Quantitative Ability

(a) Rs 8.60

Total yearly cost:

$12.90+16.00+18.00+21.90 = \text{Rs } 68.80$

Initial payment is half of this, Rs 34.40, so the remaining Rs 34.40 is split into four equal payments:

$\frac{34.40}{4} = \text{Rs } 8.60$

None of the options works, because the equation as printed has no solution.

For $x\neq 0$ (the expression is undefined at $x=0$), simplify the first term:

$\frac{2x}{x^2}=\frac{2}{x}$

so the equation becomes

$\frac{2}{x}+1=\frac{2}{x}+2 \;\Rightarrow\; 1=2,$

which is impossible for every $x$. Choice (d) $0$ is also not valid, since it makes $\frac{2x}{x^2}$ and $\frac{2}{x}$ undefined. The question appears to be misprinted in the source.

(a) $\frac{5}{\pi}$

Circumference $C=\pi d$, so

$d=\frac{C}{\pi}=\frac{5}{\pi}.$

(d) 3,072

Doubling every hour for 9 hours multiplies the count by $2^9=512$:

$6\times 512 = 3072.$

(b) $\frac{3p}{10}$

Perimeter: $p=2(x+y)$. With $x=\frac23 y$:

$p=2\left(\frac23 y+y\right)=2\cdot\frac53 y=\frac{10y}{3}$

$y=\frac{3p}{10}.$

(b) $0$

$2+a=2-a \;\Rightarrow\; a=-a \;\Rightarrow\; 2a=0 \;\Rightarrow\; a=0.$

(e) 81

Perimeter of A is 16, which is $\frac23$ of B, so B has perimeter $16\times\frac32=24$. Likewise C has perimeter $24\times\frac32=36$.

Side of C $=\frac{36}{4}=9$, so

$\text{Area}=9^2=81.$

(e) 12.5

Rye corresponds to 2 parts, so one part is $\frac52=2.5$ pounds. Wheat is 5 parts:

$5\times 2.5=12.5 \text{ pounds}.$

(e) $\frac{300}{c}\%$

$\frac{9}{3c}\times100\% = \frac{3}{c}\times 100\% = \frac{300}{c}\%.$

(d) $9+\sqrt{41}$

Points $D(-6,3)$, $E(-1,-1)$, $F(-1,3)$. $DF$ is horizontal and $EF$ is vertical, so the triangle is right-angled at $F$.

$DF=|-1-(-6)|=5,\qquad EF=|3-(-1)|=4$

$DE=\sqrt{5^2+4^2}=\sqrt{41}$

$\text{Perimeter}=5+4+\sqrt{41}=9+\sqrt{41}\approx 15.40.$