Number and letter series
Check three things in order: the differences between terms, then the ratios, then the position pattern (squares, cubes, primes, alternating rules). One of the three almost always resolves it.
Find the next term: 2, 6, 12, 20, 30, ?
42. The differences are 4, 6, 8, 10, so the next difference is 12. (Each term is n² + n.)
Find the next term: 3, 7, 16, 35, ?
74. The rule is ×2 then add an increasing constant: 3×2+1 = 7, 7×2+2 = 16, 16×2+3 = 35, 35×2+4 = 74. When differences look chaotic, test 'multiply then add'.
Find the odd term out: 4, 9, 16, 25, 36, 49, 64
Nothing is odd - they are consecutive squares from 2² to 8². Examiners include clean series to punish over-thinking, so always confirm the simplest rule first.
Find the next term: 2, 5, 11, 23, 47, ?
95. Each term is double the previous plus 1. Sequences that roughly double are almost always ×2 with a small correction.
Complete the letter series: AZ, BY, CX, DW, ?
EV. The first letter moves forward (A, B, C, D, E) while the second moves backward from Z (Z, Y, X, W, V). For letter series, write out positions 1-26 once and count numerically.
Practice this now
Coding-decoding
If MOUSE is written as NPVTF, how is TIGER written?
UJHFS. Every letter shifts forward by one. Test +1 and −1 first; they account for a large share of coding questions.
If CAT is coded as 24, how is DOG coded?
26. Add the alphabet positions: C(3) + A(1) + T(20) = 24, and D(4) + O(15) + G(7) = 26. When a word maps to a number, try the sum of positions, then the product.
In a code, EARTH is written as HTRAE. How is PLANET written?
TENALP. The word is simply reversed. Always check reversal before hunting for a shift.
If 'blue' means 'sky', 'sky' means 'cloud' and 'cloud' means 'rain', what is water falling from above called in that code?
Cloud. Real rain maps to the word 'cloud'. Substitution-code questions are answered by tracing the chain one step, not by reasoning about the real world.
Practice this now
Blood relations and family trees
Draw the tree. Use a horizontal line for spouses and siblings, a vertical line for parent to child, and mark gender only where the question states it. Three symbols solve every question in this family.
A is the son of B's father's sister. How is A related to B?
A is B's cousin. B's father's sister is B's aunt, so her son is B's first cousin.
Pointing to a photograph, a man says, 'She is the daughter of the only son of my grandmother.' How is she related to him?
She is his sister. The only son of his grandmother is his father, so the father's daughter is his sister.
P is Q's brother, R is Q's mother, S is R's father. How is P related to S?
P is S's grandson. R is Q's mother and P's mother, and S is R's father, so S is the grandfather of both P and Q.
Practice this now
Syllogisms
The only rule that matters: a conclusion follows if it must be true in every arrangement consistent with the statements. Anything that is merely possible does not follow. Venn diagrams settle these faster than words.
All roses are flowers. Some flowers fade quickly. Conclusion: some roses fade quickly. Does it follow?
No. The flowers that fade quickly might all be non-roses. The overlap is possible but not necessary, so the conclusion fails.
All engineers are graduates. No graduate is illiterate. Conclusion: no engineer is illiterate. Does it follow?
Yes. Engineers sit entirely inside graduates, and graduates are entirely outside illiterate, so engineers must be too.
Some books are pens. All pens are red. Conclusions: (i) some books are red, (ii) all pens are books. Which follow?
Only (i). The books that are pens must be red, so (i) follows. (ii) reverses the given relation, which is never valid.
Practice this now
Direction sense, seating and ranking
These are drawing problems, not thinking problems. Sketch axes for directions, a line or circle for seating, and remember that in a circular arrangement facing centre, a person's left is the clockwise direction reversed - fix that convention on paper before you place anyone.
A man walks 5 km north, turns right and walks 3 km, then turns right and walks 5 km. Where is he relative to the start?
3 km east of the starting point, facing south. Plot it: (0,0) to (0,5) to (3,5) to (3,0). The two 5 km legs cancel vertically.
In a row of 40 students, Ravi is 12th from the left. What is his position from the right?
29th. Position from right = total − position from left + 1 = 40 − 12 + 1. Forgetting the +1 is the single most common reasoning slip.
In a class, Meera ranks 7th from the top and 18th from the bottom. How many students are there?
24. Add the ranks and subtract the double-counted person: 7 + 18 − 1.
Five friends sit in a row. C is to the immediate right of D, A is at an end, B is between E and C, and D is not next to A. Who sits in the middle?
B. Working the constraints gives the order A, E, B, C, D from left to right: A takes an end, D must be away from A and immediately left of C, and B separates E from C.
Practice this now
Clocks and calendars
Both reduce to one formula each. The angle between clock hands is |30H − 5.5M| degrees. Calendars run on odd days: an ordinary year advances the weekday by 1 and a leap year by 2.
What is the angle between the hands of a clock at 3:30?
75°. The minute hand is at 180°, and the hour hand has moved to 3.5 × 30 = 105°, so the gap is 75°. Or apply |30 × 3 − 5.5 × 30| = |90 − 165| = 75.
If 1 January of a non-leap year is a Thursday, what day is 1 January of the next year?
Friday. 365 days is 52 weeks plus one odd day, so the weekday advances by exactly one. After a leap year it advances by two.
How many times do the hands of a clock overlap in 24 hours?
22 times. The hands coincide 11 times in every 12 hours, not 12, because there is no separate overlap at 12 and shortly after 11.
Practice this now
Statements, assumptions and critical reasoning
The final family is verbal-logical: statement and assumption, statement and conclusion, cause and effect, strengthen and weaken. The discipline is the same as in syllogisms - stay strictly inside the passage. An assumption is something the argument needs in order to work, not something that happens to be true in the world.
Statement: 'Use QUFF to revise - your marks will improve.' Which assumption is implicit?
That active revision through testing improves marks. The claim depends on that link; without it the advice is empty. Note that 'QUFF is the best tool available' is not assumed - the statement never compares it to anything.
A college notice says attendance below 75% bars a student from exams. Vikram sat the exam. What follows?
Only that his attendance was not below 75%. It does not follow that he attended every class or that he passed - stay with exactly what the rule guarantees.
Practice this now
A four-week practice plan
- ✓Week 1 - series, coding-decoding and odd-one-out. High frequency, quickest returns.
- ✓Week 2 - blood relations, directions, ranking. All solved by drawing; build the habit of always sketching.
- ✓Week 3 - syllogisms and puzzles (seating, floors, scheduling). Slowest to learn, so give them the most time.
- ✓Week 4 - clocks, calendars and critical reasoning, then only mixed timed sets from here on.
- ✓Throughout: one 15-question timed set daily, and re-solve every miss two days later from scratch.
Practice this now