Q&A: practice questions with answers

Concept: ${\left(\frac{a}{b}\right)}^{-n}={\left(\frac{b}{a}\right)}^n$; same base → add powers.

1. ${\left(\frac{5}{23}\right)}^9={\left(\frac{23}{5}\right)}^{-9}$.
2. LHS $={\left(\frac{23}{5}\right)}^{13-9+5}={\left(\frac{23}{5}\right)}^9={\left(\frac{5}{23}\right)}^{-9}$.
3. $6m+9=-9\Rightarrow m=-3$.

Trick: Flip the fraction, flip the sign of the power – then just equate exponents.

Answer: (D) $-3$

Concept: SP $=$ MP $\times (1-\frac{d}{100})$.

1. $840=\text{MP}\times 0.7$.
2. MP $=\frac{840}{0.7}=1200$.

Trick: 30% off → SP is 70% = 7 parts; 1 part $=120$, 10 parts $=1200$.

Answer: (C) 1,200

Concept: Let present ages be $K$ (Kavita) and $M$ (mother).

1. $K-5=\frac{M}{3}\Rightarrow M=3K-15$.
2. $(K+5)+(M+5)=75\Rightarrow K+M=65$.
3. $K+3K-15=65\Rightarrow 4K=80\Rightarrow K=20$.

Trick: Present sum is $75-10=65$; test option: $K=20\Rightarrow M=45$, and $45÷3=15=20-5$ ✓.

Answer: (D) 20 years

Concept: For 2 years, CI $=P[{(1+\frac{r}{100})}^2-1]$ and SI $=\frac{2Pr}{100}$.

1. At 10%, 2-year CI $=21\%$ of $P$: $0.21P=178.5\Rightarrow P=850$.
2. SI $=\frac{850\times 10\times 2}{100}=170$.

Trick: For 2 years, $\frac{\text{SI}}{\text{CI}}=\frac{200}{200+r}=\frac{200}{210}$ → SI $=178.5\times \frac{20}{21}=170$.

Answer: (B) 170

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

1. $(a-b{)}^2={77}^2-4\times 1392=5929-5568=361$.
2. $a-b=\sqrt{361}=19$.

Trick: The numbers are 48 and 29 ($48\times 29=1392$); difference 19.

Answer: (B) 19

Concept: When two coded words share letters, the common letters share the common digits; the leftover letter takes the leftover digit.

1. DOLE → 7 3 4 8 and LEMO → 2 7 3 8. Common letters: O, L, E; common digits: 7, 3, 8.
2. So in DOLE the uncommon letter D = 4, and in LEMO the uncommon letter M = the leftover digit 2.

Trick: Strike out the common letters and common digits – what remains pairs up.

Answer: (D) 2

Concept: Apply the rule letter by letter: vowel → +2, consonant → −1, then count repetitions.

1. W O R T H L E S S L Y → V Q Q S G K G R R K X (O→Q, E→G; W→V, R→Q, T→S, H→G, L→K, S→R, Y→X).
2. Frequencies: V1, Q2, S1, G2, K2, R2, X1.
3. Letters appearing exactly twice: Q, G, K, R = Four.

Trick: Write the new word in a row and tick pairs; here Y is a consonant.

Answer: (C) Four

Concept: Vowel → next letter (+1), consonant → previous letter (−1).

1. R E A D I N G → Q F B C J M F.
2. Only F appears twice (from E and from G); all others appear once.

Trick: Both E(+1) and G(−1) land on F – that is the designed repeat.

Answer: (D) F

Concept: Facing north, "left" is our left. Fix the most restrictive clue first and test the two ways P can sit between Q and D.

1. Let D be at position $d$; then B is at $d+3$ (third to the right of D). P is next to D with Q on the other side.
2. If P is to the right of D, A (second right of P) would land on B's seat – impossible. So P is left of D, Q left of P, and A is just right of D.
3. Q P D A _ B needs six seats: Q1, P2, D3, A4, B6 → C at 5. C is second to the right of D.

Trick: When "A is k-th right of P" collides with another fixed person, flip the side – only one case survives.

Answer: (C) Second to the right

Concept: Change each digit by the rule, then count digits that repeat.

1. 5 7 1 8 6 2 4: odd digits +2 → 5→7, 7→9, 1→3; even digits −1 → 8→7, 6→5, 2→1, 4→3.
2. New number: 7 9 3 7 5 1 3. Digits 7 and 3 appear twice each → Two digits appear more than once.

