Quantitative

Rule of Constant Example 4: How many litres of pure water should be added to 40 litres of 30% milk solution so that the resultant mixture is a 15% milk solution? We can have three different methods to solve the above problems including the rule of alligation. Let us take all of them to strengthen …

Mixture and Alligation Concepts | Tricks | Formulas for CAT Exam

Table of Content Concepts and Formulas Tricks Rule of Constant Mixing with replacement Two different Mixture Practice Problems Questions from Mixtures and Alligation topic have increased in recent CAT exam. Usually, we apply the concepts and formulas of weighted average, percentages and ratios to solve such questions. A shortcut tricks of the criss-cross method is …

3 steps to find last two digits of a number with power

Last Two digits: The objective of this article is to understand the concept and approach to solve questions like: Find the last two digits of ${2^{234}}$ ${31^{123}}$ ${73^{35}}$ There are two-three shortcut approaches to solve the above problems. But before we go and apply the same, we need to understand the following basic points. Finding …

Maxima Minima : AM-GM Concept

AM-GM-HM Concept A wide variety of questions are being framed in this area. There is no thumb rule to solve all these problems. Many a time, simple observation and hit and trial methods of putting the values work. However, to get the results quickly and accurately, there are specific categories of questions which require knowledge of …

AM-HM Concept : Time Speed and Distance

AM-HM Concept: The AM-HM concept states that if the speeds are in arithmetic progression/ harmonic progression then, the corresponding time taken are in harmonic progression /arithmetic progression and vice versa. Note: We use this AM-HM concept only when the same distance is traveled at different speeds. Here is the proof of AM-HM Concept Say, a …

Maxima Minima Concept of Set Theory and Venn Diagram

Maxima Minima Concept based on Set theory or Venn diagram is very important for CAT exam not only in Quant section but more so in LRDI section. Many varieties of questions can be framed from this area. In most of the cases, we are required to find maximum and minimum value in Venn diagram related questions. …

Number of trailing zeroes and exponents of prime number in factorial

Finding the number of trailing zeroes in 100! (read factorial 100) has become the favorite question in quant among aspirants who prepare for CAT Exam.  In this section, we will be discussing the approaches to solve similar sorts of questions. Exponent of any prime number p in n! (factorial n) The exponent of any prime …

Chinese Remainder Theorem: If a number N = a×b, where a and b are prime to each other, and M is a number such that the remainders obtained when M is divided by a and b are ${r_1}\; and\;{r_2}$ respectively, then the remainder obtained when M is divided by N is the smallest value in …