now, since it is divisible by 8, only one possible value of N exist, => $$N=64$$

$$\therefore$$ Statement B alone is sufficient.

=> Ans - (B)