15 November 2025 · Shift 1

Speed, time and distance Formula: distance = speed $\times$ time, where the time must be measured in the same unit as the speed. The speed is in km/hr, so 40 minutes has to be changed into hours: $\frac{40}{60}=\frac{2}{3}$ hr. Distance $=84\times \frac{2}{3}$ $=28\times 2=56$ km. Hence the bus covers 56 km in 40 minutes, so option (b) is correct.

Average speed The same distance is covered twice, once at each speed, so the average speed is the harmonic mean of the two speeds and not their simple average. Formula: average speed $=\frac{2xy}{x+y}$, where x and y are the two speeds. Here x=50 km/hr and y=30 km/hr. Average speed $=\frac{2\times 50\times 30}{50+30}=\frac{3000}{80}$ =37.5 km/hr. Hence the average speed for the entire trip is 37.5 km/hr, so option (b) is correct.

Subtraction of decimals The cloth left over is the whole length minus the length that was cut off. Cloth left =12-4.5 =7.5 metres. Hence 7.5 metres of cloth is left, so option (b) is correct.

LCM by prime factors Rule: the LCM is the product of every prime factor taken to the highest power in which it occurs in any one of the numbers. $8=2^3$, $24=2^3\times 3$ and $40=2^3\times 5$. The highest powers are $2^3$, 3 and 5. LCM $=2^3\times 3\times 5=8\times 15=120$. Hence the LCM of 8, 24 and 40 is 120, so option (c) is correct.

Statement and inference An inference follows only when the statement itself supports it; whatever the statement is silent about must be rejected. Inference I: the cut is being made 'due to declining profits', and falling profits are precisely a financial difficulty, so I follows. Inference II: the statement says nothing whatever about how the employees worked; the cut is tied to profits, not to performance, so II does not follow. Inference III: a workforce cut forced by declining profits is made in order to bring costs down and profits back up, which is the purpose behind the very decision reported, so III follows. Hence I and III follow, and the answer is option (d).

Number analogy Look for a single rule that turns the first number of the pair into the second one. $1000=10\times 10\times 10={10}^3$ and 10=11-1, so the rule is: subtract 1 from the number, then cube it. Applying the same rule to 6: ${\left(6-1\right)}^3=5^3$ =125. Hence the missing number is 125, so option (a) is correct.

Number series Work out the differences between the terms that are given. 12-4=8 and 28-12=16, so each difference is double the one before it. The next difference is therefore $16\times 2=32$, which makes the missing term 28+32=60. Check: the difference after that is $32\times 2=64$, and 60+64=124, the last term of the series. Hence the missing number is 60, so option (c) is correct.

Number pair series Treat the first numbers of the pairs as one series and the second numbers as another. First numbers: $5,8,11,\dots ,17$ — each one is 3 more than the one before it. Second numbers: $9,14,19,\dots ,29$ — each one is 5 more than the one before it. So the missing pair is $\left(11+3,19+5\right)=\left(14,24\right)$. Check: 14+3=17 and 24+5=29, which is exactly the pair given last. Hence the missing term is (14,24), so option (a) is correct.

Wrong number in series Find what is being subtracted at every step and look for a pattern in those subtractions. 88-69=19, 69-52=17, 52-37=15 — the numbers subtracted are odd numbers falling by 2 each time. So the next subtraction must be 13, which gives 37-13=24 and not 23. With 24 in that place the rest fits perfectly: 24-11=13 and 13-9=4. Hence 23 is the wrong number of the series, so option (d) is correct.

Odd one out (devices) Sort the four items by the work each of them does in a computer system. A mouse, a keyboard and a scanner all carry data into the computer, so all three are input devices. A monitor does the opposite — it shows the processed result to the user, so it is an output device. Hence the monitor is the odd one out, so option (d) is correct.

Odd one out (prime numbers) Test each number for a factor other than 1 and the number itself. 31, 37 and 41 have no such factor, so all three are prime numbers. 65 breaks up as $65=5\times 13$, so it has factors besides 1 and 65 and is a composite number. Hence 65 is the odd one out, so option (d) is correct.

Number series Work out the difference between each pair of consecutive terms. 13.5-12=1.5, 15.5-13.5=2, 18-15.5=2.5 — every difference is 0.5 more than the one before it. So the next difference is 2.5+0.5=3. Missing term =18+3=21. Hence the required number is 21, so option (c) is correct.

Letter series completion The series has 16 places, so break it into four blocks of four letters each. The blocks read a _ c d / _ c b a / _ b c d / d c _ a, and the pattern is 'abcd' and 'dcba' turn by turn. Block 1 needs b, block 2 needs d, block 3 needs a and block 4 needs b. So the blanks, taken in order, are filled by b, d, a, b. Hence the answer is 'bdab', so option (b) is correct.

