A must read on Numbers for GMAT Quant - Part 3
In the previous two parts of this article on Numbers, we discussed the importance of Numbers as a topic for GMAT Quant and also the important properties of Zero, that are tested very often in questions on GMAT Quant. If you have not gone through the first two parts, you can do so by clicking on these links:
https://bit.ly/302pvtjhttps://bit.ly/3Dhera6In the final part of this series, let’s take a look at some properties of the numbers ONE and TWO, relevant to GMAT questions.
ONE – The one and only! ONE is probably the most underrated positive integer by GMAT aspirants. Therefore, it’s easy to figure out that GMAT does test it quite often. You could call ONE as the ‘common man of positive integers’ – immensely important but hardly considered by a lot of test-takers.
Importance of ONE in Arithmetic A couple of properties of ONE that get tested in a lot of questions on Number properties are as follows:
One is an odd integer
One is neither prime nor composite
In a lot of Data Sufficiency questions involving Primes and Composites (especially the Yes-No type of DS questions), the number ONE is your gateway to getting an easy NO to the main question. This is because it is neither prime nor composite.
For example, if the question stem is
“Is K prime?”, all that one must do is to
take K as 1 to get a No to the question. However, sadly, many students do not realise this and struggle taking bigger composite numbers to prove a No.
Nothing changes if the question stem were to be “Is K composite?” because
1 is not a composite number either.
Result: So next time you see a GMAT question on Primes (especially the DS ones), don’t forget to consider ONE as a case. Divisibility & Remainders Moving to the concept of divisibility, ONE has a lot of significance here. The following properties come to mind when one talks of questions that have come up on the GMAT:
One is a factor of all numbers i.e. all numbers are perfectly divisible by 1
One is co-prime with any number
One is the HCF of a set of co-prime numbers Note:
A set of numbers is said to be co-prime if they have no other common factor except 1. For example, 4 and 9 are co-prime, because the only common factor that they share is 1. On a related note, ONE is an important number when you answer questions on Remainders.
ONE is THE number to gun for if you want to solve remainder questions, especially if the question involves finding the remainder when the dividend is an exponential value, and the divisor is a small number.
For example, if we need to find the remainder of \(17^{43}\) divided by 10, using remainder rules,
we need to find out the power of 17 which gives us the remainder as 1 when divided by 10 and
use that as a cycle to find out the final remainder
In both steps, ONE is the most important number.
Result: Try to obtain ONE as the remainder, as far as you can by manipulating the given expression Unitary MethodOne is the basis for the whole of Unitary method In topics like Rates, Time & Distance, Ratios and percentages, we cannot talk enough about the importance of ONE.
In all these topics, a very important technique that we use to solve questions is the Unitary method. The very foundation of the unitary method is ONE because the word ‘Unit’ literally means ‘ONE’.
Importance of ONE in Algebra When it comes to the module of Algebra, there are some properties of ONE that can come in handy in topics like Functions and Exponents.
One is the multiplicative identity / divisive identity When ONE is multiplied with any number, the final result will be the number itself. A similar inference can be drawn when ONE is divided by any number, which actually follows from the fact that 1 is a factor of all numbers
For example, if a * 1 = a, the operator * could represent either multiplication or division.
Exponents & Roots In questions on exponents and roots, it’s important to remember that:
ONE is a perfect square as well as a perfect cube.
One is the approximation for higher order roots like cube root of 2 or fourth root of 3 and so on.
Any number (except ZERO) yields ONE when raised to the power of ZERO i.e. \(x^0\) = 1 (provided x itself is not equal to zero because \( 0^0\) is not defined) Result: \(x^0\) holds the key to solving many questions on exponents. Probability Lastly, moving on to a topic like Probability, the following property is applied quite frequently in questions on Probability.
The sum of all probabilities is ONE The corollary of this is P(E) + P(E`) = 1 which turns out to be invaluable in solving a lot of questions in Probability.
That’s it folks, that’s all about the special number ONE!
We now discuss the number making a Cameo appearance (or at least it seems like amid the two bigwigs we have discussed till now)
TWO to Tango In terms of significance, the number TWO cannot be compared to either of the previous two numbers. However, owing to some interesting properties, GMAT does test it quite often.
Questions on primes and composites test the following properties quite often:
TWO is the smallest prime number
TWO is the only even prime number
The fact that TWO is even actually opens up the possibility of solving questions on Primes using the concept of Odds and evens. Unfortunately, many test takers do not take this route and instead, resort to number plugging, which should be avoided as far as one can.
Result: Take advantage of the even nature of TWO to solve questions on Primes Rare questions can also test the following property of TWO and hence it’s important to know such minutiae:
TWO is one of the numbers that is a part of the ONLY pair of consecutive primes Divisibility & Remainders Questions on the topic of divisibility usually tend to test the following concepts of TWO.
TWO is a factor of all even numbers i.e. any even number is always divisible by 2
TWO is the only number which has ONE odd and ONE even factor
However, these questions are few are can be found far in between.
And that’s all we had folks on these three special numbers. By now, it’s amply clear to a lot of you who have gone through all the three parts of this article, that the numbers ZERO and ONE have so many important features that you should never even think of ignoring them while solving questions from the various topics we mentioned as part of the discussion of properties.
The number TWO does have some interesting properties, but we saw that the application was limited to mostly questions on Number properties and divisibility.
We sincerely hope that you have enjoyed reading through this article and refreshing your memory about aspects that you already knew / found something that you did not know and jotted it down and vowed to use it in questions. We certainly have loved creating this article for all of y’all and would like to believe that this will help you improve your performance on the GMAT Quant section for sure.
In the next couple of days, we shall post a set of questions which highlight the properties of Zero, One and Two as discussed in this article. This way, you get to apply what you learned by reading this article.
Until the next article on GMAT Quant, it’s Ciao from us!