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GRE Quant > Ch. 1 Essential Quant Skills > Flashcards

Ch. 1 Essential Quant Skills Flashcards

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1
Q

What is a proper fraction vs. improper fraction?

A

Proper fraction = numerator is less than denominator; ex: 1/2, 2/3, 4/5, etc.
Improper fraction = numerator is greater than denominator; ex: 3/2, 5/4, 17/5

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2
Q

What is a mixed number?

A

A whole number followed by a proper fraction. Ex: 4 1/2

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3
Q

What is the LCD (Least Common Denominator)?

A

The smallest whole number that is divisible by the denominators of the fractions. Ex: LCD of 1/5, 1/6 and 1/12 is 60.

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4
Q

What is the reciprocal of a?

A

1/a
AKA multiplicative inverse

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5
Q

What is the product of a number and its reciprocal?

A

1

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6
Q

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

A

0 b/c 1/0 is undefined

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7
Q

What are complex fractions?

A

Fractions whose numerator, denominator, or both are also fractions

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8
Q

What are the two ways to simplify complex fractions?

A
  1. Write the numerator and or denominator as single fractions
  2. Multiply both the numerator and denominator by the LCD, then simplify
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9
Q

What are the three methods for comparing the size of two (or more) fractions?

A
  1. Bow-tie method (can only do with two fractions and ONLY if fractions are positive)
  2. LCD - make all fractions have the same denominator
  3. Make all fractions have the same numerator (the fraction with the LARGEST denominator is the SMALLEST number, e.g., 1/2 is larger than 1/8)
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10
Q

What happens if you add the same nonzero constant to the numerator and denominator of a fraction?

A

If the fraction is between positive 0 and 1 (e.g., 1/2), it will bring the fraction CLOSER to 1, make it bigger.
If it’s greater than 1, it’ll bring the fraction CLOSER to 1, make it smaller.

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11
Q

What happens if you subtract the same nonzero constant to the numerator and denominator of a fraction?

A

If the fraction is between positive 0 and 1 (e.g., 1/2), it will move the fraction AWAY from 1, make it smaller.
If it’s greater than 1, it’ll move the fraction AWAY from 1, make it bigger.

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12
Q

x% = ?

A

x/100 (and reduce the fraction if possible!)

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13
Q

How to convert fraction to percent?

A

x/y * 100 = ___%

For example,
3/2 * 100 = ___%
300/2 = 150%

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14
Q

√64? (note: radical sign used)

A

8 ONLY. NOT -8!!!
Radical sign denotes PRINCIPAL square root, i.e., POSITIVE square root only

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15
Q

Perfect squares (9, 16, 25,…) can have a units digit of what? Which units digits DO NOT have perfect squares?

A

0, 1, 4, 5, 6, and 9.
A perfect square CANNOT have a units digit of 2, 3, 7, or 8. For example, 4,398 and 10,347 cannot be perfect squares.

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16
Q

What is the communicative property of addition? What is the associative property of addition?

A

a + b = b + a
(a + b) + c = a + (b + c)
Changing the order will not change the sum.
The order in which we add does not matter.

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17
Q

What is the communicative property of multiplication? What is the associative property of multiplication?

A

a x b = b x a
(a x b) x c = a x (b x c)
The order in which we multiply does not matter.

18
Q

0! =

A

1

19
Q

1! =

A

1

20
Q

When using strategic numbers to compare quantities, what types of numbers should you use?

A

Positive integers (2, 3, 4), positive proper fractions (1/2, 2/3), zero, negative proper fractions, and negative integers.
Be systematic and strategic!

21
Q

If 0 < x < 1, what is the relationship of x, x^2, and √x?

A

x^2 < x < √x

22
Q

If a fraction is between 0 & 1, and you add a positive constant to the numerator AND denominator, will the fraction become larger or smaller?

A

Larger.
For example, 1/2
(1+1) / (2+1) = 2/3, which is larger than 1/2

23
Q

If a fraction is greater than 1, and you add a positive constant to the numerator AND denominator, will the fraction become larger or smaller?

A

Smaller.
For example, 2/1
(2+1) / (1+1) = 3/2, which is 1 and 1/2, which is smaller than 2

24
Q

What are the place values called to the right of the decimal and left of the decimal?

A

Counting from the right of the decimal point are tenths, hundredths, thousandths, and so on.
Counting from the left of the decimal point, the place values are ones (or units), tens, hundreds, thousands, and so on.

25
Q

How do you compare the size of two decimals? For example, 0.9098 vs. 0.907

A

Add the missing zero and compare place-by-place:
0.9098
0.9070

0.9098 is bigger

26
Q

When we have two positive fractions being squared, which number will have the larger square?

A

The larger number will have the larger result when squared.
For example, 1/2 and 2/3:
1/2 < 2/3
1/4 < 4/9
Even though the square is smaller than the original, the larger number will still have the larger square.

27
Q

If you have two large numbers being multiplied, what’s a good time-saving strategy?

A

A. Look at the units digit!
B. Estimation - if the answers are far enough apart, just try estimating!

28
Q

What are two strategies for comparing negative fractions?

A

A. Draw the number line - numbers to the right are always greater than numbers on the left! If two numbers are negative, the farther away the number is from the number 0, the smaller its value.
B. First decide which number would be larger if the numbers were positive. Once you know which number is the largest (without the negative sign), that “largest number” is actually the smallest negative number.

29
Q

PEMDAS: what priority do absolute value bars & square root symbols get?

A

Same as parentheses

30
Q

How can you split up an equation but still follow PEMDAS?

A

Since addition and subtraction that are outside of the parentheses should be done last, we can break each section separated by plus or minus sign into TERMS & then perform PEMDAS within those terms.

31
Q

What is the order of operations in fractions?

A

Think of the numerator of a fraction as having parentheses around it. Think of the denominator as having its own parentheses too.

32
Q

What does the distributive property allow us to do?

A

Factor out common factors! You should always be on the lookout for opportunities to factor out common factors.

You can do this with integers, fractions, FACTORIALS, variables.

33
Q

How to re-express numbers with addition and subtraction

A

If you find yourself running up against a calculation that will be difficult or time-consuming, take a moment to see whether a small adjustment could make the problem easier.
For example, instead of 1,000 - 857, you can do 999 - 857 + 1 (you can subtract each of the digits individually and you don’t have to “borrow” like in 1,000)

34
Q

Does xz*xy = x(yz)?

A

No, you can only use the distributive property on separate terms. xz*xy is ONE term!

35
Q

As x & y become larger, what happens to the gap between x! & y!?

A

Gap becomes way larger.
See examples below:
(1!) = 1
(2!) = 2
(3!) = 6
(4!) = 24
(5!) = 120
(6!) = 720
(7!) = 5,040

36
Q

Can you do fractions in a factorial?

A

No, factorials are only defined for whole numbers

37
Q

What are some values of x,y,z where x! + y! = z! ?

A

x, y, z have to be very small to satisfy that equation:
0, 0, 2
1, 1, 2
0, 1, 2

38
Q

What is ((5+x) * 2 * 2)?

A

((5+x)22)
= (10+2x)*2
= 20+4x

You have to multiply both 5 & x by 2 and then BOTH again by 2. Remember the associative property, you can multiply in any order & you’ll get the same answer, so pretend you multiply the 2*2 first!

39
Q

What is the distributive property?

A

a(b + c) = ab + ac

Other versions:
(b + c)a = ba + ca
a(b + c + d) = ab + ac + ad
a(b - c) = ab - ac

40
Q

When two positive numbers are raised to the SAME positive power, which one is larger?

A

The larger number will have the larger result

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