np2
The std dev of two groups of number is the same if the distance from the mean is the same. The mean matters. True or false.
False.
The sum from 1 to 9 is 9(9)/2. True or False.
False.
The tens digit of n+1 is 7 means that n is 69. True or False.
False.
The total factors decrease when a number is raised. True or False.
False.
The total prime factors decrease when a number is raised. True or False.
False.
The total prime factors increase when a number is raised. True or False.
False.
Then compare.
False.
There are negative prime numbers. True or False.
False.
There is no non-integer that can be multiplied by itself and become an integer. True or False.
False.
This is a GCD problem.
False.
This is an LCM problem.
False.
This is false.
False.
This is false. 1+9×10⁴ is the same as 1²+9×10⁴
False.
To find the number of even factors of 2²x3³x7², take the exponents on odd numbers then multiply those numbers by each other. True or false.
False.
To find the number of odd factors of 2²x3³x7², take the exponents on odd numbers then multiply those numbers by each other. True or false.
False.
To find the remainder when dividing by 2 just divide the last two digits by 2. True or False.
False.
To find the units digits since both units digit are the same number, and since you are adding two terms, all you need is the sum of n+o. You don't need the individual values of n+o. 573ⁿ+673°
False.
Total factors formula is not one of the steps that will produce the different ways K could have 9 factors. True or False.
False.
True or False.
False.
True or False. A prime factor can be a GCF prime factor (A,B) without a prime factor of A and B.
False.
True or False. A problem has two variables along with %s of each. There is always a relationship between the two variables quantities.
False.
True or False. If given LCM and GCD of (M,N), you will not need the value of MxN as a ceiling to help find M,N.
False.
True or False. In an odd quantity of odd consecutive numbers, the median will not be the avg.
False.
True or False. In ratio 4:5 is 4x:5x and the x is the LCM, not GCD.
False.
True or False. The dividend is the denominator
False.
True or False. The divisor is the numerator.
False.
True or False. The sign (negative or positive) does change the odd/even number properties.
False.
True or False. The sum of an even quantity of odd number will always be odd.
False.
True or False. The sum of an odd quantity of odd numbers will always be even.
False.
True or False. Variables with even coefficients will always come out odd.
False.
True or False. X+Y=10 Are you only considering integers.
False.
True or False. Zero is composite
False.
True or false
False.
True or false.
False.
True or false. "the smallest integer that is divisible by...." doesn't hint that the problem is an LCM problem.
False.
True or false. A number with only two factors can be composite.
False.
True or false. Absolute values help you determine the mean, standard deviation, and range.
False.
True or false. If N is divisible by 2 and 8, N must be divisible by 16.
False.
True or false. P is a factor of T is the same as P is divisible by T.
False.
True or false. The problem says approx and the answer choices are 10⁸, 10⁹ etc. you shouldn't round.
False.
True or false. The remainder can be less than the dividend but greater than the divisor.
False.
True or false. if a/b=integer then every number that divides a must divide b.
False.
Two less then 20-10 is the number of #s in between 20 and 10 (and for any two numbers). True or False.
False.
Variables are always integers. True or False.
False.
When a problem says if x..... that is a suggestion. True or False.
False.
When a question asks if a variable or an expression or a quantity is divisible by 3, the question is asking whether that entity is odd.
False.
When a question asks if a variable or an expression or a quantity is multiple of 2, the question is really asking whether that entity is even.
False.
When dividing an even number by an odd number, the remainder must be even. True or False.
False.
When testing numbers never test zero or decimals. True or False.
False.
When you are told, simply, what one of the prime factors are, it is best to write it without an exponent placeholder e.g. 2. True or False.
False.
When you see prime numbers greater 3, think (6n+1) or (6n-1). This is the prime number >3 formula.
False.
Y must be 3.
False.
Y must be 6 or 0.
False.
Y must be odd.
False.
You can break a number down past it's prime factors. True or false.
False.
You plug in 3k only
False.
ab+ba is in its' simplest terms. True or false.
False.
and you break the equation out 9xB (-1), the remainder is -1
False.
and y¹⁰⁰ must be divisible by 2¹⁰⁰
False.
ax+yz= (10x+a)+(10z+y). True of false.
False.
even / odd equals an integer, always.
False.
n=Q10+12 The remainder is 12. True or False.
False.
n=Q10-13 The remainder is 13. True or False.
False.
odd / even equals an integer.
False.
y and √y do not have the same prime factors. True or False.
False.
you should try to round to the nearest hundred or two zeros.
False.
¾ (is the same as 3x:4x). These are definite values. True or False.
False.
√(3p)x10=X⁴ p=3 only. True or false.
False.
√(3p)x10=X⁴ p=3x5x2. True or false.
False.
1 is not included in a numbers total number of factors. Yes or No.
No.
3 is a prime factor of all odd numbers. Yes or No.
