If x = y(mod z) denotes that when x is divided by z, the remainder is y, then for integers a, b, c, … and a prime number, p,
(a + b + c + …)p = (ap + bp + cp + …)(mod p)
To increase your comfort level with the kind of material that appears in Reading Comprehension passages, try reading newspaper editorials from somewhere in the middle.
If [x] denotes the greatest integer less than or equal to x, then for any positive integer, n,
[(n + 1)/2] + [(n + 2)/4] + [(n + 4)/8] + ... = n
The difficulty level of any section generally decreases with an increase in the number of questions. For example, in CAT 2008, the verbal section was easier, compared to the the other two sections.
In DS questions, one might get multiple answer values using one of the statements alone and then get a single value using both the statements together. In such cases, don't jump to the conclusion that the question can be answered using both the statements together as it is possible that some of the answer values obtained using a single statement might not be valid for that question and the question might be answerable using that statement alone itself.
While attempting RC, it is not necessary to read the entire passage and then go to the questions. You can directly go to the questions and try to solve the questions while you are reading the passage.
In an isosceles triangle, all the four centres viz. circumcentre, incentre, centroid and orthocentre lie on the median drawn from the vertex contained by equal sides to the non-equal side.
An important factor in solving Jumbled Sentences questions is learning to identify sentence pairs that can definitely be said to be consecutive. Look for links in sentences, connectors, and connecting ideas.
There is no general formula for the sum of any number of quantities in harmonic progression. Questions in H.P. are solved by inverting the terms and making use of the properties of the corresponding A.P.
Do not go by the length of questions in the verbal area. Difficult questions can be short, whereas lengthy questions, while time-consuming, may be easy.
In a right angled triangle, the mid-point of the hypotenuse is the circum-centre and the vertex containing the 90° angle is the orthocentre.
Make sure you read the instructions of verbal questions carefully. While instructions do not generally change from year to year, you should be confident and understand clearly when you attempt the question, as to what is expected. It would be useful to be familiar with the standard instructions for each question type, thus reducing the reading time for instructions.
For a fixed perimeter, the area of a regular polygon with higher number of sides will always be more than the area of a regular polygon of lesser sides. So, if an equilateral triangle, square, regular pentagon and regular hexagon have the same perimeter, then their order of areas will be: Equilateral triangle < Square < Regular pentagon < Regular hexagon.
Be prepared to be flexible in your approach while attempting mock papers. There have been occasions in past CATs where questions that have traditionally appeared in one section have been moved to another.
When three terms are in Arithmetic progression, the middle term is the arithmetic mean of the other two. It is always convenient to take three terms in an A.P. as a - d, a and a + d. Similarly four terms in A.P. could be taken as a - 3d, a- d, a + d and a + 3d.
Learn to read correctly, comprehensively, and precisely in the first iteration of reading a paragraph or a passage. This comes with practice in reading, attention to detail and unwavering concentration on the reading material.
The sum or difference of any two odd functions is an odd function.The division or multiplication of an even number of odd functions is an even function whereas that of an odd number of odd functions is an odd function.i.e. Odd function raised to an even power is an even function whereas raised to an odd power is an odd function. The derivative or integral of an odd function is an even function.
When solving verbal questions with very close answer options, have a consistent strategy: check whether spending time on questions that you are not really confident about rewards you. Depending on your analysis, either leave those questions, or spend more time in order to get them right.
Two quadrilaterals are similar if their corresponding angles are equal. Similar quadrilaterals have the ratio of any corresponding linear measurements equal to the ratio of their corresponding sides. Ratio of area of similar quadrilaterals will be equal to the square of the ratio of their sides.
In Verbal questions, learn to work with the options, especially question types such as choose the right word, FIJ, and Jumbled Sentences. This will help reduce the time taken to solve these questions.
