RRB Technician Grade III 2024, 2025 PYQs

Concept: Lights turn red together again after LCM of their intervals.

1. $\text{LCM}(30,45,60)=180$ s
2. $180$ s $=3$ min
3. $8:30+3$ min $=8:33$ a.m.

Yaad rakhein: 'Together again' $\to$ LCM; 'largest equal part' $\to$ HCF.

Answer: (B) 8:33 a.m.

Concept: Mean proportional of $a$ and $b$ is $\sqrt{ab}$.

1. $\sqrt{25\times 36}=\sqrt{900}$
2. $=30$

Trick: For perfect squares: $\sqrt{25}\times \sqrt{36}=5\times 6=30$.

Answer: (D) 30

Concept: Multiplication and division have equal priority, so work them left to right inside the bracket.

1. $15\times 32=480$
2. $480÷2=240$
3. $240\times 5=1200$
4. $1200÷75=16$

Trick: Don't do $2\times 5$ first – that would give a wrong value; go strictly left to right.

Answer: (D) 16

Concept: Average of first $n$ natural numbers $=\frac{n+1}{2}$.

1. $n=10$
2. Average $=\frac{10+1}{2}=5.5$

Trick: For any equally spaced list, average $=\frac{\text{first}+\text{last}}{2}=\frac{1+10}{2}$.

Answer: (C) 5.5

Concept: The difference between two percentages of the same number is itself a percentage of that number.

1. $30\%-20\%=10\%$ of number $=12$
2. Number $=\frac{12\times 100}{10}=120$

Trick: $10\%=12$ $\Rightarrow$ $100\%=120$ – just shift the decimal.

Answer: (B) 120

Concept: Use $(a-b)(a^2+ab+b^2)=a^3-b^3$, $(a+b)(a^2-ab+b^2)=a^3+b^3$ and $(x-y)(x+y)=x^2-y^2$.

1. $(a+b)(a^2-ab+b^2)=a^3+b^3$
2. $(a-b)(a^2+ab+b^2)=a^3-b^3$
3. $(a^3+b^3)(a^3-b^3)=a^6-b^6$

Trick: Check with $a=2,b=1$: $3\times 1\times 3\times 7=63=2^6-1^6$.

Answer: (D) $a^6-b^6$

Concept: For $10$ (even) observations in ascending order, median $=$ average of the $5^{\text{th}}$ and $6^{\text{th}}$ values.

1. $5^{\text{th}}=x$, $6^{\text{th}}=x+2$.
2. ${\displaystyle \frac{x+(x+2)}{2}}=63\Rightarrow 2x+2=126\Rightarrow x=62$.
3. Check: $50<62<64<72$, so the order stays ascending.

Yaad rakhein: Even $n$: median $=\frac{1}{2}[{\left(\frac{n}{2}\right)}^{\text{th}}+{(\frac{n}{2}+1)}^{\text{th}}]$ value.

Answer: (B) 62

Concept: Complementary angles add up to ${90}^{\circ }$.

1. $x+y={90}^{\circ }$, $x-y={18}^{\circ }$
2. Smaller $y=\frac{{90}^{\circ }-{18}^{\circ }}{2}={36}^{\circ }$
3. Larger $={54}^{\circ }$

Trick: Smaller $=\frac{\text{sum}-\text{difference}}{2}$, larger $=\frac{\text{sum}+\text{difference}}{2}$.

Answer: (A) ${36}^{\circ }$

Concept: Three consecutive even numbers can be written $2n(2n+2)(2n+4)=8n(n+1)(n+2)$.

1. $n(n+1)(n+2)$ – three consecutive numbers – is always divisible by $3!=6$
2. So product is divisible by $8\times 6=48$
3. Check: $2\times 4\times 6=48$, so nothing larger always works

Trick: Smallest case $2\times 4\times 6=48$ is itself the answer – the greatest always-divisor can't exceed it.

Answer: (B) 48

Concept: If two numbers are in ratio $a:b$, write them as $ax$ and $bx$.

1. Numbers $=7x$ and $5x$; sum $12x=360\Rightarrow x=30$.
2. Difference $=7x-5x=2x=2\times 30=60$.

Trick: Difference $=\frac{\text{sum}\times (7-5)}{7+5}=\frac{360\times 2}{12}=60$.