No.
An odd number raised can be even. Yes or No.
No.
Don't exhaust all possibilities as your work divisbility problems. Yes or No.
No.
If you are given all the prime factors you have all the factors you need. Yes or No.
No.
Prime numbers share a common prime factor. Yes or No.
No.
Problems dealing with prime factors are not tricky. Yes or No.
No.
Yes or No.
No.
You can determine the total prime factors by just knowing the total factors. Yes or No.
No.
If you have a number with only one prime factor, then add 1 to the its total exponent and that is its total factors. True or false.
True.
If y⁴ is divisible by 2⁴ then y² must be divisible by 2². True or False.
True.
In (a-b)^n the last term expanding this expression will be (-b)^n. True or False.
True.
In (a-b)ⁿ the last term upon expanding this will be (-b)ⁿ. So, if you are working with remainder questions factor out a to =(intxint) and b to =1. True or False.
True.
Instead of plugging in odd numbers, we can plug in 2k+1, which covers all odd numbers. The even version is 2k. True or false.
True.
Keep in mind, when solving a problem there may be more than one way to get the sum (product, difference, or quotient) of a number and still be sufficient. Be mindful. True or False.
True.
Knowing the relationship of x to y or y to x, will solve this equation without knowing real values. True or false.
True.
LCM is the highest power of every prime factor. True or False.
True.
Multiply (combine) the GCD of 4 and 5 with the GCD 200 and 160.
True.
Negative decimal raised to an even power is always positive. True or False.
True.
Negative decimals raised (when only raised to odd numbers) get closer to zero. True or False.
True.
No matter how long the number is, to get the remainder when dividing by 4 just use the last two digits of the dividend. True or False.
True.
No matter what n is 2n+1 will always be odd. True or False.
True.
Numbers 1to9 has four pairs of numbers that sum to 10. The number 5 is excluded. True or False.
True.
N²/72 means N²=72k k=integer placeholder. True or False.
True.
N²=2int×3² to reduce this equation int must be squared and another 2 has to be apart of the right side b/c all prime must have an even exponent, so N=3×2int. True or False.
True.
Odd numbers are based on 2(n)+1. True or False.
True.
Odd/Odd can never be even.
True.
Odd/Odd=Odd.
True.
Odd/even or Even/odd. If there is a remainder, it will always be odd. True or False.
True.
One less then 20-10 is the number of #s in between 20 and 10 (and for any two numbers). True or False.
True.
One way to get A×B is to get LCM×GCD. True or False.
True.
P/7 means how many "sevens" go into P. True or False.
True.
P/7ⁿ means how many "seven time sevens" or "seven raised" go into P. True or False.
True.
Positive decimals raised get further away zero. True or False.
True.
Prime factors do not change even when you raise them with exponents. True or False.
True.
Prime factors do not change even when you reduce the exponents. True or False.
True.
Q is odd. When divided by 4, the remainder can only be 1 or 3 b/c odd-even=odd.
True.
Q=13K +4 is divided by 2 the remainder is k. True or false.
True.
Q=24K remainder =0. True or false.
True.
Q=26K remainder =2K. True or false.
True.
Roots time roots can be a whole number. Fractions time its reciprocal is a whole number. True or False.
True.
Since 9's exponent cycle is 9²ⁿ, if the exponent is even, you know its always going to end in 1 (the second/last number in the cycle. True or False.
True.
Sometimes 3k doesn't work to decipher if you are choosing between multiple equations. Use the others.
True.
Step3: plug in an even,2 or odd,1
True.
T is divisible by P.
True.
The GCD is the lowest power of each common factor. True or False.
True.
The GCD of 3³ and 3⁴ is 3³. True or false. Even though the base is the same, you cannot choose a lower exponent (in this case an exponent less than 3). You have to pick from what is given.
True.
The GCD of any two consecutive number is 1. True or False.
True.
The GCD of two distinct numbers cannot be larger than the difference between the two numbers. True or False.
True.
The LCM for a number that is a multiple of 9 and a multiple of 10 can be written algebraically as 9y=10x . True or False.
True.
The amount of numbers from 5 to 11 exclusive is solved by the formula 11-5 minus 1. True or false.
True.
The amount of numbers from 5 to 11 inclusive is solved by the formula 11-5 plus 1. True or false.
True.
The difference between any two consecutive even number is 2. True or False.
True.
The difference between any two consecutive odd number is 2. True or False.
True.
The distance between every prime number after 2and3 is at least 2. True or False.
True.
The find the sum of the first n number is n(n+1) / 2. True or False.
True.
The first even number is 0. True or False.
True.
The first for even numbers are 0,2,4, and 6.
True.
The first number in the exponent cycle of every number is that number to the first power. True or False.
True.
The more decimal places you add to the denominator, the larger the overall number will become. True or false.
True.
