At every step in life, we face diverse problems. They may be related to our family, health, education, career and much more. There can be no one who says that I never had a problem. Srimad Bhagwatam [10.14.58] says ‘padam padam yad vipadam’ which means that at every step in life we face problems. Now how to eradicate our problems is the biggest problem. One thing is sure that we cannot escape the discomfort created because of the problems of life. So the wiser advice will be to find out the root cause of our problems and try to kill it. And remember, we must help each other by solving each other’s problems. That makes life smoother. You get dependable and caring friends which you’d like to carry along throughout life.
Coming back to our math worries, many students have repeatedly asked us to create a Quant corner where we can post our (beautiful) solutions to beautiful math problems and discuss some small concepts. So here we are! This place is open for discussions as that is the best way of learning. So let’s start today’s mathematical extravaganza.
As a stand-alone word and as a collective noun, “number” can take a singular or a plural form.
e.g. Two hundred persons were at the party; the number(s) is (are) just astounding.
However, when preceded by an article and followed by the preposition “of”, “number” is singular and the verb that follows “number” will be conjugated singular or plural depending on whether there is a definite or indefinite article in front. The expression ‘the number of . . .’ is singular, while ‘a number of . . .’ is plural.
One question that will never stop coming from the students who prepare for CAT is “how to increase the vocabulary?” Suggestions such as read a lot, mug up words lists, make flash cards, subscribe to word a day etc. have always poured in from human race. Since I am the Queen of the Gadha Land, I am quite allergic to the advices that mortals always keep giving me. I like to make my own rules – Gadha Rules.
Each one of us must have followed some comic strip when we were kids but a few like me got addicted, and waste at least an hour each day even when we have left childhood at least 2 decades back. My day doesn’t complete without taking my daily dose of Archie, Peanuts, Nancy, Calvin and Hobbes, Dilbert, Garfield, Dennis etc.
But have you ever thought that these comics are a rich source of vocabulary and learning new words can really come with an incentive of laughter? Let me prove myself:
How do we find divisors of a number? For example, how do we calculate the number of divisors of 900?
Answer: 900 = 22 × 32 × 52. Therefore, any number that is a factor of 900 can have powers of 2 equal to 20, 21 or 22. Similarly, for 3, the powers can be 30, 31, or 32 and for 5 they will be 50, 51, or 52. Writing the powers in a line we have-
Now any combination of a power of 2, a power of 3, and a power of 5 will give us a divisor. For example, in the figure, 21 × 32 × 51 will be a divisor of 900. As we can select a power of 2 in 3 ways, a power of 3 in 3 ways, and a power of 5 in 3 ways, the total number of combinations will be 3 × 3 × 3 = 27. Therefore, the number of divisors of 900 is 27.