Q&A: practice questions with answers

Concept: Read the 8 border cells clockwise from top-left and compare positions.

Solution:

1. Fig 1 → Fig 2: every element shifts 2 places anticlockwise along the border.
2. Fig 3 read clockwise: 6, ↑, 5, M, ↑, P, D, S.
3. Shift by 2 anticlockwise → top row 5, M, ↑; bottom row 6, S, D – matches option B.

Trick: Track just one easy symbol (like 6): find where it lands, then confirm with one more element.

Answer: (B) Option B

Concept: Track two changes separately: number of triangles and position of the shaded cell.

Solution:

1. Triangles: 2, 3, 4, 5 → next = 6 (all pointing up).
2. Shaded cell moves one corner anticlockwise each step: TR → TL → BL → BR → next TR.
3. Figure with 6 triangles and top-right shaded = option C.

Trick: Split a figure series into independent parts – solve each, then match both.

Answer: (C) Option C

Concept: Replace signs first, then apply BODMAS. (Here '÷' stands for '−'.)

Solution:

1. Swap: − → ÷, + → ×, ÷ → −, × → +.
2. Converted: $(56÷8)\times 4-15+5$
3. $=7\times 4-10=28-10=$ 18.

Trick: Write the new expression on paper before calculating – most mistakes come from solving with old signs.

Answer: (C) 18

Concept: Insert each option's signs in order and simplify with BODMAS.

Solution:

1. Option B: $12+4\times 8÷2-5$.
2. $4\times 8÷2=16$.
3. $12+16-5$ = 23 ✔

Trick: RHS 23 is small and odd → the last sign is likely '−5' or '+5'; test those options first.

Answer: (B) $+,x,÷,-$

Concept: Number = sum of the alphabet positions of the four letters.

Solution:

1. JKMN: 10 + 11 + 13 + 14 = 48 ✔; UVXY: 21 + 22 + 24 + 25 = 92 ✔
2. FGIJ: 6 + 7 + 9 + 10 = 32 ✔
3. CDGH: 3 + 4 + 7 + 8 = 22, but 21 is given ✘

Trick: Use EJOTY (5, 10, 15, 20, 25) to get letter positions instantly.

Answer: (C) CDGH21

Concept: Letters move +2 in all pairs, so compare the numbers.

Solution:

1. 500 − 350 = 150; 725 − 575 = 150; 890 − 740 = 150.
2. 660 − 500 = 160 ✘ – different.

Trick: When the letter rule is the same everywhere, the odd one hides in the numbers.

Answer: (D) NO660 - PQ500

Concept: $\text{Left number}=(\text{right number}{)}^2$.

Solution:

1. ${21}^2=441$ ✔, ${23}^2=529$ ✔, ${26}^2=676$ ✔
2. ${24}^2=576$, not 600 ✘

Trick: 600 does not end in a square-ending pattern with a perfect root ($\sqrt{600}\approx 24.5$) – spot it without calculating others.

Answer: (C) 600-24

Concept: $\text{Middle}=\text{first}+(\text{third}{)}^3$.

Solution:

1. $142+343=485$ ✔; $215+1000=1215$ ✔; $310+1331=1641$ ✔
2. $180+{13}^3=180+2197=2377\ne 2370$ ✘

Trick: Unit-digit check: $0+7$ (${13}^3$ ends in 7) = 7, but 2370 ends in 0 → odd one at once.

Answer: (D) $(180,2370,13)$

Concept: Rule: 1st letter +1, 2nd letter −1, number ÷ 2. The blank is the first term, so reverse it.

Solution:

1. PR500 → QQ250 and BL120 → CK60 confirm the rule.
2. Reverse from DG200: D − 1 = C, G + 1 = H, $200\times 2=400$.
3. Missing cluster = CH400.

Trick: When '?' is on the left, apply the opposite operations (+ ↔ −, × ↔ ÷).

Answer: (B) CH400

Concept: Letters move +4; number becomes $(\text{number}{)}^2+5$.