The number of trailing zeros in a number depends on highest power of 10. True or False.
True.
The phrase "increasing order" does not mean consecutive. True or False.
True.
The product of 3 consecutive numbers is divisible by 3. True or false.
True.
The smallest common divisor of any group of numbers is 1. True or False.
True.
The smallest common number that divides 132 and 60 is 1. True or false.
True.
The square root of y √y has the same prime factors as y. True or False.
True.
The std dev of two groups of number is the same if the distance from the mean is the same. The mean doesn't matter. True or false.
True.
The sum from 1 to 9 is 9(10)/2. True or False.
True.
The sum of digits is not always a unique number. All 9 timetables from 9x1 to 9×10 digits sum to 10. True or False.
True.
The tens digit of n+1 is 7 means that n can be 69 or any number in the 70s up to 78. True or False.
True.
The total factors increase when a number is raised. True or False.
True.
The total prime factors do not change when a number is raised. True or False.
True.
The trap of prime numbers is that all possibilities (the value of exponents) are not listed. True or False.
True.
The trap with divisibility problems is that not all possibilities are written out. True or False.
True.
There are 40% dogs and 30% cats. If you don't know how they relate then you cannot analyze them any further. Increase in dogs may do nothing to the quantity of cats. True or False.
True.
There is only one type of non-integer that can be multiplied by itself and become an integer and that is square roots. True or False.
True.
These represent all numbers when you divide by 3.
True.
This is an LCM problem.
True.
This is not an LCM problem, rather a problem that requires using a multiple of the total of boys and girls.
True.
To find the divisibles of a number, take its square root and test every prime number under it. True or False.
True.
To find the number of even factors of 2²x3³x7², take the exponents on all numbers and add 1 then multiply those numbers by each other then subtract to the total of number odd factors (to get the odd factors is a similar process). True or false.
True.
To find the number of odd factors of 2²x3³x7², take the exponents on odd numbers and add 1 then multiply those numbers by each other. True or false.
True.
To find the remainder when dividing by 2 just divide the unit's digit by 2. True or False.
True.
To find the remainder when dividing by 3 just divide the sum of its digit by 3. True or False.
True.
To find the sum of 1 consecutively to any number, take last number, which is n use n(n+1)/2.
True.
To find the units digits since both units digit are the same number, and since you are adding two terms, you need the individual values of n+o. 573ⁿ+673°
True.
To find the units digits since both units digit are the same number, and since you are multiplying two terms, all you need is the sum of n+o. You don't need the individual values of n+o. 573ⁿX673°
True.
To make the left side a square, N could have a 2 raised to 0, a 3 raised to any odd exponent, and a 5 raised to any odd exponent.
True.
To make the left side a square, N has to have a 2 raised to any equal exponent, a 3 raised to any odd exponent, and a 5 raised to any odd exponent.
True.
Total factors formula helps to determine the different ways K could have 9 factors, which are 2 different ways. True or False.
True.
Total factors formula is one of the steps that will produce the different ways K could have 9 factors. True or False.
True.
True or False.
True.
True or False. 2 may not be the only prime factor for even numbers
True.
True or False. A prime factor cannot be a GCF prime factor (A,B) unless it is FIRST a prime factor of A and B.
True.
True or False. Always think in decimals unless not stated or working with quantities that cannot be divided into fractions (word problems with people, cars).
True.
True or False. An even expression raised to any positive power is even.
True.
True or False. Dn=Dr(Q)+R
True.
True or False. If a prime factor exists in A and B then it will be a GCF prime factor of A,B.
True.
True or False. If every prime factor has an even exponent then that number is a perfect square.
True.
True or False. If given LCM and GCD of (M,N), you will need the value of MxN as a ceiling to help find M,N.
True.
True or False. In an even quantity of "even, odd, plain consecutive" numbers, the avg of the two middle numbers is the same as the avg of the whole.
True.
True or False. In an odd quantity of consecutive numbers, the median will be the avg.
True.
True or False. In an odd quantity of even consecutive numbers, the median will be the avg.
True.
True or False. In ratio 4:5 is 4x:5x and the x is the GCD.
True.
True or False. Looking at answer choices signal how you can round numbers to make calculations easier.
True.
True or False. Number lines can have integers and numbers with decimals.
True.
True or False. Prime numbers are not negative.
True.
True or False. The dividend is the numerator.
True.
True or False. The divisor is the denominator.
True.
True or False. The larger you make the denominator the smaller the overall value will become.
True.
True or False. The remainder is less than the dividend and divisor.
True.
True or False. The sum of an even quantity of odd numbers will always be even.
True.
True or False. The sum of an odd quantity of odd numbers will always be odd.
True.
True or False. There is a ton of wealth in the DS question stem.
True.
True or False. To find the remainder when dividing by 4, you only have to divide 4 by the last two digits.
True.
