Quant

Question 1

Using the last digit shortcut, find the units digit of (7²)(9²)(3³) . . .

Answer 1

7 x 7 = 49; drop the tens and keep only the digit 9

9 x 9 = 81; drop the tens and keep only the digit 1

3 x 3 x 3 = 27; drop the tens and keep only the digit 7

9 x 1 x 7 = 63; the units digit of the final product is 3

Question 2

When testing cases in Data Sufficiency, try F0N1S numbers. . .

Answer 2

Fractions

(0) Zero

Negatives

(1)

Square Root

Question 3

An integer is divisible by

5 if:

Answer 3

The integer ends in 0 OR 5

e.g. 75 or 80

Question 4

Cylinder Volume?

Answer 4

V = π r² h

Question 5

• What happens when you increase the numerator of a fraction while holding the denominator constant?
• Increase the denominator while holding the numerator constant?
• Add the same number to both the numerator and denominator?

Answer 5

• Approaches infinity, increases in value
• Approaches 0
• Approaches 1, no matter if the fraction is larger than 1 or smaller than 1

Question 6

Note:

If one of the sides of a triangle inscribed in a circle is a diameter of the circle, then the triangle must be a right triangle.

Answer 6

Question 7

Rate x Time = Distance

Set-up the chart to solve for an average when you know the going and the return rates, and the total distance

Answer 7

• Working together: add the rates
• Running away: subtract the rates
• Chasing each other: subtract the rate

Question 8

An integer is divisible by

6 if:

Answer 8

The integer is divisible by both 2 AND 3

e.g. 48

Prime Factors: 2, 2, 2, 2, 3

Question 9

What is the Quant Timing Strategy?

Answer 9

Complete 8 questions every 15 min.

Question 10

Common relationships in word problems:

• Total Cost = Unit Price x Quantity Purchased
• Profit = Revenue - Cost
• Total Earngings = Wage Rate x Hours Worked
• Miles = Miles per Hour x Hours
• Miles = Miles per Gallon x Gallons

Question 11

What is the greatest common factor?

Between 100, 140, and 250

Answer 11

The greatest number that divides evenly into the two numbers.

Factor them down to Prime Factors

100: 2, 2, 5, 5; 2², 5²
140: 2, 2, 5, 7; 2², 5¹, 7¹
250: 2, 5, 5, 5; 2¹, 5³

Look at the minimum from each column the numbers have in common; 2¹ x 5¹ = 10

Question 12

Set-up the chart to determine overlapping sets between men, women, and employees. . .

Answer 12

• Pay attention to sub-sets of sub-sets wording
• Look out for given contraints (when there is a null value inherent)

Question 13

Note:

• When absolute value of variable is less than, the answer will be -4
• When absolute value of variable is greater than, the answer will be x > 2 or x

Answer 13

• x > 2 or x

| 2x + 2 |

• -4

2x + 2 | > 6

Question 14

What are the 3 special products of quadratic expressions?

Answer 14

• x² - y² = (x + y)(x - y)
• x² + 2xy + y² = (x + y)(x + y) = (x + y)²
• x² - 2xy + y² = (x - y)(x - y) = (x - y)²

^{* Look out for sq. roots hidden as special quadratic expessions. Look to use substiution to solve quickly.}

Question 15

Note:

For some probability problems it may be easier to calculate the probability of something NOT occurring.

Answer 15

A bag contains R, G, B and Y marbles. 3 marbles are pulled, what is the probability at least 1 will be red.

Not Red:

2/3 X 2/3 X 2/3 = 8/27

Red:

1 - 8/27 = 19/27

Question 16

Even * Even =

Odd * Odd =

Even * Odd =

Answer 16

Even * Even = Even^

Odd * Odd = Odd

Even * Odd = Even^

^ If one Even number is present, the result will be Even. If only Odd numbers exist, the result will be Odd

Question 17

An integer is divisible by

3 if:

Answer 17

The sum of the integer’s digits is divisible by 3

e.g. 72 = 7 + 2 = 9

9 is divisible by 3

e.g. 83 = 8 + 3 = 11

11 is not divisible by 3

Question 18

Circle:

Circumference?

