Q&A: practice questions with answers

Concept: Overall average $=\frac{\text{total amount}}{\text{total members}}$.

1. Group totals: $25\times 101=2525$, $32\times 249=7968$, $31\times 269=8339$.
2. Total amount $=2525+7968+8339=18832$; total members $=25+32+31=88$.
3. Average $=\frac{18832}{88}=214$.

Trick: Take 214 as base: deviations $25(-113)+32(35)+31(55)=-2825+1120+1705=0$ ✓.

Answer: (C) 214

Concept: If SP of $x$ articles = CP of $y$ articles, then gain/loss$\%=\frac{y-x}{x}\times 100$.

1. SP of 25 books = CP of 19 books ⇒ $\frac{\text{SP}}{\text{CP}}=\frac{19}{25}$ per book.
2. SP is less than CP, so it is a loss.
3. Loss$\%=\frac{25-19}{25}\times 100=\frac{6}{25}\times 100=24\%$.

Trick: Divide by the number attached to SP (25). More articles sold for the cost of fewer ⇒ loss.

Answer: (C) 24% loss

Concept: Average of the first $n$ multiples of $k$ $=k\times \frac{n+1}{2}$.

1. Here $k=9$, $n=13$.
2. Average $=9\times \frac{13+1}{2}=9\times 7=63$.
3. Check: the multiples 9, 18, …, 117 form an AP; the middle (7th) term $=9\times 7=63$.

Trick: For an odd count of terms in AP, the average is simply the middle term.

Answer: (D) 63

Concept: If A is $x\%$ more than B, then B is $\frac{x}{100+x}\times 100\%$ less than A.

1. Let B = 100, so A = 243.
2. B is less than A by $\frac{143}{243}\times 100$.
3. $\frac{14300}{243}\approx 58.85\%$.

Trick: "More" → divide by $100+x$; "less" → divide by $100-x$. Here $\frac{143}{243}$, a little under 60%.

Answer: (D) 58.85%

Concept: Mode $=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$, where $f_1$ is the highest frequency.

1. Highest frequency 35 → modal class 50–60; $l=50$, $h=10$, $f_1=35$, $f_0=26$, $f_2=20$.
2. Mode $=50+\frac{35-26}{70-26-20}\times 10=50+\frac{9}{24}\times 10$.
3. $=50+3.75=53.75$.

Trick: $f_0$ = frequency just before, $f_2$ = just after the modal class; the answer always lies inside the modal class (50–60).

Answer: (A) 53.75

Concept: Boat speed $=\frac{\text{downstream}+\text{upstream}}{2}$, current $=\frac{\text{downstream}-\text{upstream}}{2}$.

1. Downstream speed $=\frac{72}{8}=9$ km/h.
2. Upstream speed $=\frac{72}{12}=6$ km/h.
3. Boat $=\frac{9+6}{2}=7.5$ km/h; current $=\frac{9-6}{2}=1.5$ km/h.

Trick: Downstream is always the faster one; average of the two = boat, half the gap = stream.

Answer: (A) 7.5 km/hr and 1.5 km/hr

Concept: Two successive discounts $d_1,d_2$ leave $(1-d_1)(1-d_2)$ of the marked price.

1. SP of X $=2300+460=2760=\text{MP}\times 0.54\times 0.32=0.1728\text{MP}$.
2. SP of Y $=0.27\text{MP}$. Ratio: $\frac{{\text{SP}}_Y}{{\text{SP}}_X}=\frac{0.27}{0.1728}=\frac{25}{16}$.
3. ${\text{SP}}_Y=2760\times \frac{25}{16}=4312.5$; profit $=4312.5-2300=2012.5$.
4. Profit$\%=\frac{2012.5}{2300}\times 100=87.5\%$.

Trick: Same MP for both – work with the ratio of net multipliers ($0.27:0.1728=25:16$) instead of finding MP.

Answer: (A) 87.5%

Concept: When two coded words share a common letter, the common digit in their codes is that letter's code.

1. CAST → 3519 and SIDE → 8645.
2. Common letter in both words: only S.
3. Common digit in both codes: only 5. So S = 5.

Trick: Match the common letter with the common digit – no need to decode the rest.

Answer: (B) 5

Concept: Check each letter position separately and the number separately.

1. 1st letters M, H, C, X → each $-5$ → X$-5$ = S.
2. 2nd letters P, K, F, A → each $-5$ → V; 3rd letters W, R, M, H → each $-5$ → C.
3. Numbers 30, 25, 20, 15 → $-5$ → 10. Term = SVC 10.

Trick: All three letters move $-5$ in a loop (A$-5$ = V, X$-5$ = S).

Answer: (C) SVC 10

Concept: Each letter position follows its own fixed step; the number has a separate pattern.

1. 1st letters H, G, F, E → $-1$ → D.
2. 2nd letters A, Y, W, U → $-2$ → S; 3rd letters K, H, E, B → $-3$ → B$-3$ = Y.
3. Numbers 8, 11, 14, 17 → $+3$ → 20. Term = DSY 20.