True or False. Variables with even coefficients will always come out even.
True.
True or False. When you see all fractions, you can convert all of them to decimals or to whole numbers.
True.
True or False. You must extract inferences from the question prompt even the easiest of problems have jewels.
True.
True or False. Zero is a multiple of every number?
True.
True or False. Zero is neither prime nor composite.
True.
True or False. if a/b=integer then every number that divides b must divide a.
True.
True or False. y=2k+2 would not produce a reminder like y=2k+1 or 2k+3 therefore 2k+2 is divisible by 2.
True.
True or false
True.
True or false.
True.
True or false. "base ten" notation is a fancy word for the way we normally right numbers.
True.
True or false. "the smallest integer that is divisible by...." hints that the problem is an LCM problem.
True.
True or false. 1+9×10⁴ is the same as (1²+3×10²)×(1²-3x10²)
True.
True or false. A remainder can equal 0.
True.
True or false. If N is divisible by 2 and 8, N may not be divisible by 16 b/c N could equal 8 and still have 2 as a factor.
True.
True or false. If a number has two factors, 1 is always one of the factors.
True.
True or false. Prime number only have two factors.
True.
True or false. The divisor must be greater than the remainder.
True.
True or false. The less zeros in the answer choices the less you can round.
True.
True or false. The problem says approx and the answer choices are 10⁸, 10⁹ etc. you round a lot.
True.
True or false. The remainder must be less than the divisor.
True.
True or false. The sum of 3 consecutive digits (consecutive even or odd too) is always divisible by 3.
True.
True or false. Two numbers are reciprocal when their product is one.
True.
True or false. Whenever you see even think 2k.
True.
Use Total factors formula to determine different ways K could have 9 factors. True or False.
True.
Use √ check marks or X when working DS problems to keep good notes. True or False.
True.
Variables are not always integers. The problem may not tell you specifically, so don't forget.
True.
WOTF... means that you should always start from answer choice E.
True.
When Odd / even number has a reminder, the reminder will always be odd.
True.
When a problems says if x.... that is a fact, so write it down and use it. True or False.
True.
When a question asks if a variable or an expression or a quantity is divisible by 2, the question is really asking whether that entity is even.
True.
When dividing an odd number by an even number, the remainder must be odd b/c dividend - divisor is odd - even. True or False.
True.
When negative decimals are raised to larger odd number, the get smaller and closer to zero. True or False.
True.
When solving problems don't forget to check back at the rules and info from the question stem. True or False.
True.
When you are doing odd and even problems, please watch the coefficients. True or False.
True.
When you are told a number is prime it is best to write it as 2ⁿ not 2. Two is still a prime factor when it is raised to 2¹ or 2¹⁰⁰. True or False.
True.
Whenever you see odd think 2k+1. True or false.
True.
X leaves a remainder when divided by 3. Out of x-1, x+1, x must be divisible by 3 and at least one must be even. Nor more than two will be even. Similarly, for odd numbers. True or false.
True.
X leaves a remainder when divided by 3. the remainder can be any positive number less than 3. True or false.
True.
X leaves a remainder when divided by 3. x-1 or x+1 must be divisible by 3. True or false.
True.
X>1 includes whole numbers such as 1,2,3... and decimals such as 1.01,1.1,1.2 even 1.001. True or False.
True.
Y has many numbers, but it must be divisible by 6.
True.
Y must be 0.
True.
Y must be divisible by 13 AND (2v-57)
True.
You are NOT adding exponents when you are calculating GCF or LCM. GCF (lowest exponent, common prime). LCM (only the highest exponent of all prime). True or False.
True.
and you break the equation out 9xB (-1), back out the -1 9xB - (9-8). The remainder is 8.
True.
ax+yz= (10a+x)+(10y+z). True of false.
True.
aⁿ×bⁿ=(ab)ⁿ and (aⁿ/bⁿ) = (a/b)ⁿ. True of False
True.
even/odd=even, always.
True.
n=12 This is wrong. N should be greater than 12
True.
n=Q10+12 The remainder is too big. break it down. n=10(Q+1)+2 The remainder is 2. True or False.
True.
o-o=e two different options to get e, so insufficient.
True.
odd / even equals decimal, always.
True.
the other 2 helps t become 24.
True.
true or false.
True.
x-1 or x+1, one of these is divisible by 3. True or false.
True.
y=2k+1 If the 1 was a 2 then 2k+2 would be divisible by 2. True or False.
True.
¾ is the same as 3x:4x, therefore, these are not definite values. To get a definite value we need another rule like X is a perfect square. True or False.
True.
A/B means A has all the factors of B. True or False.
True.
If the sum of any 5 numbers on a list equals 8 then all numbers are the same value. True or false.
False.
If x is a factor of y then y/x=decimal. True or False.
False.
If y=2k+1 then y is divisible by 2. True or False.
False.
