Arithmetic Reasoning: SSC CGL Reasoning

Formulas (2)

• Squares, cubes and the digit-sum test · Term n of a geometric progression
  $$T_n = a\,r^{\,n-1}$$
• LCM, HCF and remainders · HCF, LCM and remainders
  $$\text{HCF} \times \text{LCM} = a \times b \qquad N = k \times \text{LCM} + r$$

Watch out for (7)

• Multiplying before adding the sum
  → Order of operations and quick totals
• Squaring each number inside a bracket
  → Order of operations and quick totals
• Taking a square or a fourth power for a cube
  → Squares, cubes and the digit-sum test
• Using the digit sum for 7 or 11
  → Squares, cubes and the digit-sum test
• Raising the ratio to the power n
  → Squares, cubes and the digit-sum test
• Using HCF times LCM for three numbers
  → LCM, HCF and remainders
• Forgetting to add the remainder
  → LCM, HCF and remainders

Formulas (3)

• Two facts about two numbers · Two numbers from their sum and difference
  $$\text{Larger} = \frac{S + D}{2} \qquad \text{Smaller} = \frac{S - D}{2}$$
• Ages: the gap never changes · An age now and an age t years ago
  $$x = k(x - t)$$
• Fixed totals and equal shares · New share and the average of evenly spaced numbers
  $$\text{New share} = \frac{\text{Old count} \times \text{Old share}}{\text{New count}} \qquad \text{Average} = \frac{\text{First} + \text{Last}}{2}$$

Watch out for (8)

• Stopping at the middle number
  → Two facts about two numbers
• Taking the digit difference as the change
  → Two facts about two numbers
• Trusting one number test
  → Which relation follows from two equations
• Picking numbers that break the given equations
  → Which relation follows from two equations
• Ageing only one person
  → Ages: the gap never changes
• Keeping the ratio fixed
  → Ages: the gap never changes
• Dividing the old share instead of the total
  → Fixed totals and equal shares
• Finding the last term by adding the count
  → Fixed totals and equal shares

Formulas (3)

• Splitting a total in a ratio · Size of one part
  $$\text{One part} = \frac{T}{a + b} \qquad \text{One part} = \frac{\text{Difference}}{b - a}$$
• Chained ratios and profit shares · Joining ratios and sharing profit
  $$\frac{A}{C} = \frac{A}{B} \times \frac{B}{C} \qquad \text{Share} \propto \text{Capital} \times \text{Time}$$
• Adding to a mixture · Amount to add
  $$\text{New amount of added part} = \text{Fixed part} \times \frac{\text{its new ratio term}}{\text{fixed part's new ratio term}}$$

Watch out for (6)

• Dividing the total by one term
  → Splitting a total in a ratio
• Checking only the sum
  → Splitting a total in a ratio
• Joining ratios without matching the middle term
  → Chained ratios and profit shares
• Ignoring time in a partnership
  → Chained ratios and profit shares
• Changing the part that was not added
  → Adding to a mixture
• Giving the new amount instead of the amount added
  → Adding to a mixture

Formulas (3)

• A percentage as a fraction · A part, the whole, and selling price
  $$p\% \text{ of } N = \frac{p}{100} \times N \qquad N = \frac{A \times 100}{p} \qquad SP = CP \times \frac{100 + p}{100}$$
• Two changes one after the other · Net effect of two changes
  $$\text{Net change} = a + b + \frac{ab}{100}$$
• Simple and compound interest · Simple interest, k times, and compound rate
  $$SI = \frac{PRT}{100} \qquad R \times T = 100(k - 1) \qquad R = \frac{A_{n+1} - A_n}{A_n} \times 100$$

Watch out for (6)

• Using the share spent when the amount given is what is left
  → A percentage as a fraction
• Taking profit on the selling price
  → A percentage as a fraction
• Adding the two percentages
  → Two changes one after the other
• Dropping the sign of a fall
  → Two changes one after the other
• Counting the whole amount as interest
  → Simple and compound interest
• Dividing by the later amount
  → Simple and compound interest

Formulas (3)

• Speed, trains and average speed · Speed, units and average speed
  $$v = \frac{d}{t} \qquad 1\ \text{km/h} = \frac{5}{18}\ \text{m/s} \qquad \bar{v} = \frac{2ab}{a + b}$$
• Boats and streams · Boat and stream from the two speeds
  $$b = \frac{d + u}{2} \qquad s = \frac{d - u}{2}$$
• Work, taps and pipes · Same job, and pipes working together
  $$W_1 T_1 = W_2 T_2 \qquad \frac{1}{T} = \frac{1}{a} - \frac{1}{b}$$

Watch out for (6)

• Using the equal-distance shortcut for equal times
  → Speed, trains and average speed
• Forgetting the platform's length
  → Speed, trains and average speed
• Swapping the boat and the stream
  → Boats and streams
• Averaging distances instead of speeds
  → Boats and streams
• Treating workers and time as direct
  → Work, taps and pipes
• Adding the emptying pipe
  → Work, taps and pipes

Formulas (3)

• Counting pairs · Pairs and diagonals
  $$\text{Pairs} = \frac{n(n - 1)}{2} \qquad \text{Diagonals} = \frac{n(n - 3)}{2}$$
• Probability as a fraction · Probability and its complement
  $$P(E) = \frac{\text{favourable}}{\text{total}} \qquad P(\text{not } E) = 1 - P(E)$$
• Shape facts: volumes and diagonals · Cylinder, cone and diagonal
  $$V_{\text{cyl}} = \pi r^2 h \qquad V_{\text{cone}} = \tfrac{1}{3}\pi r^2 h \qquad d = \sqrt{l^2 + b^2}$$

Watch out for (5)

• Counting each pair from both ends
  → Counting pairs
• Counting the sides as diagonals
  → Counting pairs
• Dividing by the wrong total
  → Probability as a fraction
• Taking the cone as half the cylinder
  → Shape facts: volumes and diagonals
• Treating an approximate diagonal as exact
  → Shape facts: volumes and diagonals