Numerical Reasoning Test Made My Day!

Everyday when I got free time at work or whenever I feel bored when I’m at home I always check the My Day feature of Facebook’s Messenger. Earlier, I’m upset of the blue circles that are surrounding the My Day of my friends in Facebook, especially those My Day that are the latest ones which is like blinking of blue lights since I am sensitive to blue lights and my eyes will start to get in pain and then eventually my forehead. But as time passes by, I get used to it since my girl friends in Facebook post their My Day everyday and they are all beautiful, sometimes I react and sometimes not. Filipino women are so beautiful, I could resist myself to watch them.

So today, while I was laying in my bed I suddenly felt bored and I don’t want to sleep so I opened my Messenger app and then I started clicking the My Day of my friends and I was amazed to see a photo (see below) wherein it is a stuff related to Mathematics.

It is all about Numerical Reasoning.

So upon seeing that picture I quickly get up from my bed and then I look for my scientific calculator, a ballpen and a paper (for this case I utilized the back page of each sheet of this photocopied copy of a book in Calculus).

So I started with the first question:
1. 2187, 729, 243, 81, 27, 9, ___?
First looking to it i can say that 3 is the answer and there are many ways to obtained and prove that 3 is the answer which are as follows: (I am going to show just two ways.)

• Just using these three numbers namely: 81, 27 and 9. Divide 81 by 27, the quotient is 3. And then divide 27 by 3, the quotient is 9. So we can say we need to divide the preceeding number by 3. So we divide 9 by 3 and we get 3.
• The mathematical way of solving it by using the formula for the geometric progression which is: A_n = A₀r^{n - 1} . Wherein A_n is the n^th term; whereas A₀ is the 1^st term, r is the ratio and lastly, n is the number of terms. For this problem, the first term is 2187, the ratio is 1/3, the number of terms is 7 and we are asked for the 7th term. Using the aforementioned formula.
  
  

A₇ = 2187*(1/3)⁶
A₇ = 3

For the second question:
2. 1, 4, 9, 16, 25, 36, 49, 64, ___?

• Just looking at it we can say that the answer is 81. The squares of the counting numbers are being made in a sequence.

For the third question:
3. 13 -21 34 -55 89 ___?

• The answer for this one is -144. Why? The solution goes like this, based on the sequence we can notice that the positive and negative signed numbers are alternating. Next is that, the next number in the sequence is the sum of the absolute values of two preceeding numbers. So, 55 plus 89 is equal to 144. And since the previous number is a positive one, we have -144 as an answer.

For the fourth question:
4. AZ CX EV GT ___?

• Based on the choices provided, they are asking for two consecutive answers. My answer is IR KP. Why? The solution goes like this, I had observed that for AZ (A is the 1^st letter of the alphabet and Z is the 26^th letter of the alphabet) and for CX (C is the 3^rd letter of the alphabet and X is the 24^th letter of the alphabet) when I substitute the values of the pairs of letters they had a common sum of 27. And at the same time the first letter of the pair of letters is always odd starting from A(1^st letter) up to G (7^th letter). Therefore, the 5^th and 6^th terms are IR and KP, wherein I is the 9^th letter and K is the 11^th.

For the fifth question:
5. A5 D25 G125 J625 M3125 ______?

• Just by looking at the given, we can observed that the numbers in sequence are the powers of 5. And those letters if replaced with their arrangement in the alphabet we can notice that there is a difference of 3 between each sequence of letter. So the 6^th term is the P15625, wherein P is the 16^th letter of the alphabet and 15625 is the 6^th power of 5.

For the last question:
6. What is -25 + 16 ?

• No need to explained further, the answer is -9.

Well I didn’t expect this kind of an instance in the My Day’s of my friends in Facebook, but it did made my day that awesome. It is always fun for me to solve some mathematical problems.

Well I guess that would be all for this blog post.

Much love and respect.

Ace | @josephace135