Q&A: practice questions with answers

Concept: Price after discounts = MP × product of $(1-d)$ factors.

1. $0.82\times 0.76\times 0.82$
2. $0.82\times 0.82=0.6724$
3. $0.6724\times 0.76=0.511024\approx 51.10\%$

Trick: Two equal 18% discounts: ${0.82}^2=0.6724$ first, then ×0.76.

Answer: (A) 51.10%

Concept: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

1. $a=3,b=-7,c=1$
2. $D=49-12=37$
3. $x=\frac{7\pm \sqrt{37}}{6}$

Trick: Sum of roots $=\frac{7}{3}$ must be positive — check options with it.

Answer: (B) $\frac{7+\sqrt{37}}{6}$ & $\frac{7-\sqrt{37}}{6}$

Concept: Profit% = $\frac{\text{SP}-\text{CP}}{\text{CP}}\times 100$ on the goods actually given.

1. He charges for 1134 g: $\text{SP}=1.134\times 17=19.278$
2. He gives 567 g: $\text{CP}=0.567\times 20=11.34$
3. Profit $=7.938$; $\%=\frac{7.938}{11.34}\times 100=70\%$

Trick: $\frac{\text{SP}}{\text{CP}}=\frac{17}{20}\times \frac{1134}{567}=\frac{17}{10}=1.7$ → 70% profit.

Answer: (C) Profit of 70%

Concept: B's rate = combined rate − A's rate.

1. $\frac{1}{14}-\frac{1}{56}=\frac{4-1}{56}=\frac{3}{56}$
2. B alone: $\frac{56}{3}$ days
3. $\frac{3}{4}$ work: $\frac{3}{4}\times \frac{56}{3}=14$ days

Trick: Total work 56 units: A = 1, B = 3 per day; $\frac{3}{4}$ of 56 = 42 → $42÷3=14$.

Answer: (A) 14

Concept: $\text{Area of sector}=\frac{1}{2}\times l\times r$

1. $l=5,r=16.2$
2. $\text{Area}=\frac{1}{2}\times 5\times 16.2=40.5$ sq units

Trick: No angle needed when arc length is given.

Answer: (B) 40.5 units²

Concept: Track the position as coordinates, taking Y as origin, East as $+x$ and North as $+y$.

1. East 47: $(47,0)$; right turn → South 23: $(47,-23)$.
2. Right → West 26: $(21,-23)$; right → North 52: $(21,29)$.
3. Left → West 21: $(0,29)$; left → South 11: $Z=(0,18)$.
4. Z is 18 km directly north of Y, so he must drive 18 km towards the south.

Trick: Net E–W: $47-26-21=0$; net N–S: $-23+52-11=18$ north. Return trip is the opposite direction.

Answer: (B) 18 km towards the south

Concept: Facing the centre, “left” means moving clockwise and “right” anticlockwise.

1. Fix F; B is third to the left of F.
2. Only F sits between A and C, so A and C are on either side of F; with C second to the left of D, only the order C, F, A (clockwise) with D two places right of C works.
3. G is not next to B, so E sits beside B and A: order clockwise A, E, B, D, G, C, F.
4. From the left of D (clockwise): D → G, C, F → A, i.e. 3 people between.

Trick: Place the person named most often (F) first, then fix the “only one between” clue.

Answer: (D) Three

Concept: Find the letter shift from the right pair and apply it to the left pair.

1. Option B: F+5 = K, N+5 = S, W+5 = B (after Z, back to A), so FNW → KSB.
2. Apply +5 to NVE: N+5 = S, V+5 = A, E+5 = J → SAJ.
3. Both blanks are satisfied only by # = FNW, % = SAJ.

Trick: Check each option’s shift on the first pair; the matching one must give the same shift on the second pair.

Answer: (B) # = FNW, % = SAJ

Concept: Check every symbol: the element just before and just after it must both be numbers.

1. 7 € 2 ✓, 3 © 8 ✓, 8 © 4 ✓, 4 € 9 ✓, 3 € 5 ✓, 7 $ 1 ✓.
2. #, % and * fail (they are next to other symbols).
3. Total = 6.

Trick: Skip blocks of consecutive symbols — none of them can qualify.

Answer: (C) 6

Concept: Decode each symbol step by step and draw the family tree.

1. P + Q: P is sister of Q (P female).
2. Q – R: Q is father of R; R ÷ S: R is son of S, so S is R’s mother and Q’s wife.
3. S × T: S is daughter of T.
4. So Q is T’s daughter’s husband, and P is his sister: P is T’s daughter’s husband’s sister.

