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  #2  
Old 21st August 2014, 10:53 AM
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Join Date: Apr 2013
Default Re: Tricks for Solving Maths Questions

Here I am providing you some tricks for solving Maths Questions easily

Squaring
In this simple trick we need to modify the equation and make the units digit zero. After all it is easy to multiply when units digit is zero.
For example - Find square of 43
= (43+3) * (43-3) + (3*3)
=(46*40) + 9
= (460*4) + 9
= 1840 + 9 = 1849

Time and Work
Every question in in time and work chapter can be solved easily by finding efficiency of workers or subject (such as pipes).

For example - A takes 10 days to complete a job. B takes 20 days to complete the same job. In how many days they will complete the job if they work together ?
A's efficiency = 100/10 = 10% per day
B's efficiency = 100/20 = 5% per days
A and B can do 15% of the work in a day if they work together. So they can do the whole job in 100/15 = 6.66 days or 6 days and 18 hours.

. Add or Subtract 2 or 3 Digit Numbers
To add numbers that aren’t already a multiple of ten or one-hundred, round the number to the nearest tens or hundreds digit, add, and then add or subtract by the number you rounded off. Do the opposite when subtracting.
Examples:
144 + 48 = 144 + 50 – 2 = 192
1385 – 492 = 1385 – 500 + 8 = 893
Why?
This math trick comes down to the order of operations- adding and subtracting occur in the same step and can happen in either order. Like many other computation tricks, this one comes down to replacing one tricky computation with two simpler ones.

2. Multiply or Divide by 5
To multiply a number by 5, divide by 2 and then multiply by 10. To divide a number by 5, divide by 10 and then multiply by 2.
Example:
82 × 5 = 82 Õ 2 x 10 = 410
Why?
This math trick comes down to the order of operations- multiplying and dividing occur in the same step and can happen in either order. But instead of doing the (somewhat) difficult task of multiplying by 5, do the easier task of multiplying by the fraction 10/2. And since you can do this in either order, you can start by dividing a number by 2 or multiplying the number by 10. Starting with division is usually easier when you start with an even number (34 × 5 = 17 x 10 = 170) while starting with multiplication is easier when beginning with a non-integer (6.4 × 5 = 64 Õ 2 = 32). And instead of thinking about dividing by 5, think about multiplying by 2/10 (455 Õ 5 = 45.5 × 2 = 91).
3. Multiply Numbers Between 11 & 19
To multiply two numbers that are between 11 and 19, add the ones digit of one number to the other number, multiply by 10, and then add the product of the ones digits.
Example:
14 × 13 = (17 × 10) + (4 × 3) = 182
Why?
In the standard way that most American-students are taught to multiply numbers, you set up two numbers on top of one another like this:
14
× 13
42
140
182

This leads to a problem where you multiply 3 by 14, then multiply 10 by 14 and add the two products together. But you can rearrange this problem further to say you want to multiply 3 by 4, 3 by 10, and 10 by 14. Because you are multiplying both 3 and 14 by the same factor of 10 (which only happens when both numbers are between 11-19), you can combine this into one step. So instead of doing one tricky computation (3 × 14) and two easy ones (10 × 14 and 42 + 140), you make four easy computations (14 + 3, 17 × 10, 4 × 3, and 170 + 12).
4. Square Any Number Between 11 & 99
To square any number n, first find the nearest multiple of 10 and find out how much you would have to add or subtract (k) to get to that number. Then do the opposite function (addition or subtraction) to get two numbers that average out to n (i.e. n + k and n – k). Multiply those two numbers and add the square of k.

