18 November 2025 · Shift 1

Numbers from sum and product Let the larger number be x and the smaller be y, so that x-y=20. The square of their difference is ${20}^2=400$. Given: xy+400=1200, hence xy=800. Use the identity ${\left(x+y\right)}^2={\left(x-y\right)}^2+4xy$. ${\left(x+y\right)}^2=400+4\times 800=400+3200=3600$, so x+y=60. Adding x-y=20 and x+y=60 gives 2x=80, i.e. x=40 and y=20. Check: $40\times 20+400=800+400=1200$, so the larger number is 40 and option (c) is correct.

Average: missing value Total of all five scores $=\mathrm{average}\times \mathrm{number}\mathrm{of}\mathrm{students}=82\times 5=410$. Total of the four known scores =75+85+90+80=330. Score of the fifth student =410-330=80. So option (d) is correct.

Partnership: profit sharing All three invest for the same period of one year, so the profit is divided in the ratio of the investments alone. P:Q:R=5000:3000:2000=5:3:2. Total number of parts =5+3+2=10. Q's share $=\frac{3}{10}\times 2000=600$, i.e. ₹600. So option (b) is correct.

Average of numbers Formula: $\mathrm{Average}=\frac{\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{numbers}}{\mathrm{count}\mathrm{of}\mathrm{the}\mathrm{numbers}}$. Sum =14+20+34+32+46=146. There are 5 numbers, so the average $=\frac{146}{5}=29.2$. So option (c) is correct.

Average speed Formula: $\mathrm{Average}\mathrm{speed}=\frac{\mathrm{total}\mathrm{distance}}{\mathrm{total}\mathrm{time}}$. Substituting, $\mathrm{Average}\mathrm{speed}=\frac{220}{5}=44$ km/hr. So option (c) is correct.

Successive percentage change Take the number as 100 — any convenient starting value gives the same percentage answer. After the increase: 100+20=120. The decrease is now taken on 120, not on 100: $\frac{20}{100}\times 120=24$, so the value becomes 120-24=96. Net change =96-100=-4 on a base of 100, i.e. a decrease of 4%. Shortcut for two successive changes: net $=a+b+\frac{ab}{100}$, and with a=20, b=-20 this gives $20-20+\frac{20\times \left(-20\right)}{100}=-4$. So option (b) is correct.

Position in a row Rule: for one object in a row, position from the left + position from the right = total + 1. Red candle: 20+41=61=60+1, so this information is consistent. Blue candle: 15+46=61=60+1, so this too is consistent — the arrangement is possible. Both positions are now counted from the same end, so the number of candles between them =20-15-1=4. These are the candles standing at places 16, 17, 18 and 19, so option (a) is correct.

Discount and marked price A discount of 20% is always taken on the marked price, so the selling price is the remaining 80% of it. $\mathrm{SP}=\frac{80}{100}\times \mathrm{MP}$, and therefore $\mathrm{MP}=\frac{100}{80}\times \mathrm{SP}=\frac{5}{4}\times \mathrm{SP}$. With the selling price of ₹800, $\mathrm{MP}=\frac{5}{4}\times 800=1000$, i.e. ₹1000. Check: 20% of ₹1000 is ₹200, and ₹1000 − ₹200 = ₹800, the selling price. So option (b) is correct.

Direction sense The first leg of 18 km is towards the west and the last leg of 18 km is towards the east. They are equal in length and exactly opposite in direction, so they cancel each other out completely. Only the 24 km walked towards the north is left as the net displacement. Hence he ends up 24 km due north of his starting point, and option (a) is correct.

Direction sense The 16 km walked towards the north and the 16 km walked towards the south are equal and opposite. They cancel out, so the man is back on the same east–west line as his starting point. What remains is the 18 km walked towards the west. Hence he is 18 km due west of his starting point, and option (d) is correct.

Letter series Write the alphabet position of each letter: F = 6, C = 3, Z = 26, W = 23. Every step moves back 3 places, counting round the alphabet: 6-3=3 gives C, and 3-3=0 wraps round to 26, which is Z. Continuing, 26-3=23 gives W, so the next term is 23-3=20. The 20th letter of the alphabet is T, so option (c) is correct.

Fibonacci number series Test the simplest additive rule: is each term the sum of the two before it? 55+89=144, 89+144=233 and 144+233=377 — the rule holds throughout, so this is a Fibonacci-type series. Therefore the missing term =233+377=610. So option (b) is correct.

Alternating number series No single rule joins neighbouring terms, so split the series into the terms at the odd places and the terms at the even places. Odd places: 22, 44, 132, ? — here $22\times 2=44$ and $44\times 3=132$. Even places: 18, 36, 108, 432 — here $18\times 2=36$, $36\times 3=108$ and $108\times 4=432$. Both chains follow the same rule: multiply by 2, then by 3, then by 4. So the missing term $=132\times 4=528$, and option (a) is correct.

