Simplification and Approximation Questions for RBI GRADE B

BODMAS Rule — The Foundation

Every simplification question follows a strict order of operations. BODMAS stands for Brackets, Orders (powers and roots), Division, Multiplication, Addition, Subtraction. Violating this order is the single biggest source of errors. Always resolve innermost brackets first, then move outward.

• Order: Brackets first (round, curly, square in that inner-to-outer order), then powers/roots, then left-to-right for division and multiplication, then left-to-right for addition and subtraction.
• Division and Multiplication have equal priority — solve left to right, do NOT always divide before multiplying.
• Same rule applies to Addition and Subtraction — left to right, not always add first.
• A negative sign outside a bracket flips all signs inside when bracket is removed.
• Nested brackets: resolve () first, then {}, then [].

Key Arithmetic Identities to Memorize

RBI Grade B setters embed these algebraic identities inside large expressions to test whether you can spot and shortcut rather than expand laboriously. Recognizing a perfect square or difference of squares cuts calculation time by 70 percent.

• (a + b)^2 = a^2 + 2ab + b^2
• (a - b)^2 = a^2 - 2ab + b^2
• (a + b)(a - b) = a^2 - b^2 — most exam-friendly identity
• a^3 + b^3 = (a + b)(a^2 - ab + b^2)
• a^3 - b^3 = (a - b)(a^2 + ab + b^2)
• Sum of first n natural numbers = n(n+1)/2; sum of squares = n(n+1)(2n+1)/6

Fraction and Decimal Conversion Table

Approximation questions often hide fractions like 5/8 or 7/9 inside large expressions. If you know the decimal equivalent by heart, you avoid long division entirely. Memorize fractions with denominators 2 through 12.

• 1/2=0.5, 1/3=0.333, 1/4=0.25, 1/5=0.2, 1/6=0.1667, 1/7=0.1428, 1/8=0.125, 1/9=0.111, 1/10=0.1
• 3/4=0.75, 2/3=0.667, 3/8=0.375, 5/8=0.625, 7/8=0.875
• 1/11=0.0909, 1/12=0.0833
• Percentage shortcuts: 1/6 = 16.67%, 1/7 = 14.28%, 1/8 = 12.5%, 1/9 = 11.11%
• Trick: To find 37.5% of any number, use 3/8 of that number instead.

Approximation Technique — Round and Adjust

Approximation questions explicitly tell you to find the nearest value. The strategy is to round each number to the nearest convenient figure (usually a multiple of 10, 100, or a recognizable fraction), compute quickly, then pick the answer option closest to your estimate. You do NOT need the exact answer.

• Round to nearest 10 or 100 to simplify multiplication and division.
• If you round one number up, try to round another down to keep the error balanced.
• Square roots: memorize perfect squares up to 30^2 = 900, and cube roots up to 10^3 = 1000.
• For sqrt of non-perfect-square, e.g., sqrt(527): 22^2=484, 23^2=529, so sqrt(527) is approximately 22.96, round to 23.
• In approximation MCQs, options are usually spaced at least 5-10 units apart — so a rough estimate is sufficient.

Squares, Cubes, and Surds — Quick Reference

RBI Grade B Phase 1 regularly tests expressions with large squares, cubes, and square roots. Knowing these by heart eliminates calculation entirely.

• Squares: 1 to 30 must be memorized cold. Key ones: 17^2=289, 18^2=324, 19^2=361, 24^2=576, 25^2=625, 27^2=729.
• Cubes: 1^3=1, 2^3=8, 3^3=27, 4^3=64, 5^3=125, 6^3=216, 7^3=343, 8^3=512, 9^3=729, 10^3=1000.
• Surd rule: sqrt(a) x sqrt(b) = sqrt(ab); sqrt(a)/sqrt(b) = sqrt(a/b).
• Rationalize surds: multiply numerator and denominator by conjugate. E.g., 1/(sqrt5 - sqrt3) x (sqrt5+sqrt3)/(sqrt5+sqrt3) = (sqrt5+sqrt3)/2.

• Treating Division-before-Multiplication as absolute: 12 / 4 x 3 should be solved left to right as (12/4) x 3 = 9, NOT 12/(4x3) = 1. Many aspirants get this wrong under time pressure.
• Ignoring negative sign outside bracket: -(3 + 4) = -7 not -3+4. In long expressions this error compounds quickly.
• Over-rounding in approximation: rounding 4798 to 5000 instead of 4800 introduces too much error. Round to the nearest logical number, not just the nearest thousand.
• Not memorizing fraction-decimal equivalents: spending 30 seconds doing long division for 5/8 in an approximation question kills your time budget.
• Confusing (a-b)^2 with a^2 - b^2: these are completely different identities. (a-b)^2 = a^2 - 2ab + b^2, not a^2 - b^2.

• BODMAS mnemonic story: Big Orange Dogs Mostly Ate Samosas — B-O-D-M-A-S. Say it once before starting any complex simplification.
• Fraction-decimal anchor: think of a clock. 1/4 hour = 15 min = 0.25. 1/2 hour = 30 min = 0.5. 3/4 hour = 45 min = 0.75. Anchors the 4-series firmly.
• Difference of squares visual: imagine a square tile of side a with a smaller corner square of side b cut out. The remaining area factors into (a+b)(a-b).
• For cube roots: 5 cubed looks like 5 sides of a dice (5^3=125). 7 cubed = 343 — remember 7-Eleven = 7 x 11 = 77, double it = 343 (rough hook).

• Phase 1 Quant typically has 30 questions in 60 minutes — simplification and approximation questions should take no more than 30-40 seconds each. Treat them as free marks.
• Recent RBI Grade B papers embed approximation inside DI sets — a column of values needs to be rounded before calculating ratios or percentages. Practice DI with approximation together.
• The difficulty is LOW-MEDIUM for direct simplification. Do these first to build a score buffer before moving to difficult arithmetic or data sufficiency.
• Watch for questions mixing surds with basic operations — e.g., sqrt(1764) + (13)^2 - 45 percent of 80. These test whether you know perfect squares cold.
• In the Phase 2 ESI/FM paper, approximation appears inside macroeconomic calculations (e.g., estimating GDP growth or fiscal deficit ratios). The same rounding instinct applies there too.