## GMAT MAth Knotes 5

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jaizen  on May 24, 2011

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# GMAT MAth Knotes 5

 Name the sides proportion of 3 common right angled triangles?1) 3-4-5 2) 5-12-13 3) 8-15-17 4)6-8-10
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#### Definitions

Name the sides proportion of 3 common right angled triangles? 1) 3-4-5
2) 5-12-13
3) 8-15-17
4)6-8-10
What is the difference between two numbers that have the same integers in reverse order? 9
How to find the units digit of a sum or product of numbers? The units digit doesnt change so ignore the other places and add or multiply the units place alone.
How to simply division with large divisors? Bring the divisor to a single digit. e.g. 1530798\/314988 ~= 15\/3
What are proper fractions? Fractions that fall between 0 and 1. Or the numerator is lesser than the denominator.
Are mixed fractions proper? No. They are improper fractions as the numerator is greater than one.
What is the result of adding the same number to both numerator and denominator of a proper fraction? It brings the number closer to one.
What steps do you take to compare to proper fractions as being greater or smaller with respect to each other? Cross-multiply the numbers and write the answer on top of each respective numerator to compare.
What technique to use when solving large fractions? Use bench mark rounded values. eg. What is 10\/22 of 5\/18 of 2000 can be simplified as 1\/2 of 1\/4 of 2000
When do you pick smart numbers for word problems? When no quantities or totals are given
How to pick a smart number? Try to pick the least common denominator
What are integers? They are whole numbers that have no fractional part. They are non fractional and non decimal.
When is an integer said to be divisible? When it has no remainder. R=0
When is an integer said to be divisble by 2? When it is an even integer.
When is an integer said to be divisble by 3? When the sum of its digits are divisible by 3
When is an integer said to be divisble by 4? When it is divisible by 2 two times.
When is an integer said to be divisble by 5? When the units place has either a 5 or a zero.
When is an integer said to be divisble by 6? When the number is divisible by both 3 and 2
When is an integer said to be divisble by 8? When it is divisible 3 times.
When is an integer said to be divisble by 9? When the sum of the digits is divisible by 9.
When is an integer said to be divisble by 10? When the units place is a zero.
When is an integer said to be divisble by 11? ??
What phrase to use to differentiate factors vs multiples? Fewer factors and more multiples.
What happens if you add or subtract a multiple of N with another multiple of N? The resulting value is a multiple of N.
What happens if you add or subtract a multiple of N with a non-multiple of N? The resulting value is a non multiple of N.
What happens if you add or subtract a non multiple of N with a non-multiple of N? It is either a multiple or non multiple of N.
What is result of multiplying the GCF and LCM of two numbers m & n m*n.
How many factors do perfect squares have? Odd number of TOTAL factors - including prime factors.
What sort of integers have an odd number of total factors? Perfect squares of integers.
How to calculate total number of factors for an integer? Break the integer down to the exponential representation of its primes and then add the powers of each primes with one and then multiply all the powers plus one together.
How many prime factors are present for a perfect square? An even number of primes. The powers of the primes will be even.
What is the formula to represent the dividend in terms of the divisor, remainder and quotient x = Q*N + R where x is the dividend, q is the quotient, n is the divisor and r is the remainder.
What is the relationship between a remainder and the dividend? The remainder if any +ve integer N has to be +Ve integer and lesser than the number N.
What is the range of a remainder with respect to a dividend N? 1 to (N-1)
What will be the remainder of the sum of two numbers x and y. The remainder will be the sum of the remainder of x and the remainder of y divided by the same divisor
What to do when the remainder calculated is more than the dividend? Then subtract the dividend with the remainder to get the final remainder.
Is the LCM of any two integers greater than, equal to or lesser than the integers? It is at least as large as any one of the integers.
How to determine if an integer is a factor of another integer? If the product of its primes is a factor of that integer.
When trying to determine whether an integer can be a factor/divisible by another number, what rule to keep in mind? All the factors and its powers must be accounted for. If even one is missing, the answer cannot be determined
If two numbers are a multiple of N, what about the sum of the two numbers? It is also a multiple of N
How do you identify if a number that is a factor of two other numbers is a factor of current number? e.g. if j is a factor of 12 and 10, is it a factor of 24? 1) Take the maximum number of common primes
2) Take the maximum number of independent primes
3) The primes of the number to be tested should all be accounted for in the consolidated list.
What is GCF in terms of factors? It is a the product of all shared factors.
What is the GCF of consecutive multiples of N? N itself.
What is the length of an integer? The total number of prime factors.
What is the solution to a system of equations? A solution to a system of equations is a point at which the graph of each equation intersects. There are four points of intersection, thus there are four solutions

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