Quant

Question 1

Equivalent Fractions

Answer 1

if a×d=b×c for 2 fractions a/b and c/d

Question 2

Addition of fractions

Answer 2

If 1/a + 1/b = 1/3, a+b is not equal to 3

Question 3

Addition of fractions with unlike denominatiors

Answer 3

1. LCM Method
2. a/b + c/d = ad+bc/bd

Question 4

Comparing the size of fractions

Answer 4

1. Using a reference point to compare the sizes of the fractions
2. Bow tie method (DO NOT SIMPLIFY WHILE MULTIPLYING, YOU MUST MULTIPLY DIRECTLY)
3. 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
4. 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

Question 5

Comparing the size of fractions

Answer 5

1. Using a reference point to compare the sizes of the fractions
2. Bow tie method (DO NOT SIMPLIFY WHILE MULTIPLYING, YOU MUST MULTIPLY DIRECTLY)
3. 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
4. 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

Question 6

Multiplying or dividing the same constant to the num and den will not change the value of the constant

Question 7

Adding or subtracting the same constant to the num and den will change the value of the constant

Question 8

Adding or subtracting the same constant to the num and den will change the value of the constant

Question 9

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

Question 10

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

Question 11

Multiplication of decimals

Answer 11

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

Question 12

Multiplication of decimals

Answer 12

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

Question 13

x% + y% = x+y/100

Question 14

Converting fraction to 100

Answer 14

Multiply the frac by 100

Question 15

Converting a decimal to fraction

Answer 15

Eg: 0.83 =83/100

Question 16

Base fractions

Answer 16

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

Question 17

Squares and square roots

Answer 17

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)

Question 18

Estimations

Answer 18

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

Question 19

Only nos that end with 0,1, 4, 5, 6, 9 have the possibility of being a perfect square

Question 20

Remember PEMDAS, E is exponents
MDAS must ALWAYS be starting from left to right

Answer 20

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

Question 21

Factorials

Answer 21

0! = 1
1! = 1

Question 22

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