Examples:
232 = (26 x 20) + 32 = 529
972 = (100 x 94) + 32 = 9409
Why?
a2 – b2 = (a+b)(a-b)
a2 = (a+b)(a-b) + b2
If this special product doesn’t look familiar to you, write it down right now and memorize it because there are a plethora of GMAT questions that test you on this very concept. But for this special trick, you are (once again) trading a difficult calculation (23 x 23) for a few simpler ones.
232 – 32 = (23+3)(23-3)
232 – 32 = (26)(20)
232 = (26)(20) + 32
232 = 529
Since multiplying by multiples of ten are usually easier than non-multiples of ten, you find the nearest multiple of ten. While this may be very confusing at first, it’s a neat trick if you can get quick with it and is especially helpful when squaring numbers ending in five, since you will always add 25 to the lower and higher multiple of 10:
452 = (40 x 50) + 52 = 2025
652 = (60 x 70) + 52 = 4225
5. Estimate Root 2 & Root 3
√2 ≈ 1.4
√3 ≈ 1.7
Example:
The length of some side of a figure is about equal to 13 and you are down to the following three options:
(A) 9 √2
(B) 9 / √2
(C) 15 * (1 – 1/√2)
By estimating √2 ≈ 1.4 or even 3/2, you could quickly recognize that only answer (A) could be correct in this problem.
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  #3  
Old 16th May 2015, 09:29 AM
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Default Re: Tricks for Solving Maths Questions

I want to crack aptitude paper of bank exams . Will you please provide the maths problem solving tricks to solve aptitude paper ?
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  #4  
Old 16th May 2015, 09:31 AM
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Join Date: Apr 2013
Default Re: Tricks for Solving Maths Questions

The Bank PO Quantitative Aptitude exam paper constitutes questions from following topics:

• Number System
• HCF, LCM
• Time and Distance
• Time and Work
• Profit and Loss
• Average
• Simple and Compound Interest
• Mensuration (2D and 3D)
• Algebra
• Data Interpretation
• Simplification
• Decimal Fractions
• Ratio and Proportions
• Unitary Method
• Percentage
Quantitative aptitude shortcuts Tricks
Ordinary year = 365 days = 52 weeks + 1 odd day (365/7)
Leap year = 366 days = 52 weeks + 2 odd days (366/7)
The years with multiples of 400 have “0” odd days.
1 century = 100 years -> 76 ordinary years + 24 leap years -> 76*1 + 24 * 2 = 124 odd days -> 124/7 = 17 weeks + 5 odd days. Hence, for 100 years 5 odd days
Last day of a century will be Friday, Wednesday, Monday, or Sunday.
DOOMSDAY ALGORITHM:
Doomsday: Last day of February, 4th of April, 6th of June, 8th of August, 10th of October and 12th of December, will have the same days.
Doomsday for a year = Anchor + [YY/12] + Remainder of [YY/12] + {Remainder of [YY/12] / 4}
Anchor for: 1800 – 1899 is: Friday
1900 – 1999 is: Wednesday
2000 – 2099 is: Tuesday
2100 – 2199 is: Sunday
EXAMPLES:
1) Today is Monday, what will be the day 61 days later
Sol: Monday + 61 days -> Monday + 5 odd days -> Saturday
(61 / 7 = 5 odd days)
2) If 17th march 2008 was Monday, what day was, 1st April, 2012
Sol: 17th mar’08 = Mon -> 17th mar’12 = Mon + 1 + 1 + 1 + 2 = Mon + 5 = Saturday
Since: 17th mar’09 will have 1 odd day; 17th mar’10 will have 1 odd day, 17th mar’11 will have 1 odd day and 17th mar’12 will have 2 odd days (‘cause, 2012 is a leap year)
1st apr’12 = Sat + 15 days = Sat + 1 odd day = Sunday
3) Which year will have the exact same calendar as 2009?
Sol: 2009 + 1 + 1 + 2 + 1 + 1 + 1 = 2015
2009 + number of odd days in 2010 + odd days in 2011 + and so on till the sum of the number of odd days gets equal to 7.
4) Which year will have the exact same calendar as 1983
Sol: 1983 + 2 + 1 + 1 + 1 + 2 -> 1988 will have the exact same calendar as 1983
5) What day of the week was 15th august, 1947?
Sol: Doomsday = Wednesday + (47/12) + Remainder of (47 / 12) + [Rem of (47 / 12)] /4
= Wednesday + 3 + 11 + 11/4 = Wednesday + 3 + 11 + 2 = Wednesday + 16
= Wednesday + 2 = Friday -> 8th August, 1947 = Friday
15th August = 8th August + 7 days = Friday + 7 days = Friday + 0 odd days = Friday
Hence, 15th August 1947 was Friday
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