Q&A: practice questions with answers

Concept: Brackets first, then division, then addition.

1. $(3+5)÷2=4$
2. $[6+4]=10$
3. $10÷2=5$
4. $5+5=10$

Trick: Inside a bracket, division comes before addition.

Answer: (C) $10$

Concept: Number of partners $=\frac{\text{total allocation}}{\text{average salary}}$.

1. Partners in 2022 $=\frac{13.44\times {10}^7}{21000}=6400=6.4$ thousand
2. 2021 (Emazon) $=5.0$ thousand
3. Increase $=\frac{6.4-5.0}{5.0}\times 100=28\%$

Trick: $1.4$ on $5$ is $28\%$ (since $1$ on $5$ is $20\%$).

Answer: (C) $28\%$

Concept: $x+\frac{1}{x}=2$ holds only for $x=1$.

1. $x=1$
2. $(1+\frac{4}{1})(1-\frac{4}{1})=5\times (-3)=-15$

Trick: Whenever $x+\frac{1}{x}=2$, put $x=1$ directly.

Answer: (C) $-15$

Concept: Angles ${30}^{\circ }$ at A and ${60}^{\circ }$ at C make $\angle B={90}^{\circ }$, so AC is the hypotenuse.

1. $\angle B={180}^{\circ }-{30}^{\circ }-{60}^{\circ }={90}^{\circ }$
2. $B{C}^2=A{C}^2-A{B}^2=169-144=25$
3. $BC=5$ cm

Trick: 5-12-13 is a Pythagorean triplet.

Answer: (B) $5$ cm

Concept: Total work in man-days stays constant.

1. Total $=18\times 96=1728$ man-days
2. Done in 26 days $=18\times 26=468$; left $=1260$
3. With 28 workers: $\frac{1260}{28}=45$ days
4. Total $=26+45=71$ days

Trick: Convert to man-days, subtract what is done, divide by the new strength.

Answer: (C) $71$

Concept: Use the column totals.

1. Science total $=11200$
2. MBA total $=6960$
3. Difference $=11200-6960=4240$

Trick: Read the 'Total' row instead of adding all cities again.

Answer: (A) $4240$

Concept: Under SI, interest grows equally every year.

1. Amount $=9P\Rightarrow$ SI $=8P$ in 20 years, i.e. $0.4P$ per year
2. Amount $=13P\Rightarrow$ SI $=12P$
3. Time $=\frac{12P}{0.4P}=30$ years

Trick: $(9-1):(13-1)=8:12$, so time $=20\times \frac{12}{8}=30$.

Answer: (B) $30$

Concept: Tin fraction: A $=\frac{3}{8}$, B $=\frac{1}{4}$.

1. Tin in A $=80\times \frac{3}{8}=30$ kg
2. Tin in B $=100\times \frac{1}{4}=25$ kg
3. Total tin $=55$ kg

Trick: Find each component separately, then add.

Answer: (B) $55$

Concept: Let enrolled voters $=N$; valid votes $=0.9N-75$.

1. Winner $=0.5N$; loser $=0.9N-75-0.5N=0.4N-75$
2. Margin: $0.5N-(0.4N-75)=0.1N+75=170$
3. $N=950$

Trick: Check: $N=950$: valid $=780$, winner $475$, loser $305$, margin $170$.

Answer: (C) $950$

Concept: Surface area $\propto r^2$.

1. New $r=1.4r$
2. New area $=1.96\times$ old
3. Increase $=96\%$

Trick: Successive % : $40+40+\frac{40\times 40}{100}=96\%$.

Answer: (C) $96\%$

Concept: BODMAS: powers first, then $\times$ and $÷$ left to right, then $+$ and $-$.

1. $(4^2{)}^2=4^4=256$
2. $4\times 4÷4=4$
3. $256+4-4=256=4^4$

Trick: $+4-4$ cancels, leaving $(4^2{)}^2=4^4$.

Answer: (D) $4^4$

Concept: Two successive discounts: $\text{SP}=\text{MP}\times 0.9\times 0.9$.

