IIFT Entrance Exam Quantitative Aptitude Flashcards

24 sample cards from the Quantitative Aptitude deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. State the key logarithm rules.

   log(mn) = log m + log n; log(m/n) = log m - log n; log(m^k) = k log m; change of base: log_b a = log a / log b; log_b b = 1; log_b 1 = 0; a^(log_a x) = x.

2. How do you simplify and rationalize surds like 1/(sqrt(a)+sqrt(b))?

   Multiply numerator and denominator by the conjugate (sqrt(a)-sqrt(b)): 1/(sqrt(a)+sqrt(b)) = (sqrt(a)-sqrt(b))/(a-b). Surd rules: sqrt(a)xsqrt(b)=sqrt(ab), sqrt(a)/sqrt(b)=sqrt(a/b).

3. Give the nth term and sum formulas for an arithmetic progression (AP).

   nth term: a_n = a + (n-1)d. Sum: S_n = n/2[2a + (n-1)d] = n/2(a + l), where a = first term, d = common difference, l = last term.

4. Give the nth term and sum formulas for a geometric progression (GP).

   nth term: a_n = a r^(n-1). Sum of n terms: S_n = a(r^n - 1)/(r - 1) for r != 1. Sum to infinity (|r|<1): S = a/(1 - r).

5. State the formulas for the sum of the first n natural numbers, their squares, and their cubes.

   Sum = n(n+1)/2; Sum of squares = n(n+1)(2n+1)/6; Sum of cubes = [n(n+1)/2]^2 (the square of the sum).

6. State the standard algebraic identities for (a+b)^2, (a-b)^2, a^2 - b^2, and (a+b)^3.

   (a+b)^2 = a^2 + 2ab + b^2; (a-b)^2 = a^2 - 2ab + b^2; a^2 - b^2 = (a+b)(a-b); (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3; a^3 + b^3 = (a+b)(a^2 - ab + b^2).

7. What is the identity for a^3 + b^3 + c^3 - 3abc?

   a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca). If a + b + c = 0, then a^3 + b^3 + c^3 = 3abc.

8. State the angle-sum properties of a triangle and the exterior angle theorem.

   Interior angles of a triangle sum to 180 degrees. An exterior angle equals the sum of the two remote (non-adjacent) interior angles. The largest angle lies opposite the longest side.

9. State the Pythagorean theorem and the triangle inequality.

   In a right triangle, hypotenuse^2 = sum of squares of the other two sides. Triangle inequality: the sum of any two sides exceeds the third; the difference of any two sides is less than the third.

10. Give the sum of interior and exterior angles of an n-sided polygon.

    Sum of interior angles = (n - 2) x 180 degrees. Sum of exterior angles = 360 degrees (always). Each interior angle of a regular polygon = (n-2)x180/n.

11. List the area formulas for square, rectangle, parallelogram, rhombus, and trapezium.

    Square = side^2; Rectangle = length x width; Parallelogram = base x height; Rhombus = (1/2) x product of diagonals; Trapezium = (1/2) x (sum of parallel sides) x height.

12. State the key circle theorems about angles and tangents.

    Angle at the center = twice the angle at the circumference on the same arc. Angle in a semicircle = 90 degrees. A tangent is perpendicular to the radius at the point of contact; tangents from an external point are equal in length.

13. Give the circumference and area of a circle, and arc length/sector area for angle theta degrees.

    Circumference = 2(pi)r; Area = (pi)r^2. Arc length = (theta/360) x 2(pi)r; Sector area = (theta/360) x (pi)r^2.

14. State the distance, midpoint, and slope formulas in coordinate geometry.

    Distance = sqrt[(x2-x1)^2 + (y2-y1)^2]; Midpoint = ((x1+x2)/2, (y1+y2)/2); Slope m = (y2-y1)/(x2-x1). Parallel lines have equal slopes; perpendicular slopes multiply to -1.

15. Give the equation of a line in slope-intercept form and the area of a triangle from vertices.

    Line: y = mx + c (m = slope, c = y-intercept). Triangle area from vertices = (1/2)|x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|.

16. State the surface area and volume formulas for a cube and a cuboid.

    Cube (side a): Volume = a^3, Total surface area = 6a^2. Cuboid (l,b,h): Volume = lbh, TSA = 2(lb + bh + hl), diagonal = sqrt(l^2 + b^2 + h^2).

17. State volume and surface area formulas for a cylinder, cone, and sphere.

    Cylinder: V = (pi)r^2h, CSA = 2(pi)rh. Cone: V = (1/3)(pi)r^2h, CSA = (pi)rl (l = slant height). Sphere: V = (4/3)(pi)r^3, Surface area = 4(pi)r^2.

18. State the basic trigonometric ratios and the fundamental identity.

    sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent = sin/cos. Identity: sin^2(x) + cos^2(x) = 1; also 1 + tan^2 = sec^2 and 1 + cot^2 = cosec^2.

19. In heights and distances, define angle of elevation and angle of depression.

    Angle of elevation: the upward angle from the horizontal to an object above. Angle of depression: the downward angle from the horizontal to an object below. They are equal (alternate angles) for the same line of sight.

20. How do you find the number of factors and the sum of factors of a number N = p^a x q^b?

    Number of factors = (a+1)(b+1). Sum of factors = [(p^(a+1)-1)/(p-1)] x [(q^(b+1)-1)/(q-1)]. The number of factors counts all combinations of prime powers.

21. State the relationship between HCF, LCM, and the product of two numbers.

    HCF x LCM = product of the two numbers. HCF takes the lowest powers of common primes; LCM takes the highest powers of all primes appearing.

22. State divisibility rules for 3, 4, 8, 9, and 11.

    By 3: digit sum divisible by 3. By 9: digit sum divisible by 9. By 4: last two digits form a multiple of 4. By 8: last three digits divisible by 8. By 11: difference of alternate-digit sums is 0 or a multiple of 11.

23. How do you find the number of trailing zeros in n! (factorial)?

    Count factors of 5: trailing zeros = floor(n/5) + floor(n/25) + floor(n/125) + ... (sum until terms become 0). Zeros come from pairs of 2 and 5, and 5s are the limiting factor.

24. State the formulas for permutations nPr and combinations nCr, and the binomial theorem general term.

    nPr = n!/(n-r)! (order matters); nCr = n!/[r!(n-r)!] (order doesn't matter); note nCr = nPr/r!. Binomial: (a+b)^n general term T(r+1) = nCr a^(n-r) b^r.

What this deck covers

Quantitative Aptitude flashcards FAQ