RRB NTPC Graduate CBT 1 2024 PYQs

Concept: A product stays the same if the total shift of decimal points is zero.

1. Option B: $24.184$ is $÷100$; $7958$ is $\times 10$; $3.735$ is $\times 10$
2. Net factor $=\frac{10\times 10}{100}=1$
3. Others: A $=÷10$, C $=\times 100$, D $=÷100$

Trick: Count decimal places: original total = 1+1+4 = 6; option B = 3+0+3 = 6 ✓ (same digits).

Answer: (B) $24.184\times 7958\times 3.735$

Concept: Combined average $=\frac{\text{total of all ages}}{\text{total people}}$.

1. Group 1 total $=4\times 52=208$
2. Group 2 total $=6\times 58=348$
3. Average $=\frac{208+348}{10}=\frac{556}{10}=55.6$ years

Trick: Weighted: $52+\frac{6}{10}\times 6=55.6$.

Answer: (B) 55.6 years

Concept: If SP of $x$ items = CP of $y$ items, gain $\%=\frac{y-x}{x}\times 100$.

1. Let CP of 1 book $=₹1$; SP of 30 books $=₹36$
2. Gain on 30 books $=36-30=6$
3. Gain $\%=\frac{6}{30}\times 100=20\%$

Trick: $y>x$ → gain; divide by the items sold (30), not 36.

Answer: (D) $20\%$ gain

Concept: Make Q common in both ratios, then divide the profit.

1. $Q:R=3:12=1:4$; $P:Q=9:7$ → $P:Q:R=9:7:28$
2. Sum $=44$
3. R $=\frac{28}{44}\times 25300=28\times 575=₹16100$

Trick: $25300÷44=575$ – one part.

Answer: (B) 16,100

Concept: Expand the new areas and cancel $lb$ to get two linear equations.

1. $(l+6)(b-5)=lb+7$ → $-5l+6b=37$
2. $(l-6)(b+7)=lb+31$ → $7l-6b=73$
3. Add: $2l=110$ → $l=55$; then $6b=37+275=312$ → $b=52$
4. Perimeter $=2(55+52)=214$ m

Trick: Adding the two equations removes $b$ at once ($+6b$ and $-6b$).

Answer: (D) 214

Concept: Let $x$ = ₹50 notes, $y$ = ₹100 notes.

1. $x+y=33$ and $50x+100y=3200$ → $x+2y=64$
2. Subtract: $y=31$
3. $x=33-31=2$

Trick: If all 33 were ₹100 → ₹3300; extra ₹100 ÷ ₹50 saving per note $=2$ notes of ₹50.

Answer: (C) 2

Concept: Downstream speed $=b+s$, upstream speed $=b-s$.

1. Downstream $=12+10=22$ km/h; upstream $=12-10=2$ km/h
2. Time $=\frac{24.2}{22}+\frac{24.2}{2}=1.1+12.1$
3. Total $=13.2$ hours

Trick: Slow upstream speed dominates the time – answer must exceed 12.1 h.

Answer: (C) 13.2

Concept: Leak rate $=$ pump rate $-$ combined rate.

1. Pump $=\frac{1}{6}$ per hour; with leak $=\frac{1}{22/3}=\frac{3}{22}$ per hour
2. Leak $=\frac{1}{6}-\frac{3}{22}=\frac{11-9}{66}=\frac{1}{33}$
3. Leak empties the tank in 33 hours

Trick: Shortcut: $\frac{a\times b}{b-a}=\frac{6\times \frac{22}{3}}{\frac{22}{3}-6}=\frac{44}{\frac{4}{3}}=33$.

Answer: (D) 33 hours

Concept: ${\tan }^{2}A-{\sin }^{2}A={\sin }^{2}A({\sec }^{2}A-1)={\sin }^{2}A{\tan }^{2}A$.

1. $\sqrt{{\tan }^{2}A-{\sin }^{2}A}=\sin A\tan A$
2. Expression $=\frac{3}{{\sin }^{2}A\sec A}\times 3\sin A\tan A=\frac{9\tan A}{\sin A\sec A}$
3. $\sin A\sec A=\frac{\sin A}{\cos A}=\tan A$ → value $=9$

Trick: Put $A={45}^{\circ }$: $\frac{3}{\frac{1}{2}\sqrt{2}}\times 3\sqrt{1-\frac{1}{2}}=\frac{6}{\sqrt{2}}\times \frac{3}{\sqrt{2}}=9$.

Answer: (D) 9

Concept: Write the percentage as a fraction and cross-multiply.