Diameter?

Radius?

Area?

Answer 18

C = π • d

d = 2 • r

⇒ C = 2 • π • r

A = π • r²

Question 19

An integer is divisible by

9 if:

Answer 19

The sum of the integer’s digits is divisible by 9

e.g. 4,185 = 4 + 1 + 8 + 5 = 18 / 9; yes

Question 20

Note:

• If you are given two sides of a triangle or parallelogram, you can maximize the area by placing those two sides perpendicular to each other

Question 21

What is the factor foundation rule?

Answer 21

If A is a factor of B, and B is a factor of C, then A is a factor of C

e.g. since 72 is divisible by 12, 72 is also divisible by all the factors of 12 (1, 2, 3, 4, 6, 12)

Question 22

Cylinder Surface Area?

Answer 22

SA = 2 • π • r² + 2 • π • r • h

Question 23

What is the area of a Trapezoid?

What is the area of a any polygon?

Answer 23

1. [(Base₁ + Base₂) x Height] / 2
2. Base x Height

Question 24

What are the common combinations of right triangles?

Answer 24

* Watch out for imposters; a non-right triangle with a side of 3 and a side of 4 does not have a third side of length 5.

Question 25

What are the legs of a 45 - 45 - 90 triangle?

Answer 25

If given the hypotenuse to get a leg divde by sq. root 2

Question 26

What are the legs of a 30 - 60 - 90 triangle?

Answer 26

If given the hypotenuse to get the short leg multiply by sq. root 3, divide by 2 If given the hypotenuse to get the long leg divide by 2

Question 27

Count of multiples of 3 between 1 and 150. . . What is their sum?

Answer 27

Number of terms = (Last - First) / Increment + 1 (150 - 3) / 3 + 1 = 50 * Make sure to use only the multiples of the increment as the first and last numbers Average of Set = (First + Last) / 2 (3 + 150) / 2 = 76.5 Multiply Number of Terms x Average of Set 50 x 76.5 = 3,825

Question 28

Note: When looking to calculate the distance between two points on a coordinate plane, look for special triangles

Question 29

Use an anagram grid to describe: 7 people enter a race, 4 medals given, winner gets Platinum, 2nd gets Gold, 3rd gets Silver, the rest get bronze

Answer 29

7 = number of places 1 = number of Platinum 1 = number of Gold 2 = number of Silver 3 = number of Bronze

Question 30

Is an integer X divisible by 9? * Find Prime Factors in problems of divisibility

Answer 30

X = 210 Prime Factors: 2, 3, 5, 7 No because there are not *two* 3's in the within the prime factors

Question 31

In Combinatorics, what do "OR" and "AND" mean? A restaurant has 3 main dishes: S, C, and F and 2 side dishes: P and D - How many different combinations exist?

Answer 31

OR: (S + C + F) = 3 AND: (P + D) = 2 3 \* 2 = 6

Question 32

Watch for the disguised quadratics: 3x² = 6x

Answer 32

3x² = 6x 3x² - 6x = 0 3x ( x - 2) = 0 x = 0 or x = 2

Question 33

Memorize Cubes and Cube Roots

Answer 33

1³ = 1 2³ = 8 3³= 27 4³ = 64 5³ = 125 10³ = 1,000

Question 34

What is true of Central angles related to inscribed angles?

Answer 34

An inscribed angle is equal to half of the arc it intercepts, in degrees.

Question 35

Note: Don't forget adding the inequalities is a solution \*Make sure the signs face the same way

Answer 35

3x + 4y \> 9 3x - 2y \> 3 --\> 6x - 4y \> 6 9x \> 15 x \> 5/3

Question 36

An integer is divisible by 8 if:

Answer 36

The integer is divisible by 2 *three* times OR the last three digits are divisible by 8 e.g. 24,856 = 856 / 8; yes

Question 37

What is true about any two sides of a triangle in relation to the third?

Answer 37

The sum of any two sides of a triangle must be *greater than* the third side.