Alpha-numeric series Handle the letters and the numbers as two separate patterns. Letters: X, V, T, R and P stand at places 24, 22, 20, 18 and 16, so each letter moves 2 places backwards; the next place is 14, which is N. Numbers: $9,25,49,121,169$ are $3^2,5^2,7^2,{11}^2,{13}^2$ — the squares of the prime numbers taken in order. The prime after 13 is 17, so the next number is ${17}^2=289$. Hence the next term is N289, so option (b) is correct.

Letter series Write down the position of each letter in the English alphabet. C =3, E =5, H =8, L =12, Q =17. The gaps between them are $+2,+3,+4,+5$, growing by one every time. So the next gap is +6, which gives the position 17+6=23. The 23rd letter of the alphabet is W. Hence the missing term is W, so option (d) is correct.

Missing letter series The given string has 15 places, so split it into three equal blocks of 5 letters each: b _ _ h j / _ d _ h _ / b _ f _ j. Every block that is complete enough to read shows the same five letters b, d, f, h, j, i.e. alternate letters of the alphabet. Block 1 already has b, h, j, so the two blanks are d and f. Block 2 already has d and h, so its three blanks are b, f and j. Block 3 already has b, f and j, so its two blanks are d and h. Reading the missing letters in order gives d f b f j d h, so option (c) is correct.

Mathematical sign substitution First replace every sign of the expression by the sign given against it. So + becomes $\times$, - becomes $÷$, $\times$ becomes - and $÷$ becomes +. The expression $\left(15+2\right)+6-\left(5÷4\right)+4$ therefore becomes $\left(15\times 2\right)\times 6÷\left(5+4\right)\times 4$. Simplify the brackets: $15\times 2=30$ and 5+4=9, which gives $30\times 6÷9\times 4$. By BODMAS, $\times$ and $÷$ are done from left to right: $30\times 6=180$, then $180÷9=20$. Finally $20\times 4=80$, so option (a) is correct.

Mathematical sign substitution Replace the signs exactly as instructed before doing any calculation. Only +, - and $\times$ actually occur inside the expression, so the numerator $\left(30-5\right)\times 5+2$ becomes $\left(30\times 5\right)÷5-2$. Solve the bracket first: $30\times 5=150$, so the numerator is $150÷5-2$. By BODMAS division comes before subtraction: $150÷5=30$, hence the numerator =30-2=28. The whole expression is $\frac{28}{4}=7$, so option (c) is correct.

Syllogism: definite conclusion 'All papers are copy' means the whole group of papers lies inside the group of copies. Since papers exist and each one of them is a copy, that group of papers forms a part of the copies. Therefore 'Some copies are papers' is bound to be true — a universal statement always gives this converse in the particular form. 'Some copies are clean' says nothing about where the clean part lies, so it may or may not overlap the papers; hence (a) is only possible, not certain. (b) and (d) are universal claims that the statements never make, so option (c) is correct.

Analogy: part and whole Read the complete pair first: a mouse is a part of a computer, without which the computer is not comfortably operated. The same part-to-whole relation must hold in the first pair. A string is a part of a guitar; it is the string that is plucked to produce the sound. A television, a refrigerator and a washing machine have no strings in them, so option (b) is correct.

Code language: word codes Compare the statements two at a time: the word common to a pair must own the code common to that pair. Statements 1 and 2 share only the word 'banana' and only the code 'hp', so banana = hp. Statements 1 and 3 share only 'apple' and only 'rt', so apple = rt. Statements 2 and 3 share only 'grape' and only 'ns', so grape = ns. In statement 2 the words are banana, orange, grape and the codes are hp, qw, ns; hp and ns are already fixed for banana and grape. The only code left for 'orange' is 'qw', so option (b) is correct.

Odd one out: States and UTs All four names belong to the political map of India, so compare their administrative status. Punjab, Haryana and Rajasthan are States; each has its own legislative assembly and a Governor as constitutional head. Andaman & Nicobar Islands is a Union Territory, administered directly by the Union Government through a Lieutenant Governor. Hence Andaman & Nicobar does not belong to the group of States, and option (d) is the odd one out.

Word rearrangement: position DEVELOPMENT has 11 letters: D, E, V, E, L, O, P, M, E, N, T. Arranging them in reverse alphabetical order (Z towards A) gives V, T, P, O, N, M, L, E, E, E, D. In an 11-letter word, the 11th letter from the right end is the 11-11+1=1st letter from the left, which is V. Now count 5 places to the right of V: T (1st), P (2nd), O (3rd), N (4th), M (5th). The required letter is M, so option (b) is correct.

Number series: prime multipliers The terms grow very fast, so check what each term is multiplied by to give the next one. $3\times 3=9$, $9\times 5=45$ and $45\times 7=315$. The multipliers are $3,5,7$ — successive prime numbers, so the next multiplier is the next prime, 11. Hence the required term $=315\times 11=3465$, so option (c) is correct.

Number series: differences Take the difference of each pair of consecutive terms. 289-89=200, 689-289=400, 1289-689=600 and 2089-1289=800. These differences themselves increase by 200 each time, so the next difference is 800+200=1000. Next term =2089+1000=3089, so option (a) is correct.