GMAT

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kuchak
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37536
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GMAT
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2010-09-28 20:22:49
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GMAT
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GMAT
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  1. Simplify:

    XaXb
    Xa+b
  2. Simplify:

    AxBx
    (AB)x
  3. Simplify:

    Xa/Xb
    Xa-b
  4. Simplify:

    (A/B)x
    Ax/Bx
  5. (Ax)y
    Axy or (Ay)x
  6. X-a
    1/(X)a
  7. Xa/b
    b√Xa Or b√(X)a
  8. A+xA+xAx
    3Ax

    YOU CAN ONLY ADD OR SUBTRACT NUMBERS WITH EXPONENTS IF THE BASE AND EXPONENT ARE CONSTANT
  9. Ax+By
    CANNOT BE SIMPLIFIED
  10. ABx
    CANNOT BE SIMPLIFIED
  11. Simplify:

    (2+5)3
    • 73
    • NOT 23+33
  12. Simplify:

    (2*5)3
    23*53 = 1000
  13. X2-Y2
    (X+Y)(X-Y)
  14. X2+2XY+Y2
    (x+y)(x+y) OR (x+y)2
  15. x2-2xy+y2
    (x-y)(x-y) OR (x-y)2
  16. X2-1
    (X+1)(X-1)
  17. What are the Possible values for x ?

    (x-b)(x+a)/(x-m) = 0
    +b,-a

    • ZERO in the denominator means UNDEFINED
    • ZERO in the numerator equals ZERO
  18. How do you calculate the SUM of a range of integers?

    ex. 20->100
    • Multiply the middle term(average) by the number of terms
    • ex.
    • Average = (100+20)/2 = 60
    • #of Terms = (100-20)+1 = 81
    • Sum = 60*81 = 4860
    • For any set where there is an ODD number of terms, the sum of all the integers is ALWAYS a multiple of the # of items (NOT TRUE if there is an Even number of terms) ex. 4860/81=60
  19. What is the SUM of an EVENLY spaced Set?

    ex. 4,8,12,16,20
    • The sum of an evenly spaced set is the average times the number of terms
    • ex.
    • Average = (20+4)/2 = 5
    • #of terms = (20-4)/4+1 = 5 *after subtracting the highest and lowest digits, you need to divide by the increment b/w digits in the set before adding 1
    • Sum = 12*5 = 60
  20. How many integers are there in a consecutive set?
    ex. 14->765inclusive
    (Last-First)/increment + 1 = # of integers

    ex. (765-14)/1+1=752
  21. How many integers are there in a consecutive set?
    ex. all even integers 12 to 24 inclusive
    ex. (24-12)/2+1=7
  22. How many integers are there in a consecutive set?
    ex. multiples of 7 between 100 and 150inclusive
    • ex. (147-105)/7+1=7
    • Need to use the lowest and highest multiple of 7 within that range
    • 21*7 = 147 closest integer to 150 without going outside the range
    • 15*7 = 105 closest integer to 100 without going outside the range
  23. What is the Factor Foundation Rule?
    If A is a factor of B, and B is a factor of C, then A is also a factor of C.