Question 38

Equation for the sum of interior angles of a polygon. . .

Answer 38

(n - 2) x 180 \*n is the number of sides

Question 39

On the GMAT, it generally pays to factor exponential terms that have bases in common: If x = 4²⁰ + 4²¹ + 4²², what is the largest prime factor of x?

Answer 39

x = 4²⁰ + 4²¹ + 4²² x = 4²⁰ (4⁰ + 4¹ + 4²) → Remember that this is an option to simplify the exponent x = 4²⁰ (1 + 4 + 16) x = 4²⁰ (21) x = 2^{2 x 20} (3 x 7) 7 is the largest prime factor.

Question 40

Work Backwards as a strategy

Answer 40

Start with the answer choices and solve the problem using the constraints \* When you get a match while working backwards, that is your answer

Question 41

Note: * Of all quadrilaterals with a given perimter, the *square* has the largest area

Question 42

An integer is divisible by 10 if:

Answer 42

The integer ends in 0

Question 43

An integer is divisible by 4 if:

Answer 43

The integer is divisible by 2 *twice* OR the last two digits are divisible by 4 e. g. 25,782 = 82 / 4; not an integer e. g. 25,756 = 56 / 4; yes

Question 44

Note: * Of all quadrilaterals with a giver area, the square has the minimum *perimter*

Question 45

When can Smart Numbers be used to solve a problem?

Answer 45

When there are no concrete values in the problem and the answer choices are all variables * If picking for more than one variable, pick different numbers for each on. If possible, pick numbers with different characteristics (even, odd) * Follow any constraints given in the problem (positive numbers, or even, or odd) * Avoid choosing 0, 1, or numbers that appear in the problem * Choose numbers that work easily in the problem. 100 is often best to use for percent problems

Question 46

Averages formula

Answer 46

Write the average formula at the top of the sheet when dealing with an Average * Average = Sum / (# of terms) Use an average chart for 2+ averages

Question 47

Even +/- Even = Odd +/- Odd = Even +/- Odd =

Answer 47

Even +/- Even = Even\* Odd +/- Odd = Even\* Even +/- Odd = Odd \* When they are the same, Even, otherwise Odd

Question 48

What is true of exterior angles of a triangle related to interior angles?

Answer 48

Int. A + Int. B = Ext. C

Question 49

What is the area of a Rhombus? What is true of the bisectors?

Answer 49

A = (Diagonal₁ x Diagonal₂) / 2 Diagonals of a rhombus are *always* perpendicular bisectors

Question 50

Teeter-totter method or algabraic method: P is 10% sugar, B is 2%. To make a mixuture of 4%, what ratio of P to B is needed?

Answer 50

Question Asking → P:B 10%P + 2%B = 4%(P+B) 10P + 2B = 4P + 4B 6P = 2B 3P = B 1 P : 3 B

Question 51

Unknown Multiplier and Ratio Chart The ratio of lemon juice to wine to water is 2:5:7. If all thee yield 35 mL, how much water was included?

Answer 51

Lemon + Wine + Water = Total 2x + 5x + 7x = 14x --\> (2+5+7) 14x = 35 x = 2.5 5 (2.5) = 12.5 mL \*Use a ratio chart when there are 3 or more items

Question 52

Name the first 10 prime numbers:

Answer 52

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Question 53

An integer is divisible by 2 if:

Answer 53

The integer is *even*

Question 54

Note: Be on the lookout for relative values to a total in Data Sufficiency question. i.e. what fraction of the total pies sold last month were apple pies?

Answer 54

Rephrase the question: a / (a + c) = ? DS1) the company sold 460 pies last month a / (460) = ?; not sufficient DS2) the compnay sold 30% more cherry pies than apple pies last month 1.3a = c a / (a + 1.3a) = 1 / 2.3; sufficient

Question 55

Fractions raised to Even vs. Odd Powers

Answer 55

Question 56

What is true of the area of similar triangles with corresponding side lengths A and B?

Answer 56

If two similar triangles have corresponding side lengths in ratio a:b, then their areas will be in ratio a²:b²