Q&A: practice questions with answers

Concept: New average $=\frac{\text{old sum}+\text{new numbers}}{\text{new count}}$.

1. Old sum $=12\times 38=456$.
2. New sum $=456+50+62=568$, count $=14$.
3. $\frac{568}{14}=40.571\dots \approx 40.57$.

Trick: Extras above 38: $12+24=36$ spread over 14 numbers $=\frac{36}{14}=2.57$; $38+2.57=40.57$.

Answer: (A) 40.57

Concept: Exterior angle $={180}^{\circ }-\text{interior}$, and number of sides $n=\frac{{360}^{\circ }}{\text{exterior angle}}$.

1. Exterior angle $={180}^{\circ }-{162}^{\circ }={18}^{\circ }$.
2. $n=\frac{360}{18}=20$.

Trick: Always switch to the exterior angle – it avoids solving $\frac{(n-2)180}{n}=162$.

Answer: (D) 20

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

1. Between 9 and 16: $\sqrt{144}=12$; twice of it $=24$.
2. $\sqrt{12x}=24\Rightarrow 12x=576\Rightarrow x=48$.

Trick: $\sqrt{9\times 16}=3\times 4=12$ – multiply the square roots instead of the numbers.

Answer: (C) 48

Concept: Two unknowns, two conditions (count and total value).

1. Let A $=a$, so B $=120-a$.
2. $12a+8(120-a)=1120\Rightarrow 4a+960=1120\Rightarrow 4a=160$.
3. $a=40$.

Trick: Alligation: if all 120 were B, sale $=960$; extra $160$ comes from A at ₹4 more each $\Rightarrow 40$ pens.

Answer: (A) 40

Concept: Same principal and time, so difference in SI $=P\times (\text{rate difference})\times T÷100$.

1. Rate difference $=6.5-3.5=3\%$.
2. Difference $=\frac{260000\times 3\times 2}{100}=15600$.

Trick: No need to compute both interests – work directly with the 3% gap.

Answer: (D) 15,600

Concept: Find the gap (difference in alphabetical position) between consecutive letters in each cluster; the one with a different pattern is the odd one.

1. BAE: B→A $=-1$, A→E $=+4$.
2. AZD: A→Z $=-1$, Z→D $=+4$ (wrapping past Z); EDH: E→D $=-1$, D→H $=+4$.
3. RQT: R→Q $=-1$, Q→T $=+3$ – breaks the $(-1,+4)$ pattern.

Trick: Write positions (A=1 … Z=26) and compute differences; a single different gap gives the odd one.

Answer: (B) RQT

Concept: Scan every vowel in the given sequence and check whether the letter just before it and the letter just after it are both consonants.

1. Series: V A R V Y R A C M W S A I G Z O W V R R F.
2. A (2nd): V–A–R ✓; A (7th): R–A–C ✓; O (16th): Z–O–W ✓.
3. A (12th) is followed by vowel I ✗; I (13th) is preceded by vowel A ✗. Total = 3.

Trick: Underline vowels first, then look only at their two neighbours – ignore everything else.

Answer: (A) Three

Concept: Decode each symbol step by step and build the family tree; then trace the path from Z to T.

1. T $\surd$ U: T is the father of U. U ÷ V: U is the daughter of V → V is the mother of U, so T and V are husband and wife.
2. V $\wedge$ W: V is the mother of W → T is also the father of W.
3. W ! Z: W is the wife of Z → T is the father of Z's wife, i.e. T is Z's wife's father (father-in-law).

Trick: Start from the person asked about (Z) and walk backwards: Z → wife W → her father T.

Answer: (C) Wife’s father

Concept: Find how each letter of the first cluster changes to give the second cluster, then apply the same shifts to the options.

1. FHI : GBE → F$+1$=G, H$-6$=B, I$-4$=E. KXN : LRJ → K$+1$=L, X$-6$=R, N$-4$=J. Pattern $(+1,-6,-4)$.
2. BNU → B$+1$=C, N$-6$=H, U$-4$=Q = CHQ ✓.
3. HLP → IFL (not IFM); MHD → NBZ; FKK → GEG – all fail.

Trick: Test the first letter shift on all options first; here all give $+1$, so check the second letter ($-6$) next – it eliminates nothing, then the third ($-4$) decides.

Answer: (A) BNU : CHQ

Concept: Number the positions 1 (top) to 7 (bottom) and place the boxes using the definite clues first.

1. P is 2nd from top → P = 2. N is immediately above P → N = 1.
2. Only M is below O → O = 6, M = 7. R is immediately above O → R = 5.
3. Three boxes between L and M → L = 3. Remaining Q = 4.
4. Between Q (4) and M (7): R and O → two boxes.

Trick: Fix the "ends" first (top-2, bottom-2), the middle fills itself.

Answer: (B) Two

Concept: Compare the same position of successive clusters; each position usually moves by a constant step.

