Unit 6: Interest based problems, Analytical reasoning and Non verbal reasoning

Part 1: Interest Based Problems

Interest is the cost of borrowing money or the return on investment for lending money. It is a fundamental concept in finance, banking, and general quantitative aptitude.

1. Concepts of Interest Calculations

Before diving into specific types of interest, it is crucial to understand the foundational terminologies:

• Principal (): The original sum of money borrowed, lent, or invested.
• Rate of Interest (): The percentage at which interest is charged or calculated on the principal, usually expressed per annum (p.a.).
• Time ( or ): The duration for which the money is borrowed or invested, typically expressed in years.
• Amount (): The total money returned after the given time period. It is the sum of the Principal and the Interest ().

2. Simple Interest (SI)

Simple Interest is calculated only on the original principal amount for the entire period. It remains constant for every year.

• Formula:
• Amount Formula:
• Key Concept: If a sum is invested at SI, the interest earned in the 1st year is identical to the interest earned in the 10th year.

3. Compound Interest (CI)

Compound Interest is calculated on the principal as well as on the accumulated interest of previous periods. It is "interest on interest."

• Formula for Amount:
• Formula for CI:
• Different Compounding Frequencies:
  • Half-Yearly (Semi-annually): Rate becomes , Time becomes . Formula:
  • Quarterly: Rate becomes , Time becomes . Formula:

4. Difference between CI and SI

The difference arises because CI calculates interest on previous interest, whereas SI does not. For the first year (if compounded annually), . The difference starts accumulating from the second year onwards.

• For 2 Years:
  
• For 3 Years:
  

5. EMI (Equated Monthly Installment) Calculations

An EMI is a fixed payment amount made by a borrower to a lender at a specified date each calendar month. EMIs are used to pay off both interest and principal each month so that over a specified number of years, the loan is paid off in full.

• Formula:
  
  Where:
  • = Loan Principal Amount
  • = Monthly interest rate (i.e., Annual Rate / 12 / 100)
  • = Loan tenure in months
• Conceptual Note: In the early years of a loan, a larger portion of the EMI goes towards paying the interest. Towards the end of the loan tenure, the principal repayment forms a larger proportion of the EMI.

Part 2: Analytical Reasoning

Analytical reasoning assesses the ability to visualize, isolate, and logically deduce relationships between different elements.

1. Direction Sense

Direction sense involves tracing the path of an object or person and determining their final position or the distance covered relative to the starting point.

• The Compass (Cardinal & Ordinal Directions):
  • 4 Main Directions: North (N), South (S), East (E), West (W).
  • 4 Sub-directions: North-East (NE), North-West (NW), South-East (SE), South-West (SW).
• Degrees and Turns:
  • Turning "Right" generally implies a clockwise turn.
  • Turning "Left" implies a anti-clockwise turn.
• Pythagoras Theorem:
  • Often, finding the shortest distance between the starting and ending points requires visualizing a right-angled triangle.
• Shadow Concepts:
  • Morning (Sunrise): Sun is in the East; shadows fall toward the West.
  • Evening (Sunset): Sun is in the West; shadows fall toward the East.
  • 12:00 Noon: Rays are vertically downward; no shadow is formed.

2. Blood Relation

Blood relation problems test logical reasoning based on family trees and biological relationships.

• Basic Terminology:
  • Paternal: Related through the father (e.g., Paternal Uncle).
  • Maternal: Related through the mother (e.g., Maternal Uncle).
  • Sibling: Brother or sister.
  • Spouse: Husband or wife.
• Family Tree Notation (Standard Practice):
  • Male: Denoted by a Square [ ] or a Plus sign ( + ).
  • Female: Denoted by a Circle [ ] or a Minus sign ( - ).
  • Marriage: Denoted by a double line ( = ) or a double-headed arrow ( ).
  • Siblings: Denoted by a single horizontal line ( — ).
  • Generations: Denoted by vertical lines ( | ).
• Types of Problems:
  1. Indicating/Pointing Form: A person points to someone (in a photograph or physically) and describes their relation. Strategy: Break the sentence down in reverse order or use "my" as the starting point.
  2. Puzzle Form: Information about multiple family members is given. Strategy: Draw a complete family tree step-by-step.
  3. Coded Form: Relationships are represented by symbols (e.g., means A is the father of B). Strategy: Decode the symbols one by one and build the tree.

Part 3: Non Verbal Reasoning (Visual Reasoning)

Non-verbal reasoning relies on pictures, diagrams, and figures rather than words. It tests spatial visualization and pattern recognition.

1. Mirror and Water Images

These concepts deal with reflections of given figures.

• Mirror Image:
  • Formed by placing a mirror vertically next to the object.
  • Rule: Lateral inversion occurs. The Left side of the object becomes the Right side of the image, and vice versa. Top and Bottom remain unchanged.
  • Example: The mirror image of 'b' is 'd'.
• Water Image:
  • Formed by placing a mirror horizontally below the object (reflecting on a water surface).
  • Rule: Vertical inversion occurs. The Top of the object becomes the Bottom of the image, and vice versa. Left and Right remain unchanged.
  • Example: The water image of 'M' is 'W'.

2. Paper Cutting and Folding

This assesses spatial aptitude by asking how a piece of paper will look after being folded, cut, and then unfolded.

• Folding: When paper is folded, the design on one half overlaps the other. It acts like a mirror line.
• Cutting & Unfolding:
  • Unfolding a fold is equivalent to finding the mirror image of the cut/punched hole across the crease of the fold.
  • Strategy: Work backward. Unfold the paper step-by-step in the reverse order of how it was folded, applying mirror image rules at each crease.

3. Completion of the Figure

In these problems, a complex figure is given with one part missing (usually one quadrant).

• Strategy:
  • Identify the symmetry (horizontal, vertical, or diagonal).
  • Look for rotational patterns or alternating patterns in the existing quadrants.
  • Mentally or physically draw the missing lines in the blank space before looking at the options.

4. Embedded Figure

An embedded figure problem contains a target shape that is hidden or "embedded" inside a larger, more complex design.

• Characteristics: The hidden figure is usually of the same size and orientation (unless the question specifies that rotation is allowed).
• Strategy:
  • Focus on key intersections, unique angles, or specific line combinations of the target figure.
  • Use the rule of elimination by crossing out complex figures that clearly lack the required straight lines or curves.

5. Deviation of Figure (Odd One Out / Series Progression)

This topic requires identifying the logical rule that governs a series of figures or finding the figure that does not follow the general rule.

• Rules to look for:
  • Rotation: Elements rotating clockwise or anti-clockwise by specific degrees ().
  • Movement: Elements shifting positions (e.g., from corners to center).
  • Addition/Deletion: Lines or shapes being added or removed in a sequence.
  • Inversion/Flipping: Elements transforming into their mirror or water images.
• Strategy for Deviation (Odd One Out): Find a common property shared by all figures except one. The anomaly could be based on the number of sides, type of lines (straight vs. curved), direction of arrows, or shading.