Trick: Write relations from T’s side backward: T → daughter S → her husband Q → his sister P.

Answer: (A) Daughter’s husband’s sister

Concept: Compare positions: each letter of the first cluster vs the matching letter of the second cluster.

1. NP – KM: N−3 = K, P−3 = M.
2. KM – HJ: K−3 = H, M−3 = J; HJ – EG: H−3 = E, J−3 = G.
3. MP – LK: M−1 = L, P−5 = K — different rule.

Trick: Three pairs show a uniform −3 shift; the one breaking it is odd.

Answer: (A) MP - LK

Concept: First identify the highest and lowest numbers, then pick the required digits.

1. Highest = 930 → first digit 9.
2. Lowest = 335 → third digit 5.
3. $9+5=14$.

Trick: Compare first digits only: 9 is highest, 3 is lowest.

Answer: (D) 14

Concept: Find the shift in the first pair and repeat it in the second pair.

1. Option B: T−3 = Q, V−3 = S, R−3 = O, so TVR → QSO.
2. XZV with −3: X→U, Z→W, V→S = UWS.

Trick: Letters QSO are spaced +2, −4; the answer cluster must keep the same spacing (UWS: +2, −4).

Answer: (B) # = TVR, % = UWS

Concept: Find the position-wise change from the first cluster to the second.

1. HMP → KON: H+3, M+2, P−2.
2. USQ → XUO: U+3, S+2, Q−2.
3. DLV → GNT: D+3 = G, L+2 = N, V−2 = T ✓.

Trick: Test only the first letter (+3) to shortlist: KWZ (−4) and DWP (+6), BIO (+4) fail at once.

Answer: (B) DLV : GNT

Concept: Look at the differences between consecutive terms.

1. Differences: $428-405=23$, $405-372=33$ — increasing by 10.
2. Next difference 43: $372-43=329$.
3. Check: $329-53=276$, $276-63=213$ ✓.

Trick: Differences 23, 33, 43, 53, 63 — an arithmetic pattern of +10.

Answer: (A) 329

Concept: Write the direct codes, then test each condition in order.

1. Direct codes: 3 = F, 4 = G, 9 = B, 7 = M.
2. Condition 1: first element is not a symbol — no. Condition 2: last element 7 is odd, not even — no.
3. Condition 3: second (4) and third (9) are both perfect squares → third gets the code of the second, G.
4. Code = F G G M.

Trick: Condition 3 makes two adjacent letters identical — look for a repeated letter among options.

Answer: (C) FGGM

Concept: Track each part of the term separately.

1. First letter: Q, O, M, K → −2 each → I.
2. Second letter: K, I, G, E → −2 each → C.
3. Number: 15, 26, 37, 48 → +11 each → 59.
4. Next term = IC59.

Trick: Numbers rise by 11 (tens and units both +1) — 59 eliminates options B and C immediately.

Answer: (A) IC59

Concept: Compare the first letters of the two clusters and the second letters separately.

1. TR – YP: T+5 = Y, R−2 = P.
2. VT – AR: V+5 = A, T−2 = R; GE – LC: G+5 = L, E−2 = C.
3. YW – DV: Y+5 = D but W−1 = V — breaks the rule.

Trick: Within each cluster the letters differ by −2 in all options, so check the cross-cluster shift.

Answer: (C) YW – DV

Concept: Fix the definite clues first, then the block R–V–P.

1. 4 people between T and U → they are on (Mon, Sat) or (Tue, Sun); Monday is ruled out and Saturday is Q’s, so T/U = Tue/Sun.
2. U is after P, so U = Sunday, T = Tuesday.
3. R, V, P are consecutive → Wed, Thu, Fri; S gets Monday.
4. After R (Wed): V, P, Q, U → 4 people.

Trick: A gap of 4 between two people in a 7-day week leaves only two placements — use it first.

Answer: (D) 4

Concept: Facing the centre: left = clockwise, right = anticlockwise.

1. C is third to the left of A; S is immediate right of C; S is third to the right of R.
2. Taking A first, clockwise: A, _, S, C, _, R, _ .
3. D is second to the left of T → T in 5th place and D in 7th; B (not beside C) takes the 2nd seat: A, B, S, C, T, R, D.
4. From the right of B (anticlockwise): B → A, D, R → T: 3 people between.

Trick: Chain the “third to” clues (A–C–S–R) first; they fix four seats at once.

Answer: (C) Three