State PSC (e.g. BPSC / UPPSC / MPSC) CSAT, Reasoning and General Mental Ability Syllabus

What is the formula for the average of the first n natural numbers?

Average of first n natural numbers = (n + 1) / 2. (Sum = n(n+1)/2.)

If the average of a group changes when one member is replaced, how do you find the new member's value?

Change in total = (change in average) x (number of members). New value = old value + total change.

What is the formula for Simple Interest?

SI = (P x R x T) / 100, where P = principal, R = rate% per annum, T = time in years. Amount = P + SI.

What is the formula for Compound Interest (amount) compounded annually?

Amount A = P(1 + R/100)^T; Compound Interest = A - P.

How does compounding frequency change the CI formula (half-yearly / quarterly)?

Half-yearly: A = P(1 + R/200)^(2T). Quarterly: A = P(1 + R/400)^(4T). Rate is divided and time multiplied by the frequency.

For 2 years, what is the difference between CI and SI on principal P at rate R%?

Difference = P x (R/100)^2 for 2 years. (For 3 years the difference is P(R/100)^2 x (3 + R/100).)

What are the area and perimeter formulas for a rectangle?

Area = length x breadth; Perimeter = 2(length + breadth); Diagonal = sqrt(l^2 + b^2).

What are the area and circumference formulas for a circle?

Area = pi x r^2; Circumference = 2 x pi x r; where r is the radius.

What is the area of a triangle given base and height, and Heron's formula?

Area = (1/2) x base x height. Heron's formula: Area = sqrt(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2.

What are the volume and total surface area of a cube and a cuboid?

Cube: Volume = a^3, TSA = 6a^2. Cuboid: Volume = lbh, TSA = 2(lb + bh + hl).

What are the volume and curved surface area of a cylinder and a sphere?

Cylinder: Volume = pi r^2 h, CSA = 2 pi r h. Sphere: Volume = (4/3) pi r^3, Surface area = 4 pi r^2.

State the Pythagoras theorem and the sum of interior angles of a triangle.

Pythagoras: in a right triangle, hypotenuse^2 = base^2 + perpendicular^2. Sum of interior angles of any triangle = 180 degrees.

In syllogisms, what does the statement 'All A are B' allow you to validly conclude?

'All A are B' means every A is inside B. Valid conclusion: 'Some B are A' (converse is particular). You cannot conclude 'All B are A'.

In syllogism logic, what can you conclude from 'No A are B'?

'No A are B' gives valid conclusions 'No B are A' and 'Some B are not A' (and 'Some A are not B'). The negative converse holds fully.

What is the rule about a conclusion drawn from two particular (Some) premises in syllogisms?

Two particular premises ('Some...') yield no definite conclusion. At least one premise must be universal to draw a valid conclusion.

In syllogisms, what is a 'complementary pair' (either-or) conclusion?

When neither of two conclusions individually follows but together they cover all possibilities (e.g., 'Some A are B' and 'Some A are not B' on the same terms), the 'Either...Or' pair is the valid answer.

In blood relations, who is your 'father's brother's son' to you?

Your father's brother's son is your cousin (paternal cousin). The father's brother is your uncle.

In direction sense, if you face North and turn 90 degrees clockwise, which direction do you face? And after a left turn from South?

Facing North + 90 degrees clockwise (right) = East. Facing South + left turn = East. (Clockwise: N to E to S to W.)

In a ranking problem, if a person is 7th from the top and 11th from the bottom, how many people are in the row?

Total = (rank from top) + (rank from bottom) - 1 = 7 + 11 - 1 = 17 people.

In coding-decoding by letter shift, if 'CAT' is coded as 'DBU', what is the rule?

Each letter is shifted forward by 1 position in the alphabet (C->D, A->B, T->U). The rule is +1 letter shift.

What are the alphabet position values of A, J, S, Z (useful for coding-decoding)?

A=1, ... J=10, ... S=19, ... Z=26. Tip: EJOTY (5,10,15,20,25) helps locate positions quickly.

What is the next term in the series 2, 6, 12, 20, 30, ...? Explain the pattern.

Next term is 42. Differences increase by 2 each time (4,6,8,10,12). Equivalently term n = n(n+1): 1x2, 2x3, 3x4...

Identify the type: series 3, 6, 12, 24, 48. What is the next term?

It is a geometric progression with common ratio 2; next term = 96 (each term is doubled).

In seating arrangement, what does 'facing the centre' in a circular arrangement imply about left and right?

When all face the centre, a person's left hand points clockwise direction... actually their immediate left neighbour is in the clockwise direction and right is anticlockwise (mirror of facing outward).

In a linear seating arrangement facing North, where are a person's left and right?

Facing North: left hand points West, right hand points East. So the person to one's right is on the East side.

When reading a Bar Graph, how do you compute the percentage increase between two bars?

Percentage increase = ((later value - earlier value) / earlier value) x 100. Read bar heights against the y-axis scale.

In a Pie Chart, how do you convert a sector's central angle (degrees) into the value it represents?

Value = (sector angle / 360) x total. Conversely, percentage of a sector = (angle / 360) x 100; each 1% = 3.6 degrees.

In a table-based DI question, what is the key first step before calculating?

Identify what each row and column represents and the units, note totals, and read exactly what the question asks (e.g., absolute value vs percentage vs ratio) before computing.

In a Line Graph showing a trend over time, how do you identify the period of maximum increase?

Find the segment between two consecutive points with the steepest upward slope, i.e., the largest positive difference between consecutive values.

What is a 'caselet' in Data Interpretation and how should it be approached?

A caselet presents data in a paragraph (no chart/table). Approach by extracting the numbers into your own table or Venn diagram, then solve as a normal DI set.

In Data Sufficiency, what does it mean when 'Statement I alone is sufficient but Statement II alone is not'?

Statement I by itself gives a unique answer to the question, while Statement II alone does not. You evaluate each statement independently before combining them. The goal is to judge sufficiency, not to compute the final answer.