Trick: Steps are $-1,-2,-3$ for the three letters – wrap B$-3$ around Z to get Y.

Answer: (B) DSY 20

Concept: Fix the most restricted person first, then place the rest using sums.

1. C is even but not 6 → C = 2 or 4. C + D = 3 → C = 2, D = 1.
2. F + C = 7 → F = 5.
3. Left floors 3, 4, 6 for A, B, E; B immediately above E → E = 3, B = 4, A = 6.
4. Above B (floor 4): F and A → two people.

Trick: A sum of 3 with floor numbers can only be 1 + 2 – such sums fix two people at once.

Answer: (B) Two

Concept: Decode the expression step by step and build the family tree.

1. L % R → L is father of R. R – K → R is brother of K, so L is also K's father.
2. K + V → K is mother of V (K is female). V # E → V is daughter of E (V is female).
3. So V is the daughter of K, and K is L's daughter → V is L's daughter's daughter.

Trick: "+" (mother) and "#" (daughter) fix genders instantly – use them to decide "daughter's daughter" vs "son's daughter".

Answer: (C) Daughter's daughter

Concept: Look only at symbols; check the element just before (odd number?) and just after (not even number?).

1. Series: # $ Ω 2 1 @ 4 & ~ % 8 6 9 + 5 ? £ 3 7 * =.
2. 1 @ 4 → preceded by odd 1 but followed by even 4 → rejected.
3. 9 + 5 → yes; 5 ? £ → yes (£ is not an even number); 7 * = → yes.
4. Count = three.

Trick: "Not followed by an even number" also accepts a symbol or the end of the series after it.

Answer: (C) Three

Concept: Test each statement alone, then both together, and see whether exactly one tree can be tallest.

1. Statement I: M is taller than only two → M is 3rd. T immediately taller than N → (T, N) are (1st, 2nd) or (4th, 5th). Tallest could be T, L or V → not sufficient.
2. Statement II: V > N alone says nothing about the tallest.
3. Together: if T, N were 1st, 2nd, V could not be taller than N; so T, N are 4th, 5th, and L, V occupy 1st, 2nd in unknown order → still not sufficient.

Trick: In ranking questions, "taller than only two" pins the middle position – start from there.

Answer: (C) Both statements I and II together are NOT sufficient to answer the question

Concept: Find the rule of movement from word 1 to word 2 and from word 2 to word 3.

1. AGED → DAGE → EDAG: each time the last letter moves to the front.
2. FAIL → LFAI → ILFA: same rule.
3. KING → GKIN → NGKI follows it exactly; FARM-MFAR-FMRA and the others break at the third word.

Trick: Check the third word first – that is where wrong options usually slip.

Answer: (B) KING-GKIN-NGKI

Concept: Pick each symbol and check if a number sits on both sides of it.

1. Series: \ % * 5 5 / 9 9 / + 7 * # 6 9 6 @ + 7 ? +.
2. 5 / 9 → number on both sides ✓.
3. 9 / + ✗ (followed by +); 7 * # ✗; 6 @ + ✗; 7 ? + ✗.
4. Count = one.

Trick: Scan only symbols that have a digit just before them – then check the right side.

Answer: (A) One

Concept: Find how the four letters move in each step.

1. CLAP → APCL: the two halves swap (CL|AP → AP|CL). APCL → ACPL: the middle two letters swap.
2. DIRT → RTDI → RDTI: same two steps.
3. LION → ONLI (halves swapped) → OLNI (middle swapped) ✓. MEAT → ATME → should be AMTE, not TMAE.

Trick: Step 1 = swap halves, step 2 = swap the 2nd and 3rd letters.

Answer: (D) LION-ONLI-OLNI

Concept: Use the "four people between" clue to fix the extreme floors first.

1. Four between C and D → they are on floors 1 and 6. E is above C → C = 1, D = 6.
2. F even, not 2 → F = 4.
3. E immediately below B with floors 2, 3, 5 left → E = 2, B = 3; A = 5.
4. Above A (floor 5): only D → one.

Trick: "Only four between" in a 6-floor building always means the two extreme floors.

Answer: (C) One

Concept: Two "Some" statements in a chain never give a definite conclusion between the end terms.

1. Pillows–Blankets, Blankets–Quilts, Quilts–Curtains are all "some" links.
2. (I) Some pillows are quilts: pillows may touch blankets without touching quilts → not definite.
3. (II) Some blankets are curtains: same, no direct link → not definite. Hence neither follows.

Trick: Some + Some = No conclusion (I + I rule).

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

Concept: Look at the differences between consecutive terms.

1. $91-90=1$, $90-86=4$, $86-77=9$, $77-61=16$.
2. Differences are $1^2,2^2,3^2,4^2$ → next difference $5^2=25$.
3. $61-25=36$.

Trick: Decreasing series with growing gaps → differences are usually perfect squares.

Answer: (A) 36