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GMAT > Quant > Flashcards

Quant Flashcards

1
Q

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

A

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

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2
Q

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

A

Fractions

(0) Zero

Negatives

(1)

Square Root

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3
Q

An integer is divisible by

5 if:

A

The integer ends in 0 OR 5

e.g. 75 or 80

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4
Q

Cylinder Volume?

A

V = π r2 h

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5
Q
  • 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?
A
  • Approaches infinity, increases in value
  • Approaches 0
  • Approaches 1, no matter if the fraction is larger than 1 or smaller than 1
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6
Q

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.

A
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7
Q

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

A
  • Working together: add the rates
  • Running away: subtract the rates
  • Chasing each other: subtract the rate
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8
Q

An integer is divisible by

6 if:

A

The integer is divisible by both 2 AND 3

e.g. 48

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

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9
Q

What is the Quant Timing Strategy?

A

Complete 8 questions every 15 min.

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10
Q

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
A
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11
Q

What is the greatest common factor?

Between 100, 140, and 250

A

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

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12
Q

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

A
  • Pay attention to sub-sets of sub-sets wording
  • Look out for given contraints (when there is a null value inherent)
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13
Q

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
A
  • x > 2 or x

| 2x + 2 |

  • -4

2x + 2 | > 6

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14
Q

What are the 3 special products of quadratic expressions?

A
  • 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.

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15
Q

Note:

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

A

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

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16
Q

Even * Even =

Odd * Odd =

Even * Odd =

A

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

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17
Q

An integer is divisible by

3 if:

A

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

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18
Q

Circle:

Circumference?

Diameter?

Radius?

Area?

A

C = π • d

d = 2 • r

⇒ C = 2 • π • r

A = π • r2

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19
Q

An integer is divisible by

9 if:

A

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

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

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20
Q

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
A
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21
Q

What is the factor foundation rule?

A

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)

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22
Q

Cylinder Surface Area?

A

SA = 2 • π • r2 + 2 • π • r • h

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23
Q

What is the area of a Trapezoid?

What is the area of a any polygon?

A
  1. [(Base1 + Base2) x Height] / 2
  2. Base x Height
24
Q

What are the common combinations of right triangles?

A

* 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.

25
Q

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

A

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

26
Q

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

A

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

27
Q

Count of multiples of 3 between 1 and 150. . .

What is their sum?

A

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

28
Q

Note:

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

A
29
Q

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

A

7 = number of places

1 = number of Platinum

1 = number of Gold

2 = number of Silver

3 = number of Bronze

30
Q

Is an integer X divisible by 9?

  • Find Prime Factors in problems of divisibility
A

X = 210

Prime Factors: 2, 3, 5, 7

No because there are not two 3’s in the within the prime factors

31
Q

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?
A

OR: (S + C + F) = 3

AND: (P + D) = 2

3 * 2 = 6

32
Q

Watch for the disguised quadratics:

3x2 = 6x

A

3x2 = 6x

3x2 - 6x = 0

3x ( x - 2) = 0

x = 0 or x = 2

33
Q

Memorize Cubes and Cube Roots

A

13 = 1

23 = 8

33= 27

43 = 64

53 = 125

103 = 1,000

34
Q

What is true of Central angles related to inscribed angles?

A

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

35
Q

Note:

Don’t forget adding the inequalities is a solution

*Make sure the signs face the same way

A

3x + 4y > 9

3x - 2y > 3 –> 6x - 4y > 6

9x > 15

x > 5/3

36
Q

An integer is divisible by

8 if:

A

The integer is divisible by 2 three times

OR

the last three digits are divisible by 8

e.g. 24,856 = 856 / 8; yes

37
Q

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

A

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

38
Q

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

A

(n - 2) x 180

*n is the number of sides

39
Q

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?

A

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 = 22 x 20 (3 x 7)

7 is the largest prime factor.

40
Q

Work Backwards as a strategy

A

Start with the answer choices and solve the problem using the constraints

* When you get a match while working backwards, that is your answer

41
Q

Note:

  • Of all quadrilaterals with a given perimter, the square has the largest area
A
42
Q

An integer is divisible by

10 if:

A

The integer ends in 0

43
Q

An integer is divisible by

4 if:

A

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

44
Q

Note:

  • Of all quadrilaterals with a giver area, the square has the minimum perimter
A
45
Q

When can Smart Numbers be used to solve a problem?

A

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
46
Q

Averages formula

A

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

47
Q

Even +/- Even =

Odd +/- Odd =

Even +/- Odd =

A

Even +/- Even = Even*

Odd +/- Odd = Even*

Even +/- Odd = Odd

* When they are the same, Even, otherwise Odd

48
Q

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

A

Int. A + Int. B = Ext. C

49
Q

What is the area of a Rhombus?

What is true of the bisectors?

A

A = (Diagonal1 x Diagonal2) / 2

Diagonals of a rhombus are always perpendicular bisectors

50
Q

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?

A

Question Asking → P:B

10%P + 2%B = 4%(P+B)

10P + 2B = 4P + 4B

6P = 2B

3P = B

1 P : 3 B

51
Q

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?

A

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

52
Q

Name the first 10 prime numbers:

A

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

53
Q

An integer is divisible by

2 if:

A

The integer is even

54
Q

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?

A

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

55
Q

Fractions raised to Even vs. Odd Powers

A
56
Q

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

A

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

GMAT (3 decks)

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