1. $\text{MP}\times 0.81=7290$
2. $\text{MP}=\frac{7290}{0.81}=9000$

Trick: Net discount of 10% and 10% $=19\%$.

Answer: (B) ₹9,000

Concept: Average speed $=\frac{\text{total distance}}{\text{total time}}$.

1. Distance $=2\times 12.5=25$ km
2. Time $=30+20=50$ min $=\frac{5}{6}$ h
3. Speed $=25÷\frac{5}{6}=30\text{km/h}$

Trick: Never average the two speeds ($25$ and $37.5$) directly.

Answer: (A) $30$

Concept: Simplify from the bottom upwards.

1. $2+\frac{1}{3}=\frac{7}{3}$, so $\frac{1}{7/3}=\frac{3}{7}$
2. $5+\frac{3}{7}=\frac{38}{7}$, so $\frac{1}{38/7}=\frac{7}{38}$
3. $1+\frac{7}{38}=\frac{45}{38}$, so $\frac{1}{45/38}=\frac{38}{45}$
4. $1+\frac{38}{45}=1\frac{38}{45}$

Trick: Each step: add, then flip the fraction.

Answer: (B) $1\frac{38}{45}$

Concept: Gain% $=(\frac{\text{SP of goods given}}{\text{CP of goods given}}-1)\times 100$.

1. Take CP $=1$ per kg; he charges $0.8$ for '1 kg'
2. He actually gives $0.75$ kg costing $0.75$
3. $\frac{0.8}{0.75}=\frac{16}{15}\Rightarrow$ profit $=\frac{1}{15}\times 100=6.67\%$

Trick: $\frac{100-20}{100-25}=\frac{80}{75}$.

Answer: (A) $6.67\%$, profit

Concept: $y=\frac{1}{\sin A}+\frac{1}{\cos A}=\frac{\sin A+\cos A}{\sin A\cos A}$ and $x^2=1+2\sin A\cos A$.

1. $\sin A\cos A=\frac{x^2-1}{2}$
2. $y=\frac{2x}{x^2-1}\Rightarrow x^{2}y-y=2x$
3. $y+2x=x^{2}y$

Trick: Check with $A={45}^{\circ }$: $x=\sqrt{2},y=2\sqrt{2}$; $2\sqrt{2}+2\sqrt{2}=2\times 2\sqrt{2}$ ✔.

Answer: (A) $y+2x=x^{2}y$

Concept: All percentages are of total voters.

1. B's share $=100-27-19=54\%$
2. $1\%=\frac{125982}{54}=2333$
3. A $=27\times 2333=62991$

Trick: A's 27% is exactly half of B's 54%: $\frac{125982}{2}=62991$.

Answer: (B) 62,991

Concept: Solve inner brackets first.

1. $38-(-6)=44$; $9-(8-1)=2$; product $=88$
2. $6+(-4)=2$; $4\times 2=8$
3. $88÷8=11$

Trick: Minus of a negative becomes plus.

Answer: (C) $11$

Concept: Work per hour (rate) adds up.

1. Mitu $=\frac{1}{12}$; Mitu + Situ $=\frac{1}{3}\Rightarrow$ Situ $=\frac{1}{3}-\frac{1}{12}=\frac{1}{4}$
2. Titu + Situ $=\frac{1}{2}\Rightarrow$ Titu $=\frac{1}{2}-\frac{1}{4}=\frac{1}{4}$
3. Titu alone: 4 hours

Trick: LCM 12 units: M = 1, M+S = 4, T+S = 6 ⇒ S = 3, T = 3 ⇒ $12÷3=4$.

Answer: (B) 4 hours

Concept: In an equilateral triangle the median is also the altitude: length $=\frac{\sqrt{3}}{2}a$.

1. $DG=6$, $\angle FGD={90}^{\circ }$
2. $FG=\sqrt{{12}^2-6^2}=\sqrt{108}=6\sqrt{3}$ cm

Trick: Median of equilateral triangle $=\frac{\sqrt{3}}{2}\times 12=6\sqrt{3}$.

Answer: (B) $6\sqrt{3}$