RRB NTPC Graduate CBT 1 2024 PYQs

Concept: For half-yearly compounding, rate is halved and time (in periods) is doubled: $CI=P[{(1+\frac{r}{100})}^n-1]$.

1. Rate per half-year $=\frac{2}{2}=1\%$, periods $=2$.
2. ${\left(1.01\right)}^2-1=0.0201$.
3. $CI=670000\times 0.0201=13467$.

Trick: For 2 periods at $r\%$, effective rate $=2r+\frac{r^2}{100}=2.01\%$.

Answer: (B) ₹13,467

Concept: Correct sum $=$ wrong sum $-$ wrong value $+$ correct value.

1. Wrong sum $=10\times 40=400$.
2. Correct sum $=400-32+43=411$.
3. Correct average $=\frac{411}{10}=41.1$.

Trick: Change in average $=\frac{43-32}{10}=1.1$, so $40+1.1=41.1$.

Answer: (B) $41.1$

Concept: $(a+b{)}^2-(a-b{)}^2=4ab$.

1. $(a+b{)}^2={24}^2=576$.
2. $4ab=576-268=308$.
3. $ab=\frac{308}{4}=77$.

Trick: Product $=\frac{(\text{sum}{)}^2-(\text{difference}{)}^2}{4}$.

Answer: (A) $77$

Concept: If $a:b::b:c$, then $b^2=ac$.

1. $b^2=a\times 4a=4a^2\Rightarrow b=2a$.
2. $18=2a\Rightarrow a=9$.
3. $c=4a=36$.

Trick: $c=4a$ means $b=2a$ and $c=2b$ – directly $c=2\times 18=36$.

Answer: (A) $36$

Concept: Count days (exclude the first day, include the last) and use $SI=\frac{P\times R\times T}{100}$ with $T$ in years.

1. 2024 is a leap year: February days after 9th $=29-9=20$, March $=31$, April $=10$; total $=61$ days.
2. $T=\frac{61}{366}$ year.
3. $SI=\frac{3000\times 6\times 61}{100\times 366}=\frac{10980}{366}=30$.

Trick: Note $366=6\times 61$, so $\frac{61}{366}=\frac{1}{6}$ year → $SI=\frac{3000\times 6}{100\times 6}=30$.

Answer: (C) ₹30

Concept: $\text{Increase}\%=\frac{\text{New}-\text{Old}}{\text{Old}}\times 100$.

1. Increase $=140203-123016=17187$.
2. $\frac{17187}{123016}\times 100\approx 13.97\%$.
3. Rounded to the nearest integer $=14\%$.

Trick: $10\%$ of 123016 ≈ 12302, $4\%$ ≈ 4921; together ≈ 17223 – very close to 17187, so ≈ $14\%$.

Answer: (B) $14\%$

Concept: Single equivalent discount $=100-$ final price when the marked price is 100.

1. After 28%: $100\times 0.72=72$.
2. After 20%: $72\times 0.8=57.6$.
3. After 10%: $57.6\times 0.9=51.84$.
4. Single discount $=100-51.84=48.16\%$.

Trick: For two discounts use $a+b-\frac{ab}{100}$: $28,20\to 42.4$; then $42.4,10\to 42.4+10-4.24=48.16$.

Answer: (B) $48.16\%$

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

1. Distance 1 $=20\times 80=1600\text{m}$; distance 2 $=65\times 64=4160\text{m}$.
2. Total distance $=5760\text{m}$; total time $=144\text{min}$.
3. Average speed $=\frac{5760}{144}=40\text{m/min}$.

Trick: Never average the two speeds directly unless the times are equal.

Answer: (A) $40$

Concept: A quadrilateral whose diagonals are perpendicular bisectors of each other is a rhombus; $\text{Area}=\frac{1}{2}{d}_1{d}_2$.

1. $180=\frac{1}{2}\times 3\times d_2$.
2. $d_2=\frac{360}{3}=120\text{cm}$.

Trick: Product of diagonals $=2\times$ area $=360$, so other diagonal $=\frac{360}{3}$.

Answer: (B) $120$

Concept: In the division method the last divisor is the HCF; rebuild the numbers backwards using dividend $=$ divisor $\times$ quotient $+$ remainder. Then $\text{LCM}=\frac{a\times b}{\text{HCF}}$.