Divisibility by 11 and 17 11 and 17 are both prime, so a number divisible by both must be a multiple of $11\times 17=187$. The test therefore reduces to a single question: is the number a multiple of 187? $187=187\times 1$, $374=187\times 2$, $561=187\times 3$ and $935=187\times 5$ — all four clear the test. But $198=11\times 18$, so it is divisible by 11 and not by 17; 198=187+11 is not a multiple of 187. Hence the pair (198, 374) fails, and option (d) is correct.

Letter-cluster series Only the three letters k, l and m are used and the string has 20 places, so read it in four groups of five. Filling the five blanks with k, l, k, l, m gives: kklmm / llmkk / mmkll / kklmm. Now the rule is visible — each group is the previous group with every letter moved one step along the cycle k to l, l to m, m back to k. The fourth group returns to kklmm, which is exactly what the last five given letters demand. No other option produces this pattern, so option (c) is correct.

Alternating letter-number series Every term has two independent parts — a letter and a number — so track them separately. Letters: W, U, S, Q. Each letter moves 2 places backward, so the next letter is Q minus 2, i.e. O. Numbers: 1, 2, 3, 4. Each number increases by 1, so the next number is 5. Putting the two parts together, the missing term is O5. Hence, option (a) is the most appropriate answer.

Letter-number series Split every term into its letter part and its number part. Letters: P, R, T, V — each letter moves 2 places forward, so the next letter is X. Numbers: $4=2^2$, $16=4^2$, $36=6^2$, $64=8^2$ — squares of consecutive even numbers. The next even number is 10, so the next number is ${10}^2=100$. The missing term is therefore X100. Hence, option (a) is the most appropriate answer.

Letter coding The word has 6 letters but the code has 12, so every single letter of the word becomes a pair of letters. Break the code into pairs: FE, TS, HG, SR, ZY, QP. For each letter the pair is (letter − 1, letter − 2), i.e. the two letters that come just before it, written in that order. Apply exactly the same rule to MANGO, moving backward past A to Z when needed. Joining the pairs, MANGO becomes LK + ZY + ML + FE + NM = LKZYMLFENM. Hence, option (a) is the most appropriate answer.

Assertion and Reason Step 1 — test A on its own: regular exercise is universally accepted as a way of staying healthy, so A is true. Step 2 — test R on its own: exercise makes the heart pump more efficiently and strengthens the body's defence system, so R is also true. Step 3 — test the link: better blood circulation and stronger immunity are precisely the mechanisms through which exercise produces good health, so R answers the question 'why is A true?'. Both statements are true and R is the correct explanation of A. Hence, option (a) is the most appropriate answer.

Statement and conclusions The key word is 'Only'. It turns the Mathematics score into a necessary condition: no student can enter the Science stream without 60% or more in Mathematics. Conclusion I: since admission is impossible without a Mathematics score, Mathematics has to be studied and cleared — it is compulsory for admission, so I follows. Conclusion II: 55% is below the 60% cut-off, so such a student lies outside the admitted group and will not be given admission — so II follows. Both conclusions therefore follow from the statement. Hence, option (c) is the most appropriate answer.

Exact replication check Compare each option with the reference 'New Delhi, 26/11/2008, 09:30 PM.' block by block: city, date, time, and the closing full stop. Option (a) changes the meridian marker PM to AM, option (c) drops the leading zero and writes 9:30, and option (d) changes the minutes from 30 to 25. Only option (b) repeats every character, digit, symbol and space exactly as in the reference. Hence, option (b) is the most appropriate answer.

Exact replication check Break the long address into its four checkable numbers — Plot 18, Sec. 62, PIN 201309 — and compare option by option. Option (a) shows Plot 19, option (c) shows Sec. 63 and option (d) shows the PIN 201319; each differs from the reference by a single digit. Option (b) reproduces the address exactly, including the missing spaces after 'Tower,' and 'Plot 18,'. Hence, option (b) is the most appropriate answer.

Exact replication check The reference has three checkable pieces: the day 15th, the month March and the year 1892. Option (a) changes the year to 1893, option (b) changes the day to 16th and option (d) changes the year to 1992. Option (c) matches the reference in every character, including the colon after Oxford and the comma before the year. Hence, option (c) is the most appropriate answer.

Number matrix The three numbers of each column produce the number written below that column, so read the grid column-wise. First column: $\left(4\times 5\times 6\right)-1=120-1=119$. Second column: $\left(3\times 5\times 7\right)-1=105-1=104$. The rule is therefore (product of the three numbers) -1. Third column: $\left(6\times 3\times 5\right)-1=90-1=89$. Hence, option (d) is the most appropriate answer.

Number matrix Again the bottom entry of each column is built from the three numbers standing above it. First column: $\left(4\times 6\times 7\right)-1=168-1=167$. Second column: $\left(7\times 5\times 4\right)-1=140-1=139$. Both fit the rule (product of the three numbers) -1. Third column: $\left(8\times 4\times 6\right)-1=192-1=191$. Hence, option (a) is the most appropriate answer.