If, N had a 2 raised to 0, 60N could never be a square (even if N had a 3 and a 5). True or false.
False.
Isolating variables is not a good strategy to determine if a variable is odd/even. True or False.
False.
N times a number. The number of prime factors must increase. True or False.
False.
Absolute values are not helpful at all in determining the mean, standard deviation, nor the range. True or false.
True.
Add 1 to each exponent then multiply is the total factor formula. True or False.
True.
All odd integers can be derived from 2n+1
True.
All odd numbers are divisible by 2(n)+1. True or False.
True.
All prime factors are used in making the LCM but only prime numbers in common are used to make the GCD. True or False.
True.
All prime numbers >3 will be 6n+1 or 6n-1 (some composites too). True or false.
True.
Always simplify the question statement. True or False.
True.
Always use the given coefficient (10) to back out 13.
True.
Always use the integer placeholder b/c we do not know if we have all the factors. There could be more.
True.
Any amount of even numbers added to an odd number will always make the sum of that set of numbers odd.
True.
A² when A is a negative decimal is larger than A³. True or False.
True.
A² when A is a positive decimal is larger than A³. True or False.
True.
A³, when A is a negative decimal, is larger than A¹¹. True or False.
True.
BBA= 100B+10B+A True or false.
True.
Break the numbers down to pieces
True.
Consecutive numbers that are prime is 2,3 only. True or False.
True.
Consecutive prime numbers mean 5,7,11. True or False.
True.
Consider testing POFNER (positive, 0, fractions, negative, exponents, and roots). True or False.
True.
Divisibility and finding factor problems are tricky so pay close attention to number properties. True or False.
True.
Divisor means factor (only if the answer is an integer). True or False.
True.
Don't get bogged down when you see huge number and complicated expressions. True or False.
True.
Each prime factor of a group of numbers must be in the LCM, but to what power is the next step. True or False.
True.
Even-Even=Even.
True.
Every prime factor of B is a prime factor of A if A/B=integer (always an integer if A is larger). True or false.
True.
Expression 12xy=even, always. True or False.
True.
Find the "least" number hints an LCM problem. True or False.
True.
Finding prime factors means to go to the lowest level of the factorization tree. True or false.
True.
Finding the total number or even and odd means finding the number of total factors. True or False.
True.
For AxB to be even, A or B must be even. True or False.
True.
For the product of two numbers to be odd both number must be odd. True or False.
True.
For this problem, you have to estimate/round-up and down with the numbers to establish the upper/lower boundaries. True or False.
True.
GCD is the lowest power of every common prime factor. True or False.
True.
GCD will never be greater than any number in the group it represents. Only equal or less. True or False.
True.
GMAT is not a calculative intensive exam. True or False.
True.
I don't need any more info b/c Y has two be divisible by 6 and (2v-58), but since it is a single digit number the only two numbers divisible by 6 is the number 0 and 6.
True.
If (6n-8)/4=int (neg or pos int), 6n-8 must be divisible by 4 therefore 6n-8 is a multiple of 4 too.
True.
If 2 is divisible by n then it is good to use a place holder like, K, to represent the integer. True or False.
True.
If 205>bx2x3x7, to get the right side close to 205, raise the lowest number's exponent by 1 and test the total. True or false.
True.
If 3+x=20(10-K) then 20(10-K) has to be divisible by 3+x. True or false.
True.
If 3+x=20(10-K) then 3+x has to be a multiple of 20 or (10-k). True or false.
True.
If 3+x=20(10-K) then 3+x has to be divisible by 20 or (10-k). True or false.
True.
If 3x=20(10-K) then (10-k) must be divisible by 3 because 20 is not divisible by 3. True or false.
True.
If 3x=20(10-K) then 3x has to be a multiple of 20 & (10-k), and 3x must be a multiple/divisible by 20(10-K). True or false.
True.
If 3² is a prime factor in LCM A,B then 3² must be in one of the numbers, A or B.
True.
If 3² is a prime factor in the LC of A,B then the exponent of 3 will not be higher than 3⁴ or lower than 3² when A×B. True or False.
True.
If 4+x=15, 4+x is a multiple of 15. True or false.
True.
If 8x+B=4. B must be divisble by 2 and B must be a multiple of 2. True of false.
True.
If B is even and is raised to any positive power, the product will be even. True or False.
True.
If K has a set of numbers and if the problem states "if x and y is in K then xy is in K" this value for x and y means any two different numbers. It doesn't mean x and y have any specific value. True or false.
True.
If N is prime but N≥10 then N must be odd. True or False.
True.
If N is prime but N≥3 then N must be odd. True or False.
True.
If X is a factor of B then the LCM has every factor (including prime factors) X. True or Factor.
True.
If X is divisible 8 then to see if X is divisible by 24, you need to see if X is divisible by 3 because we already know X is divisible by 2. True or False.