Trick: Write the new digits directly below the old ones to avoid slips.

Answer: (D) Two

Concept: Check letters and numbers separately for a constant step.

1. Letters: G→N→U→B (+7 each), D→K→R→Y (+7), K→R→Y→F (+7). Next: B+7 = I, Y+7 = F, F+7 = M → IFM.
2. Numbers: 12, 23, 34, 45 (+11) → 56.

Trick: Use the circular alphabet: Y(25)+7 = 32 → 32−26 = 6 = F.

Answer: (C) IFM 56

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

1. "Some fans are cars" → fans and cars overlap. "No car is a bus" → cars and buses are separate.
2. Conclusion I (some fans are buses): fans may or may not touch buses – not definite, does not follow.
3. Conclusion II (some cars are fans): the converse of "some fans are cars" is always true → follows.

Trick: "Some A are B" ⇔ "Some B are A" always; a negative statement + a "some" never gives a definite positive link.

Answer: (B) Only conclusion (II) follows

Concept: Each letter position and the number move by a fixed step.

1. Letters: M→O→Q→S (+2), H→J→L→N (+2), L→N→P→R (+2) → next S+2 = U, N+2 = P, R+2 = T → UPT.
2. Numbers: 21, 29, 37, 45 (+8) → 53.

Trick: Options differ only in the third letter (S/T) and number (53 or 54) – check just those two.

Answer: (C) UPT53

Concept: Replace each symbol by its real meaning, then apply BODMAS.

1. $322\times 23-14÷463+232$ becomes $322÷23\times 14+463-232$.
2. $322÷23=14$; $14\times 14=196$.
3. $196+463-232=659-232=427$.

Trick: Rewrite the whole expression first, then solve ÷ and × before + and −.

Answer: (D) 427

Concept: Plot the towns on a rough map with north upwards; relative direction is read from the first town towards the second.

1. I is north of G, and J is east of I → J is to the north-east corner of the rectangle whose south-west corner is G.
2. H (east of G) and K (south of J) only confirm the picture; they do not change G–J.
3. From J, G lies down-left, i.e. G is to the south-west of J.

Trick: "G w.r.t. J" = stand at J and look for G; opposite of (J w.r.t. G = north-east).

Answer: (A) South-west

Concept: Decode pairwise from left to right and build the family tree.

1. S = W → S is brother of W; W × R → W is son of R; R + T → R is wife of T; T − Z → T is father of Z.
2. So T and R are the parents; S, W and Z are their children.
3. S is male (brother), hence S is the brother of Z.

Trick: Symbols between consecutive letters each give one relation – chain them, do not skip.

Answer: (C) Brother

Concept: Compare the position differences between corresponding letters of each pair.

1. OL–JQ: O−5 = J, L+5 = Q. UR–PW: U−5 = P, R+5 = W. RO–MT: R−5 = M, O+5 = T.
2. XU–SY: X−5 = S but U+4 = Y (U+5 would be Z) → pattern broken.

Trick: Pattern (−5, +5) – check the second letter of each pair quickly.

Answer: (C) XU-SY

Concept: Find how positions 1-2-3-4 are shuffled in each step.

1. SAID → AISD: order 2-3-1-4; AISD → DIAS = reverse of SAID (4-3-2-1). MODE → ODME (2-3-1-4) → EDOM (reverse) confirms.
2. TONG → 2-3-1-4 gives ONTG ✓; reverse of TONG = GNOT ✓.
3. HOGS→OHGS swaps only first two; UGLY→GLYU is not the reverse; MIND→MNID fails the first step.

Trick: Third word = first word written backwards – test that first, it eliminates fast.

Answer: (B) TONG - ONTG - GNOT

Concept: "Only J sits to the left of W" fixes both ends of the row at once.

1. J is at position 1 (extreme left) and W at 2. Four people between J and Y → Y at 6.
2. K–I–H (or H–I–K) must be consecutive in seats 3-4-5; K cannot be next to Y (seat 6), so K3, I4, H5.
3. Z takes the last seat 7 → none sit to the right of Z.

Trick: "Only X sits to the left of Y" ⇒ X is at the extreme left, Y second.

Answer: (C) None

Concept: Take successive differences and look for a pattern.

1. $55-38=17,74-55=19,95-74=21,118-95=23$ – differences are consecutive odd numbers.
2. Next difference = 25 → $118+25=143$.

Trick: Equal second differences (2, 2, 2…) → next term is just previous + (last difference + 2).

Answer: (B) 143