1. Last step: divisor 18, quotient 9, remainder 0 → dividend $=18\times 9=162$.
2. Middle step: divisor 162, quotient 5, remainder 18 → dividend $=162\times 5+18=828$.
3. First step: divisor 828, quotient 4, remainder 162 → dividend $=828\times 4+162=3474$.
4. Numbers 3474 and 828; $\text{LCM}=\frac{3474\times 828}{18}=3474\times 46=159804$.

Trick: The LCM must be divisible by the HCF 18: only 159804 is even with digit sum 27.

Answer: (C) 159804

Concept: Every digit (even or odd) gets $+2$.

1. $4713562\to 6935784$ (each digit $+2$).
2. First two digits: $6+9=15$; last two digits: $8+4=12$.
3. Sum $=15+12=27$.

Trick: Since both even and odd digits get $+2$, simply add 2 to every digit.

Answer: (B) $27$

Concept: Compare letter positions: 1st, 2nd and 3rd letters change by fixed amounts.

1. PNQ → QQO: $P+1=Q,N+3=Q,Q-2=O$.
2. UQR → VTP: $U+1=V,Q+3=T,R-2=P$.
3. OHM: $O+1=P,H+3=K,M-2=K$ → PKK ✔.

Trick: Pattern $(+1,+3,-2)$ — check only the option whose third letter fits first.

Answer: (A) OHM : PKK

Concept: Find the change in each letter position.

1. MWC → JYA: $M-3=J,W+2=Y,C-2=A$.
2. KUR → HWP: $K-3=H,U+2=W,R-2=P$.
3. JVP: $J-3=G,V+2=X,P-2=N$ → GXN ✔.

Trick: Pattern $(-3,+2,-2)$.

Answer: (C) JVP : GXN

Concept: Check the differences between consecutive terms.

1. Differences: $5,7,9,11$ — consecutive odd numbers.
2. Next difference $=13$.
3. $40+13=53$.

Trick: Terms are $n^2+4$: $4+4,9+4,16+4,25+4,36+4,49+4=53$.

Answer: (C) $53$

Concept: Look for the pattern number – symbol – number.

1. 7 & 9 ✔, 1 * 5 ✔, 5 ≺ 2 ✔, 6 ≡ 4 ✔, 4 ∆ 3 ✔.
2. ^ (9 ^ #), # , $ (3 $ @) and @ fail.
3. Count $=5$, i.e. more than three.

Trick: Scan the series once, marking each symbol that sits between two numbers.

Answer: (C) More than three

Concept: Find the shift from the first cluster to the second.

1. Try # = CMY: $C-8=U,M-8=E,Y-8=Q$ → UEQ ✔ (shift $-8$).
2. Apply $-8$ to QAM: $Q-8=I,A-8=S,M-8=E$ → ISE.
3. So # = CMY, % = ISE.

Trick: Backward shift wraps round: $A(1)-8\to 19=S$.

Answer: (C) # = CMY, % = ISE

Concept: Track each letter position separately.

1. 1st letters: Y, W, U, S → Q ($-2$).
2. 2nd letters: R, P, N, L → J ($-2$).
3. 3rd letters: U, S, Q, O → M ($-2$).

Trick: All three positions move $-2$ each step.

Answer: (C) QJM

Concept: Check the gap inside each cluster and between clusters.

1. RV – XE: $R+4=V$, $V+2=X$, $X+7=E$.
2. NR – TA: $+4,+2,+7$; XB – DK: $+4,+2,+7$.
3. DH – IQ: $+4,+1,+8$ → breaks the pattern.

Trick: Write gaps as a triple; the odd triple is the answer.

Answer: (B) DH – IQ

Concept: Test each condition in order; if none applies, code directly.

1. Codes: 3 → C, 9 → N, 8 → B, * → S.
2. Condition 1 fails (first element 3 is a number); condition 2 fails (last element * is not a number).
3. Condition 3 fails: 9 is not a perfect cube (8 is, but both are needed).
4. Direct coding: CNBS.

Trick: Check the first and last elements' type first — it rules out conditions 1 and 2 instantly.

Answer: (B) CNBS

Concept: Find how the 2nd and 3rd numbers come from the 1st.

1. $19\times 2+1=39$, $39+5=44$.
2. $13\times 2+1=27$, $27+5=32$.
3. $11\times 2+1=23$, $23+5=28$ ✔ (others fail, e.g. $29\times 2+1=59\ne 49$).

Trick: Third − second $=5$ in all; then test $2a+1$.

Answer: (C) (11, 23, 28)