Aptitude EssentialsQuant, Reasoning & Verbal Shortcuts

Module 1 – Quantitative Aptitude Fundamentals

Quantitative Aptitude Fundamentals

• Percentage means a value per hundred. x%=x100x%=x100x%=100x​
• To convert a fraction into a percentage: Percentage=Fraction×100
• To convert a percentage into a fraction: x%=x100x%=x100x%=100x​
• If a number increases from A to B: Increase percentage=B−AA×100Increase percentage = B-AA100Increase percentage=AB−A​×100
• If a number decreases from A to B: Decrease percentage=A−BA×100Decrease percentage = A-BA100Decrease percentage=AA−B​×100
• A 20% increase followed by a 20% decrease does not give the original value.
• Net percentage change for successive changes a%a%a% and b%b%b%: a+b+ab100a+b+100ab​ Use a negative sign for a decrease.
• A 10% increase followed by a 10% decrease gives: 10−100=−1%10-100=-1%10−100​=−1%
• If the price increases by x%x%x%, the required consumption reduction to maintain expenditure is: x100+x×100x100+xx​×100
• If the price decreases by x%x%x%, consumption can increase by: x100−x×100x100-x100−xx​×100

Profit, Loss, and Discount

• Cost Price (CP) is the price paid to purchase an item.
• Selling Price (SP) is the price at which an item is sold.
• Profit occurs when: SP>CP
• Profit: Profit=SP−CPProfit=SP-CPProfit=SP−CP
• Profit percentage: Profit%=ProfitCP×100Profit% = ProfitCP100Profit%=CPProfit​×100
• Loss occurs when: SP<CP
• Loss: Loss=CP−SPLoss=CP-SPLoss=CP−SP
• Loss percentage: Loss%=LossCP×100Loss% = LossCP100Loss%=CPLoss​×100
• If profit is p%p%p%: SP=CP(1+p100)SP=CP(1+100p​)
• If loss is l%l%l%: SP=CP(1−l100)SP=CP(1-l100)SP=CP(1−100l​)
• Marked Price (MP) is the displayed price.
• Discount is the reduction from marked price.
• Discount: Discount=MP−SPDiscount=MP-SPDiscount=MP−SP
• Discount percentage: Discount%=DiscountMP×100Discount% = DiscountMP100Discount%=MPDiscount​×100
• Successive discounts a%a%a% and b%b%b%: Net discount=a+b−ab100Net discount = a+b-ab100Net discount=a+b−100ab​

Example An item costs ₹800 and is sold for ₹920. Profit=920−800=120Profit=920-800=120Profit=920−800=120 Profit%=120800×100=15%Profit%=120800100=15%Profit%=800120​×100=15% Answer: 15% profit.

Ratio and Proportion

• A ratio compares two quanties of the same type.
• Ratio a:b means: abba​
• Ratios must use the same units.
• If a:b=2:3, then a=2k and b=3k.
• If a:b=3:4 and b:c=8:9, make the common term b equal.
• In direct proportion, both quanties increase or decrease together. x1y1=x2y2x_1y_1=x_2y1​x1​​=y2​x2​​
• In inverse proportion, one quantity increases while the other decreases. x1y1=x2y2x_1y_1=x_2y_2x1​y1​=x2​y2​
• If 5 pens cost ₹100, 8 pens cost: 1005×8=16010058=1605100​×8=160
• If 5 workers complete a task in 12 days, 10 workers may complete it in: 5×1210=6 days51210=6 days105×12​=6 days assuming equal efficiency.
• In partnership problems, profit share is proportional to: Investment×Time
• If A invests ₹5000 for 12 months and B invests ₹8000 for 6 months: A:B=5000×12:8000×6A:B=500012:80006A:B=5000×12:8000×6 =600:48000=5:4

Average

• Average is: Average=Sum of valuesNumber of valuesAverage = Sum of valuesNumber of valuesAverage=Number of valuesSum of values​
• Sum of values: Sum=Average×Number of valuesSum=AverageNumber of valuesSum=Average×Number of values
• If one value is replaced: New sum=Old sum−Old value+New valueNew sum = Old sum-Old value+New valueNew sum=Old sum−Old value+New value
• If the average of 5 numbers is 20, their sum is: 5×20=100
• If a new number x is added to n values with average A: New average=nA+xn+1New average = nA+xn+1New average=n+1nA+x​
• Weighted average is used when groups have different sizes. Weighted average=∑(value×weight)∑weightsWeighted average = (valueweight) weightsWeighted average=∑weights∑(value×weight)​
• Average speed is not always the arithmetic average of speeds.
• For equal distances at speeds x and y: Average speed=2xyx+yAverage speed = 2xyx+yAverage speed=x+y2xy​

Example Average of 6 numbers is 25. If one number 30 is replaced by 42:

Old sum 6×25=150

New sum 150−30+42=162150-30+42=162150−30+42=162

New average 1626=276162​=27