True.
If X=2b+5, X will be divisible by 2b+5. And 2b+5 is a multiple of X. X is also divisible by 2b+5 and X is a multiple of 2b+5. True or false.
True.
If a fraction (division) yields an even integer the numerator must be even. True or False.
True.
If a problem list x+5, x, x-1 Consider which ones are even and odd. This could help solve the problem. True or false.
True.
If a problem says X is less than 205 that means X you cannot lock X into any number, but consider it being any value under 205. True or false.
True.
If a problem states three numbers are different, that means could only be either lesser or greater than one another. True or False.
True.
If a problems says N>4, think 5, 6.3 , 7, or 8 True or False.
True.
If a question asks if X "is closest to" or "is furthest from" you can use absolute value. False or True.
True.
If p≥1 and an integer where 300xp=X², understand that all integers on the left side must have even exponents since it equals a square (X²). The value of p will supplement value to help make the prime factors of 300 have even exponents.
True.
If the problem add 1 to K, K+1, add 2+1<K+1<6+1 (add 1 to the left and right).
True.
If the problem states something like "four EVEN numbers", consider n + n+2 n+4 n+6 for the four numbers. True or false.
True.
If the problem states something like "four consecutive numbers", consider n + n+1+ n+2 + n+3 for the four numbers. True or false.
True.
If the sum of any 2 numbers on a list equals 8 then all numbers are the same value. True or false.
True.
If the sum of any 3 numbers on a list equals 12 then all numbers are the same value. True or false.
True.
If there are not a lot of possibilities for a set of #s in the problem then list them out. True or False.
True.
If x is a factor of y then y/x=integer. True or False.
True.
If x is a multiple of y then x/y=integer. True or False.
True.
If x= P/Q and x=¾ this does not mean P=3 and Q=4 because ¾ is a ratio. You need more info. True or False.
True.
If y=2k+1 then y is not divisible by 2 even though 2 is the coefficient of k. True or False.
True.
If you are rounding to simplify your arithmetic go easy. True or False.
True.
If you are trying to determine if a variable is odd/even trying isolating it. True or False.
True.
No matter how long the number is, to get the remainder when dividing by 4 just use the last digit of the dividend. True or False.
False.
No matter how many even numbers are in a set, one odd number will make the sum of the set odd.
False.
Odd/Odd can be even.
False.
On DS problems, you don't have to check to make sure you are answering the right questions. True or False.
False.
P/7ⁿ means how many "sevens" go into P. True or False.
False.
Q is odd. When divided by 4, the remainder can be any number 0 to 3.
False.
Q=13K +4 is divided by 2 the remainder is k+4. True or false.
False.
Q=14K +4 is divided by 2 the remainder is 1. True or false.
False.
Q=14K +4 is divided by 2 the remainder is 2. True or false.
False.
Q=26K remainder =1. True or false.
False.
Squares do not always have even exponents on all prime factors and an odd total of factors. True or false.
False.
Step2: plug in an even,2 or odd,1
False.
The GCD of 3³ and 3⁴ is 3. True or false.
False.
The GCD of any consecutive number is 2. True or False.
False.
The GCD of two distinct numbers can be larger than the difference between the two numbers. True or False.
False.
The LCM for a number that is a multiple of 9 and a multiple of 10 can be written algebraically as 9y=10x+7 . True or False.
False.
The amount of numbers from 5 to 11 inclusive is solved by the formula 11-5. True or false.
False.
The average of 1,2, and 3 is the same as the average of -1,2, and 3. True or false.
False.
The difference between any two consecutive even number can vary. True or False.
False.
The difference between any two consecutive odd number can vary. True or False.
False.
The divisor can be less than the remainder.
False.
The first even number is 2. True or False.
False.
The first for even number are 2,4,6, and 8.
False.
The first number in the exponent cycle is that number to the second power. True or False.
False.
The formula of any 3 consecutive numbers 3n+3. True or false.
False.
The phrase "increasing order" means consecutive. True or False.
False.
The product of a value's prime factor(s), with their exponents, can be higher than the number itself. True or false.
False.
The smaller you make the denominator, the larger the overall number will become.
False.
The smallest common divisor of any group of numbers is 2. True or False.
False.
The smallest common number that divides 132 and 60 is 6. True or false.
False.
If p≥1 and an integer where 300xp=X², understand that all integers on the left side could have even and odd exponents since it equals a square (X²).
False.
If the problem says a variable is even, remember that excludes 0. True or False.
False.
If the sum of any 3 numbers on a list equals 8 then all numbers are the same value. True or false.
False.
If a fraction (division) yields an even integer the numerator must be odd. True or False.
False.
(CxD)/2=int, therefore, C and D, both, must be even. True or false.
False.
-2 and 2 is a pair of consecutive numbers where one is positive and one is negative. True or false.
False.