Answer: (D) 60

Concept: Negative power flips the base: $a^{-n}={\left(\frac{1}{a}\right)}^n$; power $\frac{1}{2}$ means square root.

1. ${\left(\frac{1}{4}\right)}^{-1/2}=4^{1/2}$.
2. $4^{1/2}=\sqrt{4}=2$.

Trick: First flip the fraction to remove the minus sign, then take the root.

Answer: (B) 2

Concept: $x\%$ of $N=\frac{x}{100}\times N$.

1. $1.25\%=\frac{1.25}{100}=\frac{1}{80}$.
2. $\frac{1}{80}\times 1600=20$, i.e. ₹20.

Trick: $1\%$ of 1600 is 16 and $0.25\%$ is 4, so $1.25\%=16+4=20$.

Answer: (C) ₹20

Concept: Total marks obtained $=\text{average}\%\times \text{total maximum marks}$.

1. Maximum marks $=5\times 105=525$.
2. Total obtained $=80\%\times 525=420$.
3. Given four subjects: $89+92+98+81=360$.
4. Science $=420-360=60$.

Trick: Find total first, then subtract the known marks.

Answer: (C) 60

Concept: Part of a quantity in ratio $a:b$: $\frac{b}{a+b}\times \text{total}$.

1. Total parts $=3+2=5$.
2. Water $=\frac{2}{5}\times 10=4$ litres.

Trick: One part $=10÷5=2$ litres; water has 2 parts, so $2\times 2=4$ litres.

Answer: (D) 4 litres

Concept: Simplify signs first, then add using the LCM of denominators.

1. $\frac{9}{-16}=-\frac{9}{16}$ and $\frac{-5}{-12}=+\frac{5}{12}$.
2. LCM of 16 and 12 $=48$.
3. $-\frac{27}{48}+\frac{20}{48}=\frac{-7}{48}$.

Yaad rakhein: Two negatives give a positive: $\frac{-5}{-12}=\frac{5}{12}$.

Answer: (D) $\frac{-7}{48}$

Concept: When a transversal cuts two parallel lines, alternate interior angles are equal.

1. $\angle 1$ and $\angle 2$ lie on opposite sides of the transversal, between the parallel lines.
2. So $\angle 2=\angle 1={75}^{\circ }$.

Yaad rakhein: Alternate interior angles form a "Z" shape and are always equal; co-interior angles (a "C"/"U" shape) add to ${180}^{\circ }$.

Answer: (A) ${75}^{\circ }$

Concept: $\text{SI}=\frac{P\times R\times T}{100}\Rightarrow P=\frac{\text{SI}\times 100}{R\times T}$.

1. $P=\frac{1056\times 100}{16\times 3}=\frac{105600}{48}$.
2. $P=2200$, i.e. ₹2,200.

Trick: Interest for 3 years $=3\times 16\%=48\%$ of P; $48\%=1056\Rightarrow 1\%=22\Rightarrow 100\%=2200$.

Answer: (A) ₹2,200

Concept: Mode is the value that occurs most often.

1. Without $2k+1$: 6 occurs 3 times and 7 occurs 3 times (a tie).
2. For mode to be 6 alone, $2k+1=6$.
3. $2k=5\Rightarrow k=2.5$.

Trick: The unknown term must join the value given as the mode to break the tie.

Answer: (D) 2.5

Concept: Empirical formula: $\text{Mode}=3\text{Median}-2\text{Mean}$.

1. $3\text{Median}=\text{Mode}+2\text{Mean}=61.1+2\times 58.7$.
2. $3\text{Median}=61.1+117.4=178.5$.
3. $\text{Median}=\frac{178.5}{3}=59.5$.

Trick: Median always lies between mean and mode (here between 58.7 and 61.1) – only 59.5 fits.

Answer: (A) 59.5

Concept: Half-yearly: rate $=\frac{R}{2}$, time $=2T$; $A=P{(1+\frac{r}{100})}^n$.

1. Rate $=\frac{8}{2}=4\%$, periods $=2$.
2. $A=7500\times (1.04{)}^2=7500\times 1.0816$.
3. $A=8112$, i.e. ₹8,112.

Trick: Effective rate for $4\%$ twice $=4+4+\frac{4\times 4}{100}=8.16\%$; $8.16\%$ of 7500 $=612$, so $A=8112$.

Answer: (B) ₹8,112