MAT 2005 Question Paper

Production in 2000 = $$17213\times83.2=Rs.$$ $$14,32,121.6$$

Production in 2003 = $$12338\times113=Rs.$$ $$13,94,194$$

% Change in production = $$\frac{1394194-1432121.6}{1432121.6}\times100=-2.6\%\approx-3\%$$

=> Ans - (A)

% Change in productivity = $$\frac{(113-83.2)}{83.2}\times100=35.8\%$$     [MAX]

% Change in workforce = $$\frac{(17213-12338)}{17213}\times100=28.3\%$$

Production in 2000 = $$17213\times83.2=Rs.$$ $$14,32,121.6$$

Production in 2003 = $$12338\times113=Rs.$$ $$13,94,194$$

% Change in production = $$\frac{1432121.6-1394194}{1432121.6}\times100=2.6\%$$

=> Ans - (B)

Workforce is directly proportional to workforce, it is clear that workforce and production have moved in the same direction. Both showed percentage drop over 2000-2003

=> Ans - (B)

Expression : $$-\left(\frac{3}{4}\right)x + 3 y - \left(\frac{1}{2}\right) = \left(\frac{3}{2}\right) y -\left(\frac{1}{4}\right) x$$ -------------(i)

I : $$y^2=4$$

=> $$y=\pm2$$

Case 1 : $$y=2$$ substituting in equation (i)

=> $$-(\frac{3}{4})x + 3 (2) - (\frac{1}{2}) = (\frac{3}{2}) \times(2) -(\frac{1}{4}) x$$

=> $$\frac{-2x}{4}=3-6+\frac{1}{2}$$

=> $$\frac{-x}{2}=\frac{-5}{2}$$

=> $$x=5$$

Case 2 : $$y=-2$$ substituting in equation (i)

=> $$-(\frac{3}{4})x + 3 (-2) - (\frac{1}{2}) = (\frac{3}{2}) \times(-2) -(\frac{1}{4}) x$$

=> $$\frac{-2x}{4}=-3+6+\frac{1}{2}$$

=> $$\frac{-x}{2}=\frac{7}{2}$$

=> $$x=-7$$

$$\because$$ Both cases have different values for $$x$$, thus, we cannot find value of $$x$$ using statement I alone.

II : $$y=2$$ substituting in equation (i)

=> $$-(\frac{3}{4})x + 3 (2) - (\frac{1}{2}) = (\frac{3}{2}) \times(2) -(\frac{1}{4}) x$$

=> $$\frac{-2x}{4}=3-6+\frac{1}{2}$$

=> $$\frac{-x}{2}=\frac{-5}{2}$$

=> $$x=5$$

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

=> Ans - (B)

Statement I : If x is the smallest integer on the list, then $$(x + 72)^{\frac{1}{3}} = 4$$

=> $$(x+72)=4^3=64$$

=> $$x=64-72=-8$$

Now, 11 consecutive integers starting from -8 : -8,-7,-6,-5,-4,-3,-2,-1,0,1,2

Thus, greatest integer is 2 and statement I alone is sufficient.

Statement II : If x is the smallest integer on the list, then $$\frac{1}{64} = x^{-2}$$

=> $$(x)^{2}=64$$

=> $$x=\pm8$$

Since, there are two values of $$x$$, we cannot find the greatest integer. statement II alone is insufficient.

=> Ans - (A)

Length of rectangle = $$a$$ and Width = $$b$$, => Area = $$ab$$

Statement I : $$2 a = \frac{15}{b}$$

=> $$ab=\frac{15}{2}=7.5$$

Area of rectangle is 7.5, hence statement I alone is sufficient.

Statement II : $$a = 2 b - 2$$

Since, there are no specific values of $$a$$ and $$b$$, we cannot find the area, hence statement II alone is not sufficient.

=> Ans - (A)

Let number of men and women enrolled be $$m$$ and $$w$$ respectively.

Statement I : $$w+3=\frac{m}{2}$$

=> $$m=2w+6$$

Since, we cannot find $$m:w$$, thus, statement I alone is insufficient.

Statement II : $$w=\frac{2}{5}\times m$$

=> $$\frac{m}{w}=\frac{5}{2}$$

Thus, statement II alone is sufficient to find the required ratio.

=> Ans - (B)

Statement I : $$2 a - b = 3$$

There are no specific values of $$a$$ and $$b$$, hence I alone is not sufficient.

Statement II : $$a = b - (1 - a)$$

=> $$a=b-1+a$$

=> $$b=1$$

$$\therefore$$ Statement II alone is sufficient to find the value of $$b$$.

=> Ans - (B)