Solution:

1. RJ10 → VN105: R+4 = V, J+4 = N, ${10}^2+5=105$ ✔; DL12 → HP149 ✔ (144 + 5).
2. GK14 → G+4 = K, K+4 = O, ${14}^2+5=196+5=201$.
3. Answer = KO201.

Trick: Option letters decide quickly: K+4 = O removes KP and L0 options; 201 removes 199.

Answer: (A) KO201

Concept: At x% loss, $\text{SP}=(100-x)\%\text{ of CP}$.

Solution:

1. 20% loss → $\text{SP}=80\%\text{ of CP}=\frac{4}{5}\text{ of CP}$.
2. $\text{CP}=240\times \frac{5}{4}$ = ₹300.

Trick: 20% loss means SP is 4 parts out of CP's 5 → 1 part = $240÷4=60$, CP = $5\times 60=300$.

Answer: (B) Rs. 300

Concept: $\text{Mixture price}=\text{total cost}÷\text{total quantity}$.

Solution:

1. Cost: $3\times 60+2\times 70=180+140$ = ₹320.
2. Quantity = 5 kg → $320÷5$ = ₹64/kg.

Trick: Weighted average: $60+(\frac{2}{5})\times 10=64$ (base price + share of the extra ₹10).

Answer: (B) ₹64

Concept: $\text{Time}=\text{Distance}÷\text{Speed}$.

Solution:

1. $240÷60$ = 4 hours.

Yaad rakhein: Units must match: km with km/h gives hours directly.

Answer: (C) 4 hours

Concept: Take efficiencies as units of work per day.

Solution:

1. P : Q = 2 : 1 → together 3 units/day.
2. Total work = $3\times 18=54$ units.
3. P alone = $54÷2$ = 27 days.

Trick: $\text{P alone}=\text{together-days}\times (\text{total efficiency}÷\text{P's efficiency})=18\times \frac{3}{2}=27$.

Answer: (B) 27 days

Concept: $\text{SP}=\text{MP}\times \frac{100-\text{discount\%}}{100}$.

Solution:

1. $\text{SP}=1200\times \frac{85}{100}=12\times 85$ = ₹1020.

Trick: 10% of 1200 = 120, 5% = 60 → discount 180 → $1200-180=1020$.

Answer: (B) Rs. 1020

Concept: Volume stays the same on melting; $\text{number of cubes}=\text{big volume}÷\text{small volume}$.

Solution:

1. Cuboid = $50\times 40\times 10=20,000{\text{cm}}^3$.
2. One cube = $2^3=8{\text{cm}}^3$.
3. Cubes = $20,000÷8$ = 2500.

Trick: Divide each side by 2 directly: $25\times 20\times 5=2500$.

Answer: (B) 2500

Concept: Two triangles with all three corresponding sides equal are congruent (SSS rule).

Solution:

1. All three sides of plot 1 = the matching sides of plot 2 → SSS holds.
2. SAS needs an included angle, which is not given.

Yaad rakhein: Valid congruence rules: SSS, SAS, ASA, AAS, RHS. AAA and SSA are NOT rules.

Answer: (A) Yes, by SSS

Concept: $\text{Volume of a right prism}=\text{base area}\times \text{height}$.

Solution:

1. Base area = $2400÷30$ = 80 cm².

Yaad rakhein: Same formula works for every prism and cylinder: $V=(\text{area of base})\times h$.

Answer: (C) $80{\mathrm{cm}}^2$

Concept: Split the mixture by ratio; only water changes when water is added.

Solution:

1. Milk = $\frac{3}{4}\times 80$ = 60 L, water = 20 L.
2. After adding 10 L water: water = 30 L.
3. Milk : water = 60 : 30 = 2 : 1.

Trick: Milk stays fixed – just compare milk with new water.

Answer: (D) 2 : 1

Concept: Radius ⟂ tangent at the point of contact, so use Pythagoras.

Solution:

1. $A{B}^2=O{A}^2-O{B}^2={17}^2-8^2=289-64=225$.
2. $AB=\sqrt{225}$ = 15 cm.

Trick: 8, 15, 17 is a Pythagorean triplet – answer is instant.

Answer: (C) 15 cm