Quant Flashcards
Equivalent Fractions
if a×d=b×c for 2 fractions a/b and c/d
Addition of fractions
If 1/a + 1/b = 1/3, a+b is not equal to 3
Addition of fractions with unlike denominatiors
- LCM Method
- a/b + c/d = ad+bc/bd
Comparing the size of fractions
- Using a reference point to compare the sizes of the fractions
- Bow tie method (DO NOT SIMPLIFY WHILE MULTIPLYING, YOU MUST MULTIPLY DIRECTLY)
- Using a common num or den to compare the size of the fractions
For eg: 4/17, 8/39
LCM = 8
4 × 2/ 17×2= 8/34
8×1/ 39×1= 8/39 - Check the difference between the num and den of all the answer options. if the difference is the same, you can directly compare the denominators.
PROPER FRACTION : Greater the den, greater the fraction
IMPROPER FEACTION : Greater the den, smaller the fraction
Comparing the size of fractions
- Using a reference point to compare the sizes of the fractions
- Bow tie method (DO NOT SIMPLIFY WHILE MULTIPLYING, YOU MUST MULTIPLY DIRECTLY)
- Using a common num or den to compare the size of the fractions
For eg: 4/17, 8/39
LCM = 8
4 × 2/ 17×2= 8/34
8×1/ 39×1= 8/39 - Check the difference between the num and den of all the answer options. if the difference is the same, you can directly compare the denominators.
PROPER FRACTION : Greater the den, greater the fraction
IMPROPER FEACTION : Greater the den, smaller the fraction
Multiplying or dividing the same constant to the num and den will not change the value of the constant
Adding or subtracting the same constant to the num and den will change the value of the constant
Adding or subtracting the same constant to the num and den will change the value of the constant
Addition:
If a frac is positive, adding a positive constant to the num and den if fraction is LESSER than 1, the frac will get larger and if fraction is GREATER than 1, then the fraction will get smaller and go closer to 1
Subtraction:
If a frac is positive, subtracting a positive constant to the num and den if fraction is LESSER than 1, the frac will get smaller and if fraction is GREATER than 1, then the fraction will get larger and go away from 1 AS LONG AS THE BEW NUM AND DEN ARE BOTH STILL POSITIVE
Multiplication of decimals
For eg: If you are given 0.082×0.36, then the correct ans option is the one that has 5 places after the decimal point
Loophole: If the pdt of 2 nos ends w a 0 do not use this shortcut
Multiplication of decimals
For eg: If you are given 0.082×0.36, then the correct ans option is the one that has 5 places after the decimal point
Loophole: If the pdt of 2 nos ends w a 0 do not use this shortcut
x% + y% = x+y/100
Converting fraction to 100
Multiply the frac by 100
Converting a decimal to fraction
Eg: 0.83 =83/100
Base fractions
1/2=0.5
1/3=0.33
1/4=0.25
1/5=0.2
1/6=0.167
1/7=0.143
1/8=0.125
1/9=0.111
1/0=0.1
Squares and square roots
Any no. within the root is always positive, and the root of that no. is also always positive (principal square root) but if x&^2 = 16, then x=+4 or x=-4
Root of a/b = Root a/ Root b
a/b whole square = a^2/b^2
root a × root b = root(a×b)
Estimations
Multiplication: 0.927×1.9= 1×2= 2
Addition and Subtraction: If one of the nos is big and the other is small (almost negligible) then that no. can be ignored. For eg: 1000+1/1000. 1/1000 is v small and almost negligible and it can be ignored
Only nos that end with 0,1, 4, 5, 6, 9 have the possibility of being a perfect square
Remember PEMDAS, E is exponents
MDAS must ALWAYS be starting from left to right
If you have only addition/sub or only mult/div, you can operate in any order. But if you have BOTH in a problem you must follow PEMDAS
Factorials
0! = 1
1! = 1
If x<1, root x > x > x^2
But when you are comparing the squares of nos., be it less or more than 1, if x>y, x^2 > y^2
