Q&A: practice questions with answers

Concept: Split the 15 places into three blocks of 5 and find the common unit.

1. Blocks: b__hj / _d_h_ / b_f_j → each = b d f h j (alternate letters).
2. Block 1 needs d, f; block 2 needs b, f, j; block 3 needs d, h.
3. Order: d f b f j d h.

Trick: First two blanks must be d, f (between b and h) – this alone removes (D); check the third letter 'b' to pick (C).

Answer: (C) dfbfjdh

Concept: Replace each sign as given, then simplify using BODMAS.

1. + → ×, − → ÷, × → −, ÷ → +.
2. $(15+2)+6-(5÷4)+4\to (15\times 2)\times 6÷(5+4)\times 4$.
3. $=30\times 6÷9\times 4=180÷9\times 4=20\times 4=80$.

Trick: Rewrite the whole expression first on paper; never swap signs in your head while calculating.

Answer: (A) 80

Concept: Swap the signs inside the numerator; the fraction bar stays a division by 4.

1. + → −, − → ×, × → ÷.
2. $(30-5)\times 5+2\to (30\times 5)÷5-2$.
3. $=150÷5-2=30-2=28$.
4. $\frac{28}{4}=7$.

Trick: $(30\times 5)÷5$ simply gives back 30 – cancel ×5 and ÷5 at sight.

Answer: (C) 7

Concept: 'All A are B' always gives 'Some B are A' (conversion).

1. All papers are copy → Some copies are papers ✔ (definite).
2. Some copies are clean – the clean part may lie outside papers → 'Some papers are clean' is only possible.
3. 'All clean are copies' and 'All copies are clean' are never stated.

Trick: From 'All', 'Some' in reverse is always safe; 'Some + Some' or 'All + Some' links between different terms rarely give certainty.

Answer: (C) Some copy are papers.

Concept: Mouse is a part (accessory) of a computer; find the item of which a string is a part.

1. String → part of a Guitar.
2. Television, refrigerator, washing machine have no strings.

Trick: Make a sentence: 'A ___ is a part of ___' – it must work for both pairs.

Answer: (B) Guitar

Concept: A word common to two sentences has the code common to them.

1. S1 & S2: banana ↔ hp.
2. S1 & S3: apple ↔ rt; S2 & S3: grape ↔ ns.
3. S2 = banana, orange, grape ↔ hp, qw, ns → orange = qw.

Trick: Orange appears only in S2 – remove the codes of its known neighbours from S2 and the leftover is the answer.

Answer: (B) qw

Concept: Group by administrative status in India.

1. Punjab, Haryana, Rajasthan → States with elected governments.
2. Andaman & Nicobar Islands → Union Territory run by a Lieutenant Governor.

Yaad rakhein: The capital is Sri Vijaya Puram (earlier Port Blair) – renamed in 2024.

Answer: (D) Andaman & Nicobar

Concept: Arrange letters Z→A, then convert right-end position to left-end position.

1. DEVELOPMENT has 11 letters: D, E×3, L, M, N, O, P, T, V.
2. Z→A order: VTPONMLEEED.
3. 11th from right = 1st from left = V; 5th to its right = M.

Trick: In an n-letter word, kth from right = (n − k + 1)th from left; then 1 + 5 = 6th from left = M.

Answer: (B) M

Concept: Fast-growing terms → check multiplication factors.

1. $3\times 3=9$, $\times 5=45$, $\times 7=315$.
2. Next multiplier 11: $315\times 11=3465$.

Trick: ×11 rule: 315 × 11 → 3 | 3+1 | 1+5 | 5 = 3465. Also, the answer must end in 5 and be divisible by 315 – only 3465 works.

Answer: (C) 3465

Concept: Take first differences; if they rise uniformly, extend them.

1. Differences: 200, 400, 600, 800 → +200 each.
2. Next difference 1000 → 2089 + 1000 = 3089.

Trick: Every term ends in 89 and the differences are round hundreds – only 3089 adds a clean 1000.

Answer: (A) 3089

Concept: Rational and irrational numbers are two separate (disjoint) sets that together make the real numbers.

1. Whole numbers $\{0,1,2,\dots \}\subset$ integers → (A) true.
2. Any integer $n=\frac{n}{1}$ → rational → (B) true.
3. $\text{Real}=\text{rational}\cup \text{irrational}$ → (C) true.
4. A number cannot be both rational and irrational → (D) false.