1/5 > 1/4 + 1/3 +...... True or False.
False.
10⁻⁸x5 How many zeros between the decimal? 8 True or false.
False.
10⁻⁸x5 How many zeros? 7 True or false.
False.
10⁻⁸x65 How many zeros after the decimal? 7 True or false.
False.
10⁻⁸x65 How many zeros? 8 True or false.
False.
2⁴ⁿ is the formula for the 1st number of the 2 cycle. True or false.
False.
3(d)=15 15 may not be divisible by d.
False.
3n²+2n+5=prime number. This expression must be a prime number that is even. True or false.
False.
63²⁶=[(16x4)-1]²⁶ therefore remainder=1 because of (-1)²⁶.
False.
7n-8 can be odd.
False.
A and B have two distinct prime factors. A and B, both will have those two prime factors. True or False.
False.
A negative number cubed will produce a positive number. True or False.
False.
A number is not divisible by 4 if 2x tens digit plus the one's digit is divisible by 4. True or false.
False.
A perfect square will have at least 3 factors or any larger number. True or False.
False.
A perfect square will never have an even number of factors.
False.
A perfect square will never have more than one prime factor. True or False.
False.
A positive expression with an even number of integers has either one negative or both are negative. True or False.
False.
A series (5j+1(5j+2)(5j+3)...to (5j+7) is definitely not divisible by 3. True or false.
False.
A/B =integer means B has all the factors of A. True or False.
False.
Actual values are required to solve for x and y. True or false.
False.
Add 2 to each exponent then multiply is the total factor formula. True or False.
False.
All even number are based on 2(n)+1. True or False.
False.
All even number are not divisible by 2(n). True or False.
False.
All prime number will be 6n+1 or 6n-1 (some composites too). True or false.
False.
An odd number raised to any positive exponent will always be odd.
False.
Consecutive numbers that are prime are 5,7,9. True or False.
False.
Divide that answer by 2 and that remainder is the answer.
False.
Even numbers can have odd prime factors.
False.
Even numbers cannot have odd prime factors. True or False
False.
Every prime factor of A is a prime factor of B if A/B=integer (always an integer). True or false.
False.
Expression 12xy=even, sometimes. True or False.
False.
For AxB to be even, both must be even. True or False.
False.
For the sum of two numbers to be odd. One must be even and one must be odd.
False.
If 205>bx2x3x7, to get the right side close to 205, raise the highest number's exponent by 1 and test the total. True or false.
False.
If 3+x=20(10-K) then 20 or (10-K) has to be divisible by 3+x. True or false.
False.
If 3x=20(10-K) then (10-k) must be divisible by 2. True or false.
False.
If 3² is a prime factor in LCM A,B then 3 must in both of the numbers, A or B.
False.
If 3² is a prime factor in the LC of A,B then the exponent of 3 will be higher than 3⁴ or lower than 3² when A×B. True or False.
False.
If 7+v=17, 17 is divisible by v. True or false.
False.
If B>5 and 5X/B=integer then X/B=integer, always. True or false.
False.
If N is prime but N≥1 then N must be odd. True or False.
False.
If X is divisible by 2. Write it as x/2. True or false.
False.
If X=2b+5, X may not be divisible by 2b+5. True or false.
False.
0.91 is the same as 1-9×10⁻² (remember the order of operations). Right or Wrong.
Right.
0.99 is the same as 1-1×10⁻² (remember the order of operations).
Right.
Check the # against the prime numbers under its square root to see if that # is prime. Right or Wrong.
Right.
Decimal times decimal causes the product to have even more decimal places. It is best to convert decimals using power of 10 Right or Wrong.
Right.
J(j+1)(j-1) This is the multiplication of 3 consecutive numbers. Right or wrong.
Right.
R/D = 0.32
Right.
Right or Wrong.
Right.
Right or Wrong. Remember 1-X² is the difference of two squares because 1² is the same as 1.
Right.
Right or wrong.
Right.
Right or wrong. If a variable (integer) is divisible by a number, it can be written in a formula. X is (integer) divisible by 2 x=2(int) or x is greater than 4 and divisible by 2. x=2(int+3).
Right.
If the problem states something like "four odd numbers", consider n + n+2 + n+4 + n+6 for the four numbers. True or false.
True.
A/B =integer means that every prime factor of B is a prime factor of A. True or False.
True.
(1/5)⁴ harder because (1/625). (2/10)⁴ easier because (2⁴/10⁴) and they are all equal. True or False.
True.
(CxD)/2=int, therefore, C or D must be a multiple of 2 and CxD is a multiple of 2. True or false.
True.
(CxD)/2=int, therefore, C or D must be even. True or false.
True.
(t-3)(t-2) no matter what t is one expression will be even and one will be odd.
True.
-1 and 1 is a pair of consecutive numbers where one is positive and one is negative. True of false.
