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GMAT Quant > GMAT Quant Chapter 3: Properties of Numbers > Flashcards

GMAT Quant Chapter 3: Properties of Numbers Flashcards

1
Q

For the GMAT, is 0 considered to be positive or negative?

A

Neither.

The GMAT does not consider 0 to be positive or negative.

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2
Q

What is the square root of 0?

Is 0 even or odd?

0 is the only number that …?

A

0

Even

is equal to its opposite.

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3
Q

What is the number with only 1 factor?

What is the first prime number?

A

2.

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4
Q

What do even exponents always produce?

A

Positive results.

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5
Q

How can we determine all the factors of a number?

A

Start at 1 and list all of the factors.

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6
Q

What are the first 25 prime numbers?

A

2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97

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7
Q

Define a composite number.

How can we express the factors of this type of number?

A

Any number that is not prime.

As a product of its prime factors.

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8
Q

How do we find the number of factors for a given number?

A

Step I. Prime Factorize
Step II. +1 to the value of each exponent of the PFs.
Step III. Multiply all of the (PFs +1) together

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9
Q

What is the difference between a unique prime factor and a prime factor?

A

A unique prime factor is the only prime factor for a given number.

A prime factor is any number that is only divisible by 1 and itself.

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10
Q

How do we calculate the Lowest Common Multiple (LCM) of two numbers?

A
  1. Prime Factorize each integer
  2. If any PFs are repeated, take only the largest exponent
  3. Take all non-repeated PFs
  4. Multiply the values from Steps 2 & 3
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11
Q

How do we find the LCM for more than 2 integers?

A
  1. PF
  2. Find repeated PFs with highest exponent (PF shared by at least 2 numbers)
  3. Take all non-repeated PFs
  4. Multiply steps 2 & 3 values
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12
Q

How do we calculate the LCM if two integers do not share PFs?

A

Multiply the integers together.

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13
Q

How do we find the Greatest Common Factor (GCF)?

A
  1. PF each number
  2. Find repeated PFs
  3. take smallest exponents of repeated PFs
  4. Multiply numbers from step 3
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14
Q

How do we calculate the GCF if there are no repeated PFs?

A

take only those with the smallest exponent

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15
Q

What is the GCF if a set of integers has no prime factors?

A

1.

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16
Q

If we have two integers x and y, and we know the LCM of one and the GCF of another, what can we calculate?

A

LCM x GCF of two seperate integers = the product of those two integers.

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17
Q

What is the result when we multiply all of the unique prime factors?

A

The LCM.

18
Q

To check whether a certain number is divisible by another, what must we do?

A

Prime factorize to see if the denominator cancels out with the numerator.

19
Q

If x is divisible by y, then what must be true about the divisibility of x?

A

x must be divisible by all of the factors of y

20
Q

If z is divisible by x and y, what must be true about the divisibility of z?

A

Z must be divisible by the LCM of x and y but not higher multiples of the LCM.

21
Q

Is 0 divisible?

A

0 is divisible by any number other than itself.

22
Q

How do we know if a number is divisible by 11?

A

If the sum of the odd numbered placed digits minus the sum of the even placed digits is divisible by 11

23
Q

How do we know if a number is divisible by 12?

A

If it is both divisible by 3 and 4.

24
Q

What will the product of any n consecutive integers be divisible by?

A

n!

25
Q

what is the algebraic form of factored and non-factored consecutive integers?

A

n(n -1)
n(n+1)

n squared – n
n squared + n

26
Q

What is the product of n consecutive even integers divisible by?

A

2 to the power n
*
n!

27
Q

What is the division formula?

A

Dividend = Divisor x Quotient + remainder

28
Q

How do we calculate the remainder for two integers multiplied together?

A

calculate remainders for each integer individually, multiply the remainders together,
divide result so that remainder is less than the original divisor

29
Q

Can remainders be added and subtracted?

A

Yes if we make sure the result is not larger than the divisor

30
Q

How do we calculate the number of trailing 0s for any given number?

A

PF and the number of (5x2) pairs is the number of trailing 0s.

31
Q

What do we know about a factorial greater than or equal to 5?

A

0 will always be its units digit.

32
Q

How do we calculate the total number of digits for a calculation involving massive exponents?

A
  1. PF the numbers.
  2. Count the number of (5x2) pairs. Each pair = one 0
  3. Collect the number of unpaired 5 or 2s & any other nonzero PFs. Multiply them all together. Count number of digits in product.
  4. Sum number of digits from steps 2 & 3
33
Q

How can we quickly determine how many leading 0s a decimal has?

A

If X is an integer with k digits & x is not a power of 10. Then 1/x will have (k-2) leading 0s in its decimal form.

34
Q

What is the product of any consecutive integers always divisible by?

A

Any of the integers in the set or by any of the factor combinations of the numbers

35
Q

How do you determine the number of a given prime number in a factorial?

A

Divide the integer by the PF in its progressive powers.
e.g.
integer / 3 = x
integer / 9 = y
integer / 27 = z
integer / 81 = 0

The sum of x,y, and z is the number of PFs in that factorial.

36
Q

What are the first 9 perfect cubes?

A

0
1
8
27
64
125
216
343
512

37
Q

Define terminating decimal.

A

A number with a finite number of digits to the right of the decimal point.

38
Q

How do we know if a fraction produces a terminating decimal?

A

If, when factorized, the denominator contains only 2s or 5s then the decimal will terminate.

A factorized denominator with any other prime factors will produce a decimal that does not terminate.

39
Q

Name the pattern of the units digits when a number is divided by the integers 1 through 9.

A

2: 2-4-8-6 Repeat
3: 3-9-7-1 Repeat
4: 4-6 Repeat
5: All end in 5
6: All end in 6
7: 7-9-3-1 Repeat
8: 8-4-2-6 Repeat
9: 9-1 Repeat

40
Q

What do we know about 2 consecutive integers and their PFs?

A

They will never share the same prime factors.

41
Q

What is the GCF of two consecutive integers?

A

1

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