## Tuesday, 14 May 2013

### Numerator/Denominator confusion

I observed that a bit of confusion prevails while simplifying fractions. The confusion is about which number will go to numerator part and which number will go to denominator part. This post is intended to clear the confusion.

Consider a fraction in the form (a/b)/(c/d).
Let us call the variables like this:
a – Numerator-numerator
b – Numerator-denominator
c – Denominator-numerator
d – Denominator-denominator

The rules:
Numerator-numerator remains in the the numerator part of the result fraction
Numerator-denominator remains in the the denominator part of the result fraction
Denominator-numerator always goes to the denominator part of the result fraction
Denominator-denominator always goes to the numerator part of the result fraction

The thumb rule here is:
If the number is either of type “Numerator-numerator” or “Denominator-denominator”, then it will go to numerator part. In other cases, it will go to denominator part.

So applying these rules, the given fraction takes the following form:
'a' remains in numerator, 'b' goes to denominator, 'c' remains in denominator and 'd' comes up to the numerator.
(a/b)/(c/d) = (a*d)/(b*c)

It's not like always there exist four parts in such fractions. Sometimes it is like this: (x/y)/z. This contains only three numbers. Here
x is Numerator-numerator,
y is Numerator-denominator,
and z is Denominator-numerator.
Applying the thumb rule, x remains in numerator while y and z settle in denominator.
=> (x/y)/z = x/(y*z)

If we take the other form p/(q/r), it changes like this: (p*r)/q

Try out the following examples:
Question set:
1.      (3/4)/(7/8)
2.      3/(4/5)
3.      (3/4)/5
4.      (2/3)/4
5.      (8/9)/(2/3)
Solution set:
1.      (3/4)/(7/8) = (3*8)/(4*7) = 6/7
2.      3/(4/5) = (3*5)/4 = 15/4
3.      (3/4)/5 = 3/(4*5) = 3/20
4.      (2/3)/4 = 2/(3*4) = 1/6
5.      (8/9)/(2/3) = (8*3)/(9*2) = 4/3

## Wednesday, 1 May 2013

### Stuff for school kids (standard 5 to 10)

I thought of providing some stuff for students studying in the range 5th to 10th standard. This stuff is a combination of two sets. One is Math&Logic based and the other is Knowledge based. This stuff is a mix of some questions that are based on math fundamental concepts and remaining questions that are based on commonsensical and out-of-box thinking. These do not look like standard questions that are given in school-level exams but mostly resemble or can act as base for the math and logic aptitude sort of questions that are asked in various entrance exams. My primary intention is to inculcate in kids an interest and liking on maths. I strongly opine that math solving skills are very much needed to excel in diverse fields of studies ranging from Science, Engineering to Economics, Management studies etc.
To be frank on my part, I am starting this post with small number of questions at hand but I will try to enrich this bit bank by updating it from time to time.
Math and Logic Based Set:
1.      A number when used in denominator results in an 'undefined' value. What's that number?
2.      X is a number. If you add X to any other number you get the other number. If you subtract X from any other number, even then you get the other number. What is the number X?
3.      Y is a number. If you multiply Y with any other number you get the other number. If you divide any other number with Y, even then you get the other number. What is the number Y?
4.      It's a geometric figure and there is one point 'X' with in that figure. All points on that figure are equidistant from X. What is that geometric figure?What is the point X called?
5.      The one and only number which is even and prime is_____
6.   Which of the English alphabets are symmetric in shape when written in upper case? (If bisected vertically)
7.  Which of the English alphabets are symmetric in shape when written in upper case? (If bisected horizontally)
8.      How many two digit numbers having both identical digits are there?
9.    Consider a two digit number such that if you add it's two digits, you should get a sum of 9. How many such two digit numbers are possible?
10.  How many three digit numbers can be formed by using all the digits 0,1,2. Here repetition  of a digit in a number is not allowed.
11.  What are all the years in twenty first century that use all the four digits 0,1,2,3?
12.  What are all the years in twenty first century that are palindromes?
13.  Is 2013 a prime number?
14.  For a right triangle, if 24 and 25 are two sides then what is the other side?
15.  What is the square of 995?
16. Ram walked 6 m Eastwards and turned 90 degrees to his left and continued to walk for 8m and stopped there. At what distance and direction is the final point positioned with respect to the initial point if we join the two points by a straight line?
17.  Amar can do a work in 60 days and Akbar in 90 days. In how many days both of them can jointly do that work?
18.  Anthony started a journey by car to his home town which is 100 km away. He travels first 40 km at a speed of 40 kmph, next 40 km at a speed of 80 kmph and the remaining distance at a speed of 40 kmph. What is the average speed with which he travelled to reach the destination?
19. Given the radius of a circle is 5 cm, what is the distance between two points on the circle which are located exactly opposite to each other?
20.  “The radius of a circular path is 7 m. If I start at a point on the path and travel 88 m along the path, then I will reach the same point at which I have started”. Is this statement True/False?
21.  The statement “X/X = 1” does not work when X=____
22.  “Square root of 16 is 4”- is this sentence perfectly correct?
23.  “Square of 4 is 16”- is this sentence perfectly correct?
24.  If I say “A/B = C/D”, does it mean A=C and B=D?
25.  If I say “A*B = C*D”, does it mean either A=C or A=D?
26.  If XY = 0, then X must be___, irrespective of the value of Y.
27.  If XY = 1, then Y must be___, irrespective of the value of X.

Knowledge Based Set:
1.      That's an English word, which is an acronym representing all the four sides. What's it?
2.      We all remember him for his magic square. Who is that great Indian mathematician?
3.   The great Indian lady mathematician famously known for her quick calculations on large numbers (recently she has passed away)________
4.      The great Indian mathematician who invented Pujyam ('0') is ____
5.    “For a right angle triangle if 'a' is hypotenuse and 'b' and 'c' are sides then, a2=b2+c2” - whose theorem is this?
6.      “Any three points which are not collinear can form a triangle”. Is this statement True/False?
7.      “For any two points on a plane, if we join them by a straight line, it gives the shortest path”. Is this statement True/False?
8.      “In a right angle triangle, hypotenuse is the largest side”. Is this statement True/False?
9.    “In a right angle triangle, length of hypotenuse is the greater than sum of the lengths of other two sides”. Is this statement True/False?
10.  If the length and breadth of a rectangle are made equal, then it becomes a _____

## Monday, 11 February 2013

### A land mark on GATE exam day

Yesterday (10th Feb'13) GATE exam was conducted. It's an all India exam conducted by IITs annually for entry to M.Tech courses. Some PSUs also consider the GATE scores for offering jobs. In GATE, there are a total of 65 questions carrying a total of 100 marks, out of which 10 questions carrying total of 15 marks are in General Aptitude (GA). The remaining 85% of the total marks is devoted to the Engineering syllabus. From last year (GATE-2012),

## Sunday, 10 February 2013

### GATE-2013 Solutions (General Aptitude)(EC/EE/IN)

1. A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third quarter. The average speed of the car in km per hour over the entire journey is
(A)30   (B)36   (C)40   (D)24
Sol:
This is a simple formula based one.