True.
1/5 < 1/4 + 1/3 +...... True or False.
True.
10⁻⁸x5 How many zeros between the decimal? 7 True or false.
True.
10⁻⁸x5 How many zeros? 8 True or false.
True.
10⁻⁸x65 How many zeros after the decimal? 6 True or false.
True.
10⁻⁸x65 How many zeros? 7 True or false.
True.
11a+11b is in its' simplest terms. True or false.
True.
2 is the only prime factor for all even numbers.
True.
2(6)=12 therefore 12 is divisible by 2 and 6.
True.
2n+odd# will always be odd. True or False.
True.
2⁴ⁿ is the formula for the 4th number of the 2 cycle. And 2 only has four numbers in its cycle. True or false.
True.
2⁴ⁿ⁺¹ is the formula for the 1st number of the 2 cycle. True or false.
True.
3n²+2n+5=prime number. This expression must be a prime number greater than 10. True or false.
True.
3n²+2n+5=prime number. This expression must be a prime number that is odd b/c the expression cannot equal 2. True or false.
True.
3⁴ⁿ⁺³ is the formula for the 3rd number in the 3 cycle and 4 means 3 has four number in the exponent cycle. True or False.
True.
5 is prime which means it is not divisible therefore B must be divisible by X.
True.
5<4+3+...... True or False.
True.
6n+1 and 6n-1 are prime numbers >3 or products of prime numbers >3. True or false.
True.
7n-8 must be even.
True.
A and B have two distinct prime factors. A and B, both may have 1 of each prime factor. True or False.
True.
A number is divisible by 4 if 2x tens digit plus the one's digit is divisible by 4. True or false.
True.
A perfect square can look like 4, or X⁸ or 16x². True or False.
True.
A perfect square may have more than one prime factor. True or false.
True.
A perfect square must have even exponents on its prime factors. True or False.
True.
A perfect square will always have an odd number of factors. True or False.
True.
A perfect square will have at least 3 factors or any larger odd number. True or False.
True.
A series (5j+1(5j+2)(5j+3) is definitely divisible by 3. True or false.
True.
A thorough analysis of the question stem is a must. True or False.
True.
D/R = 0.32
Wrong.
Right or Wrong.
Wrong.
Right or wrong.
Wrong.
"A² divided by 4 has the quotient 1" means A² is 4<A²<8. If it is greater than 8, the quotient would be 2 or if A² is less than 4, the quotient would be a decimal less than 1. Yes or No
Yes.
"Does X have a factor B" B represents possibility of a value therefore the question is asking if B exists. Yes or No.
Yes.
"What is the remainder when a is divided by b?" To answer this you need to know the value of b and a. Yes or No.
Yes.
(2k)(2k+2) is divisible by 2,4, and 8. K and K+1 can be factored out and K or K+1 have to be a multiple of 2 since they are consecutive, therefore, the expression above becomes 4k(k+1) then (4)(2)(int), which is a multiple of 8. Yes or No.
Yes.
(2k)(2k+2) is divisible by 2,4, and 8. K and K+1 can be factored out and K or K+1 have to be a multiple of 2 since they are consecutive. Yes or no.
Yes.
2 is a prime factor of all even numbers. Yes or No.
Yes.
8 factors can have different sets of prime factors that make up the 8 factors. Yes or No.
Yes.
Conciously simplify statements as you read quant problems for ex. "Is a+b-4 even?" Summarize by thinking "is a+b" even b/c that is what you need to know to solve the problem. Yes or No.
Yes.
Divide that sum by 2 and that remainder is the answer.
Yes.
Even if you are given all the prime factors, you only have a piece of the puzzle because sometimes a variable is attached to that number or your are not given the powers of each prime factor. Yes or No.
Yes.
Even numbers share a common prime factor. Yes or No.
Yes.
Exhaust all possibilities as your work divisibility problems. Yes or No.
Yes.
If K is a factor X then X has every prime factor K has. Yes or No.
Yes.
If X is a factor of K then K may have prime factors that X does not have. Yes or No.
Yes.
If a number is squared, all of its' exponents of the prime factors must be even.
Yes.
If a problem states a/3=b/4=c/8, make a/3= a variable like x. It would be easier to do calculations.
Yes.
K+1 is divisible by 2 (maybe 4 too), but k+3 is divisible by 2 and 4. Yes or No.
Yes.
N² and 8 will never share the same prime factors if N is odd. Yes or No.
Yes.
Perfect squares (or even exponents greater than 2) have an odd number of factors. Yes or No.
Yes.
Perfect squares can have even and odd factors. Yes or No.
Yes.
Problems dealing with prime factors are tricky so examine all possibilities. Yes or No.
Yes.
Total factors include 1 and the number itself. Yes or No.
Yes.
When a problem states which of the following, start with E.
Yes.
Yes or No.
Yes.