RRB NTPC Graduate CBT 1 2024 PYQs

Concept: If $X\propto \frac{1}{Y}$ and $Y\propto \frac{1}{Z}$, then $X\propto Z$, i.e. $X=kZ$.

1. $X=\frac{k_1}{Y}$ and $Y=\frac{k_2}{Z}$ give $X=\frac{k_1}{k_2}Z=kZ$.
2. $\frac{1}{2}=k\times \frac{1}{74}\Rightarrow k=37$
3. When $Z=7$: $X=37\times 7=259$

Trick: Two inverse variations make a direct variation: $\frac{X_2}{X_1}=\frac{Z_2}{Z_1}$, so $X=\frac{1}{2}\times 7\times 74=259$.

Answer: (A) $259$

Concept: $\text{SP}=\text{MP}\times (1-d_1)(1-d_2)$ and $\text{SP}=\text{CP}\times (1+\text{gain})$.

1. Required SP $=3300\times 1.33=4389$
2. Net factor after discounts $=0.75\times 0.70=0.525$
3. $\text{MP}=\frac{4389}{0.525}=8360$

Trick: Successive 25% and 30% = single discount of $25+30-\frac{25\times 30}{100}=47.5\%$.

Answer: (B) ₹8,360

Concept: Every factor of $x$ must divide the LCM, and the LCM must still be reached.

1. $44=2^2\times 11$, $86=2\times 43$, $7568=2^4\times 11\times 43$
2. $\text{LCM}(44,86)=2^2\times 11\times 43=1892$; so $x$ must supply $2^4$ and have no other primes.
3. $176=2^4\times 11$ ✔; 145, 165 contain 5, and 101 is prime – they do not divide 7568.

Trick: Quick test: the option must divide 7568 – only $7568÷176=43$ works.

Answer: (D) $176$

Concept: At a loss of $l\%$, $\text{SP}=\text{CP}\times \frac{100-l}{100}$.

1. $344=\text{CP}\times \frac{43}{100}\Rightarrow \text{CP}=800$
2. For 71% profit: $\text{SP}=800\times \frac{171}{100}=1368$

Trick: Direct ratio: $\text{new SP}=344\times \frac{171}{43}=8\times 171=1368$.

Answer: (A) $1,368$

Concept: $\cos A\cos B-\sin A\sin B=\cos (A+B)$

1. $\cos {42}^{\circ }\cos {18}^{\circ }-\sin {42}^{\circ }\sin {18}^{\circ }=\cos ({42}^{\circ }+{18}^{\circ })$
2. $=\cos {60}^{\circ }=\frac{1}{2}$

Trick: 'cos cos minus sin sin' → cos of the sum; angles here add to ${60}^{\circ }$.

Answer: (B) $\frac{1}{2}$

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

1. $\text{SI}=\frac{2200\times 7\times 2}{100}$
2. $=22\times 14=308$

Trick: 1 year interest = 154; two years = 308.

Answer: (D) ₹308

Concept: Powers first, then ÷ and × from left to right, then + and −.

1. $3^2=9$; $91÷13\times 9=7\times 9=63$
2. $18\times 14÷2=252÷2=126$
3. $z=63-126+11=-52$

Trick: Do × and ÷ strictly left to right – never multiply before an earlier division.

Answer: (D) $-52$

Concept: Total = average × number of items.

1. Total of 5 students $=5\times 60=300$
2. Total of 6 students $=6\times 62=372$
3. New student $=372-300=72\text{kg}$

Trick: New member = new average + (old count × rise) $=62+5\times 2=72$.

Answer: (D) $72\text{kg}$

Concept: For an odd number $n$ of observations, median = ${\left(\frac{n+1}{2}\right)}^{\text{th}}$ value after arranging in order.

1. Ascending: 15, 19, 26, 46, 53, 72, 80, 82, 86, 87, 91
2. $n=11\Rightarrow \frac{11+1}{2}=6^{\text{th}}$ value
3. 6th value = 72

Trick: Always sort first; the unsorted middle value (91) is a trap.

Answer: (B) $72$

Concept: Sum of exterior angles of any polygon $={360}^{\circ }$; sum of interior angles $=(n-2)\times {180}^{\circ }$.

1. 200% more than 360° means $3\times {360}^{\circ }={1080}^{\circ }$.
2. $(n-2)\times 180=1080\Rightarrow n=8$
3. Each interior angle $=\frac{{1080}^{\circ }}{8}={135}^{\circ }$

Trick: Each exterior angle $=\frac{{360}^{\circ }}{8}={45}^{\circ }$, so interior $={180}^{\circ }-{45}^{\circ }={135}^{\circ }$.