Trick: Chain to remember: $\text{Natural}\subset \text{Whole}\subset \text{Integer}\subset \text{Rational}\subset \text{Real}$; Irrational sits beside Rational, never inside it.

Answer: (D) Every rational number is an irrational number

Concept: Terminating or recurring decimal ⇔ rational; otherwise irrational.

1. Irrational numbers cannot be written as $\frac{p}{q}$.
2. So their decimals never end and never repeat a block, e.g. $\sqrt{2}=1.41421\dots$, $\pi =3.14159\dots$

Trick: If the decimal 'stops' or 'loops', it is rational – an irrational number does neither.

Answer: (C) Non-terminating and non-repeating

Concept: Net profit = profit on one − loss on the other, using a variable for cost price.

1. CP of 2nd = x, CP of 1st = 1.5x.
2. Gain = 20% of 1.5x = 0.3x; loss = 10% of x = 0.1x.
3. Net = 0.2x = 200 → x = 1000.
4. CPs: ₹1,500 and ₹1,000.

Trick: Option test: first must be 1.5 × second – only (C) and (D) qualify; (D): 300 − 100 = 200 ✔.

Answer: (D) ₹1,500 and ₹1,000

Concept: Overall % = weighted average of the individual profit/loss % (weights = cost).

1. Total CP = $30\times 500=$ ₹15,000.
2. 20 kettles (₹10,000) at +20% → +₹2,000; 10 kettles (₹5,000) at −10% → −₹500.
3. Net profit = ₹1,500 → $\frac{1500}{15000}\times 100=10\%$.

Trick: Weighted average: $\frac{2\times 20+1\times (-10)}{3}=\frac{30}{3}=10\%$ profit.

Answer: (C) 10% Profit

Concept: $\text{Discount }\%=\frac{\text{discount}}{\text{marked price}}\times 100$.

1. Marked price = $15\times 320=$ ₹4,800.
2. Discount = $4800-4000=$ ₹800.
3. $\frac{800}{4800}\times 100=\frac{1}{6}\times 100=16.67\%$.

Trick: Per plate: $\frac{4000}{15}\approx 266.67$, i.e. ₹53.33 off ₹320 $=\frac{1}{6}\to 16.67\%$.

Answer: (D) 16.67%

Concept: Successive change: net % = $a+b+\frac{ab}{100}$.

1. Mark-up +30%, discount −20%.
2. Net = $30-20+\frac{30\times (-20)}{100}=10-6=4\%$.
3. Check: MP = 15,600; SP = 12,480; profit = 480 = 4% of 12,000.

Trick: Use $a+b+\frac{ab}{100}$ – the CP of ₹12,000 is not even needed.

Answer: (C) 4%

Concept: $\text{Change in average}=\frac{\text{correct value}-\text{wrong value}}{\text{number of items}}$.

1. Error = $85-45=40$ (too little).
2. Average rises by $\frac{40}{20}=2$.
3. New average = $65+2=67$.

Trick: Never recompute the full total – just spread the error over 20 students.

Answer: (B) 67

Concept: Use ratio: 25% more means History : English = 5 : 4.

1. Total = $2\times 81=162$.
2. English : History = 4 : 5 → 9 parts = 162 → 1 part = 18.
3. English = $4\times 18=72$ (History = 90).

Trick: $25\%=\frac{1}{4}$ → ratio 4 : 5 directly; total $162÷9=18$.

Answer: (A) 72

Concept: n(A ∪ B) = n(A) + n(B) − n(A ∩ B).

1. At least one = 55 + 65 − 40.
2. = 80%.

Yaad rakhein: Failed in both = 100 − 80 = 20% – a common follow-up question.

Answer: (A) 80%

Concept: Profit ratio = capital × months.

1. P: $20\times 12=240$; Q: $30\times 12=360$ (in thousands).
2. R joins after 5 months → 7 months: $40\times 7=280$.
3. 240 : 360 : 280 = 6 : 9 : 7.

Trick: Drop the zeros and divide by a common factor early: $2\times 12:3\times 12:4\times 7$ = 24 : 36 : 28 → ÷4.

Answer: (D) 6 : 9 : 7