1. 1st letters: D, H, L, P → $+4$ each → next T.
2. 2nd letters: X, C, H, M → $+5$ each (X$+5$ = C wrapping) → next R.
3. 3rd letters: N, R, V, Z → $+4$ each → next D (Z$+4$ = D). So TRD.

Trick: Steps of $+4$ and $+5$: after Z continue from A (Z→A→B→C→D).

Answer: (C) TRD

Concept: Apply the rule letter by letter: vowel → next letter, consonant → previous letter, then count repeats.

1. B A C K L O G → B$-1$=A, A$+1$=B, C$-1$=B, K$-1$=J, L$-1$=K, O$+1$=P, G$-1$=F.
2. New group: A B B J K P F.
3. B appears exactly twice; K, P appear once and J once.

Trick: Write the word vertically and convert each letter – avoids skipping one.

Answer: (B) B

Concept: Number seats 1 to 7 from left to right (all face north, so left/right are as we see them). Place people from the most definite clue.

1. Only two to the left of O → O = 3. Three between O and Z → Z = 7.
2. One between Z and D → D = 5. A is immediately left of J → the only free adjacent pair is (1, 2): A = 1, J = 2.
3. B is not a neighbour of Z → B = 4, T = 6. So T sits immediately right of D.

Trick: For north-facing rows: right = higher seat number. "Only two to the left" pins a seat instantly.

Answer: (A) T

Concept: Look at the successive differences; here they themselves change by a constant.

1. Differences: $184-164=20$, $164-145=19$, $145-127=18$, $127-110=17$, $110-94=16$.
2. Differences decrease by 1, so next difference $=15$.
3. $94-15=79$.

Trick: When numbers fall slowly, test differences first – a neat 20, 19, 18 … settles it.

Answer: (D) 79

Concept: Compare corresponding letters of consecutive clusters to find the constant shift.

1. 1st letters: T, V, X, Z → $+2$ → next B (Z→A→B).
2. 2nd letters: W, Y, A, C → $+2$ → next E.
3. 3rd letters: Y, A, C, E → $+2$ → next G. Answer BEG.

Trick: Every position moves $+2$; after Z wrap round to A.

Answer: (B) BEG

Concept: Number positions 1 (top) to 7 (bottom) and use the definite clues first.

1. No box above E → E = 1. Only B between E and Q → B = 2, Q = 3.
2. Only R below C → C = 6, R = 7.
3. One box between Q and D → D = 5. Remaining S = 4.
4. Between S (4) and R (7): D and C → two boxes.

Trick: "No box above X" / "only Y below X" fix the top and bottom immediately.

Answer: (C) Two

Concept: Number positions 1 (top) to 7 (bottom). Convert each clue into a position.

1. Five boxes above D → D = 6. Three between D and C → C = 2 (position 10 is impossible).
2. Four between C and S → S = 7. Only E between C and B → E = 3, B = 4 (upward is impossible).
3. R is above C → R = 1. Remaining Q = 5.
4. Between Q (5) and S (7): only D → one box.

Trick: With 7 boxes, "$n$ between" has two candidates – reject the one that falls outside 1–7.

Answer: (B) One

Concept: Replace the letters by the given operators and simplify using BODMAS (division and multiplication before addition and subtraction).

1. $22\text{C}10\text{D}9\text{A}21\text{B}42=22+10-9÷21\times 42$.
2. $9÷21\times 42=\frac{9}{21}\times 42=18$.
3. $22+10-18=14$.

Trick: Do $÷$ and $\times$ left to right first; $\frac{9}{21}\times 42$ is just $9\times 2$.

Answer: (C) 14

Concept: Find the shift from the first letter to the third and from the second to the fourth in each pair.

1. OR–LE: O→L $=-3$, R→E $=-13$. BE–YR: B→Y $=-3$ (wrap), E→R $=-13$ (wrap). MP–JC: M→J $=-3$, P→C $=-13$.
2. KM–HA: K→H $=-3$, but M→A $=-12$ – different.
3. So KM–HA is the odd one.

Trick: Treat the alphabet as a circle (26 letters): E$-13$ → R, B$-3$ → Y.

Answer: (A) KM – HA

Concept: Draw a Venn diagram from the statements and test each conclusion; a conclusion follows only if it is true in every possible diagram.

1. "All diesels are petrol" → Diesel circle lies inside Petrol. "Some petrol are fuels" → Petrol and Fuel overlap.
2. Conclusion I "No fuel is petrol" contradicts the given overlap → does not follow.
3. Conclusion II "No petrol is diesel" contradicts "All diesels are petrol" (some petrol are definitely diesel) → does not follow.

Trick: A "No…" conclusion can never follow when the statements already say "All/Some" between the same two terms.

Answer: (A) Neither conclusion (I) nor (II) follows