1. $\frac{66}{100}x=\frac{5}{7}y$
2. $\frac{x}{y}=\frac{5}{7}\times \frac{100}{66}=\frac{500}{462}$
3. $=\frac{250}{231}$

Trick: $\frac{500}{462}$ – halve both: $250:231$.

Answer: (C) 250 : 231

Concept: Place the fixed person first, then the blocks of consecutive days.

1. P = Wednesday; 3 people between P and S ⇒ S = Sunday.
2. Q, T, V must be consecutive (Q–T–V); free days are Mon, Tue, Thu, Fri, Sat ⇒ Q = Thu, T = Fri, V = Sat.
3. 3 between U and T ⇒ U = Monday; R = Tuesday.
4. After Q (Thu): T, V, S = 3 people.

Trick: Fix the "exactly n between" person at the week ends first.

Answer: (A) 3

Concept: Identify the highest and lowest numbers, then pick the required digit.

1. Numbers: 190, 735, 494, 761, 781.
2. Highest = 781 → second digit 8.
3. Lowest = 190 → second digit 9.
4. $9-8=1$.

Trick: Order matters: "A subtracted from B" means $B-A$.

Answer: (D) 1

Concept: Find the positional shift of each letter.

1. Z→T, R→L, V→P, Y→S: each letter moves 6 places back.
2. W→Q, O→I, S→M, V→P: again −6.
3. U→O, M→G, Q→K, T→N ⇒ OGKN.

Trick: Check just the first letter of each option: U−6 = O rules out C and D; M−6 = G and Q−6 = K fixes B.

Answer: (B) OGKN

Concept: Common letters in two words share common digits.

1. LINK = 9236, SINK = 6349.
2. Common letters I, N, K ↔ common digits 9, 3, 6.
3. So L = the leftover digit of LINK = 2, and S = the leftover digit of SINK = 4.

Trick: Remove common digits; the remaining digit belongs to the remaining letter.

Answer: (D) 4

Concept: Apply the rule digit by digit.

1. 5637482: odd digits +1, even digits −2.
2. 5→6, 6→4, 3→4, 7→8, 4→2, 8→6, 2→0 ⇒ 6448260.
3. 6 appears twice, 4 appears twice; 8, 2, 0 once.
4. Digits appearing more than once: 6 and 4 ⇒ 2.

Trick: Write the new number under the old one to avoid slips.

Answer: (C) 2

Concept: Find the rule linking the three numbers of each set.

1. (29, 41, 53): $29+12=41,41+12=53$.
2. (37, 49, 61): $37+12=49,49+12=61$.
3. (53, 65, 77): $53+12=65,65+12=77$ ✓.
4. Others fail: $79+12=91\ne 101$, $48+12=60\ne 50$, $52+12=64\ne 74$.

Trick: Each set is an AP with common difference 12.

Answer: (A) (53, 65, 77)

Concept: Track each part of the cluster separately.

1. First letters: P, O, N, M → next L (−1).
2. Second letters: K, J, I, H → next G (−1).
3. Numbers: 23, 34, 45, 56 → next 67 (+11).
4. Next term = LG67.

Trick: Split the term into letter 1 | letter 2 | number.

Answer: (C) LG67

Concept: Test each possible position of the "4 between" pair.

1. T = Wednesday. 4 between S and R ⇒ pairs (Mon, Sat) or (Tue, Sun); Monday is not allowed ⇒ S, R on Tue and Sun.
2. Case S = Sun: U = Sat, R = Tue; then Q–P–V needs 3 consecutive days among Mon, Thu, Fri – impossible.
3. Case S = Tue: U = Mon, R = Sun; Q = Thu, P = Fri, V = Sat ✓.
4. Sunday ⇒ R.

Trick: Reject a case as soon as a consecutive block cannot fit.

Answer: (C) R

Concept: Find the shift for each letter position.

1. A→D, S→V, X→A, Z→C: each +3 (wrap Z→C).
2. M→P, E→H, J→M, L→O: each +3.
3. V→Y, N→Q, S→V, U→X ⇒ YQVX.

Trick: Only option A keeps the order "+3 on every letter": V+3 = Y, N+3 = Q, S+3 = V, U+3 = X.

Answer: (A) YQVX

Concept: Check every symbol for the pattern: number – symbol – symbol.

1. Series: @ 2 % * 4 2 & £ % 1 £ & 9 7 & 9 7 $ 9 1 $ 2.
2. 2 % * ✓; 2 & £ ✓; 1 £ & ✓.
3. 7 & 9, 7 $ 9 and 1 $ 2 fail (followed by a number).
4. Count = 3.

Trick: Look only at symbols whose left neighbour is a digit, then check the right neighbour.

Answer: (C) 3