Answer: (D) $135$

Concept: Change every digit by the given rule, then read the required position.

1. Number: 8 3 1 5 4 7 6.
2. Odd digits +1: 3→4, 1→2, 5→6, 7→8. Even digits −2: 8→6, 4→2, 6→4.
3. New number: 6 4 2 6 2 8 4.
4. From the right: 4 (1st), 8 (2nd), 2 (3rd).

Trick: For 'third from right' you only need the last three digits: 5476 → …2 8 4.

Answer: (D) 2

Concept: Find the rule from the complete pair LHF : FBZ, then apply it backwards to get #.

1. L(12)−6=F(6), H(8)−6=B(2), F(6)−6=Z (wrap-around). So the rule is: each letter −6.
2. # → XTR means #−6 = XTR, so # = XTR + 6 each: X+6=D, T+6=Z, R+6=X → DZX.
3. Check: D−6=X, Z−6=T, X−6=R ✓.

Trick: Backward 6 in the alphabet = forward 20; going past A, continue from Z.

Answer: (B) # = DZX, % = FBZ

Concept: Check differences, and then the differences of the differences.

1. Differences: 7−4=3, 13−7=6, 24−13=11, 42−24=18.
2. Second differences: 3, 5, 7 → next 9, 11.
3. Next differences: 18+9=27, 27+11=38.
4. ? = 42+27 = 69; check 69+38 = 107 ✓.

Trick: Second differences forming odd numbers 3, 5, 7, 9… is a very common RRB pattern.

Answer: (C) 69

Concept: Apply the rule to each digit and count the digits that repeat.

1. Number: 7 1 5 6 4 2 3.
2. Odd +2: 7→9, 1→3, 5→7, 3→5. Even −1: 6→5, 4→3, 2→1.
3. New number: 9 3 7 5 3 1 5.
4. 3 appears twice and 5 appears twice; 9, 7, 1 appear once → two digits repeat.

Trick: Count distinct digits that repeat, not total repetitions.

Answer: (A) Two

Concept: Track the facing direction after each turn and add/subtract along each axis.

1. South 21 (facing S); right → West 19; right → North 26; right → East 19.
2. Net so far: 26−21 = 5 km north of A, 19−19 = 0 east-west.
3. Right → South 2 (now 3 km N); left → East 4; right → South 3 (now 0 km N).
4. P is exactly 4 km east of A, so he must drive 4 km to the west.

Trick: Right turn from S = W, from W = N, from N = E, from E = S — the clockwise order N→E→S→W.

Answer: (D) 4 km to the west

Concept: Check the conditions in order; apply the one that fits, else use direct codes.

1. Group: # 6 @ 2 → first is a symbol (#), last is a number (2): condition (i) applies.
2. (ii) fails (first is not odd number); (iii) fails (6 and @ are not perfect squares).
3. Direct codes: # = D, 6 = L, @ = Z, 2 = E.
4. Interchange first and last codes: E L Z D.

Trick: Write the direct code first (DLZE), then just swap the ends → ELZD.

Answer: (C) ELZD

Concept: Draw the minimum Venn diagram: 'Animals' lies inside Deer, Bears and Cows together.

1. Animals are both cows and bears, so the region of cows and bears overlaps → 'Some cows are bears' is definite. (II) follows.
2. Deer and Cows only share the animals; some deer may lie outside Cows → 'All deer are cows' is not certain. (I) does not follow.

Trick: All A are B + All A are C ⇒ Some B are C (always). 'All B are C' never follows.

Answer: (D) Only conclusion (II) follows.

Concept: Check each condition on the group @ 9 # 7.

1. First element @ is a symbol, last 7 is a number → condition (i) applies.
2. (ii) fails; (iii) fails because # is not a perfect square (only 9 is).
3. Direct codes: @ = A, 9 = D, # = G, 7 = P → A D G P.
4. Interchange first and last: P D G A.

Trick: In condition (iii) BOTH the 2nd and 3rd elements must be squares; one square is not enough.

Answer: (C) PDGA

Concept: Write the original and the arranged numbers one below the other and compare place by place.

1. Original: 1 6 7 3 4 5 9.
2. Ascending: 1 3 4 5 6 7 9.
3. Same place: 1st (1) and 7th (9); all others differ.

Trick: Smallest digit already first and largest already last — check these two quickly.

Answer: (D) Two

Concept: Draw the family tree with gender signs.

1. D is A's father and B is A's mother, so B is D's wife.
2. C is D's sister and E is C's brother, so E is D's brother.
3. B is the wife of E's brother.

Trick: Sister's brother of a father = father's brother (or the father himself); here E ≠ D, so E is the uncle.

Answer: (A) Brother’s wife