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GMAT - Quant > Chapter 2 - Essential GMAT Quant Skills > Flashcards

Chapter 2 - Essential GMAT Quant Skills Flashcards

1
Q

What is the difference between a proper fraction and an improper fraction?

A

In a proper fraction, the numerator is smaller than the denominator, while in an improper fraction, the numerator is larger than the denominator.

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2
Q

How is a mixed number A b/c expressed as an improper fraction?

A

(c • A + b)/c

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3
Q

What is the Least Common Denominator of a fraction?

A

The smallest nonzero whole number that is divisible by each of the denominators.

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4
Q

How can you tell if two fractions are equivalent?

A

Two fractions a/b and c/d are equivalent if a x d = b x c

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5
Q

What is the distributive property of division over addition?

A

a/b + c/b = (a + c)/b

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6
Q

What is the distributive property of division over subtraction?

A

a/b - c/b = (a - c)/b

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7
Q

How do you add or subtract fractions with unlike denominators?

A

If fractions don’t have the same denominator, we must first express the fractions with a common denominator before adding or subtracting

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8
Q

How do you multiply fractions?

A

To multiply fractions, multiply the numerators, then multiply the denominators, then place the product of the numerators over the product of the denominators, and then finally simplify the fraction. In general, (a/b) x (c/d) = ac/bd.

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9
Q

How do you divide fractions?

A

To divide fractions, change the division sign to a multiplication sign, invert the fraction to the right of the multiplication sign, and then multiply the fractions. In general, (a/b) ÷ (c/d) = (a/b) x (d/c) = ad/bc.

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10
Q

How do you multiply a whole number by a fraction?

A

When we multiply a whole number and a fraction, we multiply the whole by the numerator, and write this product over the denominator. In general, A x b/c = (A x b)/c

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11
Q

How do you find the reciprocal of a nonzero number?

A

To get the reciprocal of a non-zero number, divide 1 by that number. Another way to say this is to “take 1 over that number,” or to “take the multiplicative inverse of that number.”

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12
Q

What is the only number that doesn’t have a reciprocal?

A

Zero

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13
Q

What is a complex fraction?

A

Complex fractions are fractions whose numerator or denominator or both are also fractions.

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14
Q

What are three methods for simplifying complex fractions?

A

1) Multiply both the numerator and the denominator by the LCD
2) Write The Numerator and Denominator as a Single Fraction and then Divide
3) The Product of the Means Is The Denominator, and the Product of the Extremes is the Numerator

If a, b, c and d are nonzero, (a/b)/(c/d) = ad/bc

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15
Q

What is the bowtie method?

A

If we have two positive fractions, A and B, and if the product of Denominator B and Numerator A is greater than the product of Denominator A and Numerator B, then A is greater than B. In general, given two positive fractions a/b and c/d, a/b > c/d if ad > bc.

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16
Q

What are four methods for comparing the size of fractions?

A

1) Use a reference point - If you are given a set of fractions and asked to determine which is smallest or largest, consider using a reference point among the fractions.
2) Use the bowtie method - If we have two positive fractions, A and B, and if the product of Denominator B and Numerator A is greater than the product of Denominator A and Numerator B, then A is greater than B. In general, given two positive fractions a/b and c/d, a/b > c/d if ad > bc.
3) Use a common denominator - in a set of positive fractions, if all fractions share a denominator, the largest numerator is the largest fraction.
4) Use a common numerator - If positive fractions have the same numerator, the larger the denominator, the smaller the fraction. Inversely, the smaller the denominator, the larger the fraction.

17
Q

How do you multiply two decimals?

A

1) First, ignore the decimal point; treat the two numbers like whole numbers and find the product
2) Count the total number of decimal places to the right of the decimal point in both numbers that were multiplied
3) In the product, move the decimal point to the left the same number of spaces as indicated in step 2

18
Q

How do you divide two decimals?

A

1) Move the decimal point of the divisor (the number after the division sign) to the right until it becomes a whole number
2) Move the decimal point of the dividend (the number before the division sign) to the right the same number of spaces
3) Divide the numbers via long division. For the quotient, keep the decimal point in the same location as the new dividend.

19
Q

What is a base fraction?

A

A base fraction has a numerator of 1. Every other fraction with the same denominator will be a multiple of this fraction.

20
Q

What is 1/2 as a decimal?

A

.5

21
Q

What is 1/3 as a decimal?

A

.333

22
Q

What is 1/4 as a decimal?

A

.25

23
Q

What is 1/5 as a decimal?

A

.2

24
Q

What is 1/6 as a decimal?

A

.167

25
Q

What is 1/7 as a decimal?

A

.143

26
Q

What is 1/8 as a decimal?

A

.125

27
Q

What is 1/9 as a decimal?

A

.111

28
Q

What is 1/10 as a decimal?

A

.1

29
Q

Given a fractional base such as 2/3, what is (2/3)^2?

A

4/9. In general, (a/b)^2 = (a^2/b^2), where b ≠ 0.

30
Q

Perfect squares never end in which numbers?

A

Perfect squares never end in 2, 3, 7 or 8. If a number is a perfect square, the units digit will be 0, 1, 4, 5, 6 or 9.

31
Q

What is the commutative property of addition?

A

The Commutative Property of addition states that changing the order of two addends will not change the sum. a + b = b + a

32
Q

What is the associative property of addition?

A

The Associative Property of addition states that changing the order in which we add will not change the sum. (a + b) + c = a + (b + c)

33
Q

What is the commutative property of multiplication?

A

Commutative property of multiplication: a x b = b x a

34
Q

What is the associative property of multiplication?

A

Associative property of multiplication: (a x b) x c = a x (b x c)

35
Q

What is the distributive property?

A

The distributive property states that multiplying a number by the sum of two numbers gives the same result as multiplying this number by each addend and then adding the products together.

36
Q

What is a factorial?

A

If n is a whole number > 1, n! represents the product of all the whole numbers from n to 1, inclusive.

37
Q

What is the factorial of 0?

A

1

38
Q

What is the factorial of 1?

A

1

GMAT - Quant (6 decks)

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