    The product of any combination of factors of integer N is in an of itself a factor of integer N
  24. What is the forumal for DIRECT proportionality?
    ex. Height is the square of the velocity of an object, if an object is moving at 16ft/s reaches 4ft, what speed is required to reach 9ft?
    • (Y1/X1) = (Y2/X2)
    • ex.
    • (4/162) = (9/v22)
    • v22= 9(162/4) = 576
    • √V = 24
  25. What is the formula for INVERSE proportionality?
    ex. Current is inversley proportional to resistance, if a wire carries 4amps of current but the resistance decreases by 1/3 of its original value how many amps of current will flow?
    • Y1X1 = Y2X2
    • C1R1 = C2R2
    • 4*3=C2*1
    • C2 = 2
  26. Use patterns when finding terms in a sequence.
    ex. What is the units digit of S65 if Sn = 3n
    • S1 = 31 = 3
    • S2 = 32 = 9
    • S3 = 33 = 27
    • S4 = 34 = 81
    • S5 = 35 = 243 65 is a multiple of 5, so it will share the same units digit of 3
  27. 3√1
    1
  28. 3√8
    2
  29. 3√27
    3
  30. 3√64
    4
  31. 3√125
    5
  32. 13
    1
  33. 23
    8
  34. 33
    27
  35. 43
    64
  36. 53
    125
  37. √2
    ~1.4
  38. √3
    ~1.7
  39. √5
    ~2.25
  40. √121
    11
  41. √144
    12
  42. √169
    13
  43. √196
    14
  44. √225
    15
  45. √256
    16
  46. √625
    25
  47. n√xy
    (n√x)(n√y)
  48. n√(x+y)
    CANNOT BE SIMPLIFIED FURTHER
  49. n√(x/y)
    (n√x)/(n√y)
  50. Solve 4-3x<10
    • 4-3x<10
    • -3x<6
    • x>-2 REMEMBER when multiplying or dividing an inequality you need to FLIP the sign
  51. Solve for ab 1>1-ab>0
    • 1>1-ab>0
    • 0>1-ab>-1
    • 0<ab<1 All actions need to be done to ALL sides of the inequality
  52. What is the test to see if an integer is divisible by 3?
    • if all the sum of the integers is divisible by 3.
    • ex 72, 7+2 = 9 9/3=3
  53. What is the test to see if an integer is divisible by 4?
    • If the integer is divisible by 2 TWICE or the last two digits are divisible by 2.
    • ex. 24/2 = 12 12/2 = 6
  54. What is the test to see if an integer is divisible by 6?
    • If the integer is divisible by BOTH 2 and 3
    • ex. 90, 90/2 = 45 90/3 = 30 -> 90/6=15
  55. What is the test to see if an integer is divisible by 8?
    • If the integer is divisible by 2 THREE times or the last 3 digits are divisible by 8.
    • ex118 128/2= 64 64/2 = 32 32/2=16 128/8=16
  56. What is the test to see if an integer is divisible by 9?
    • If the sum of the integers digits is divisible by 9
    • ex 126 1+2+6=9 126/9=14
  57. What is the lowest PRIME number?
    2
  58. What number is a MULTIPLE(more) of EVERY number?
    0
  59. What is the Greatest Common Factor (GCF)?
    • The largest divisor of two or more integers. Calculated by multiplying ONLY the common factors a set of integers has.
    • Ex. GCF of 30 and 24
    • Factors of 30: 2 3 5
    • Factors of 24: 2 2 2 3
    • Common Factors: 2 3 = 2*3 = 6
  60. What is the Least Common Multiple (LCM)?
    • The smallest multiple of two or more integers. Calculated by multiplying all the primes of each integer but ONLY counting the common factors ONCE.
    • Ex. LCM of 30 and 24
    • Factors of 30: 2 3 5
    • Factors of 24: 2 2 2 3
    • Multiply Factors: 2*2*2*3*5 = 120
  61. What is a remainder?
    • The number LEFT OVER from long division.
    • ex 3
    • 5| 17
    • -15
    • 2 is the remainder
  62. How can you pick a number with a desired remainder?
    • If you need a desired remainder of N after division by X, pick a multiple of X and ADD N
    • ex. Need a number with a remainder of 4 after division by 7,
    • 14+4=18
    • 2
    • 7| 18
    • -14
    • 4 is the remainder
  63. ODD+EVEN = ?
    ODD
  64. ODD-EVEN = ?
    ODD
  65. ODD+ODD = ?
    EVEN
  66. ODD-ODD = ?
    EVEN
  67. EVEN-EVEN = ?
    EVEN
  68. EVEN+EVEN = ?
    EVEN
  69. ODD*ODD = ?
    ODD
  70. ODD*EVEN = ?
    EVEN
  71. EVEN*EVEN = ?
    EVEN (also it will always be divisible by 4)
  72. If the sum of 2 primes is ODD, what must one of the primes be?
    2
  73. EVEN/EVEN = ?
    Can be EVEN, ODD, or NON-INTEGER
  74. EVEN/ODD = ?
    Can be EVEN, or NON-INTEGER not ODD
  75. ODD/EVEN
    Can ONLY be a NON-INTEGER, not ODD not EVEN
  76. ODD/ODD = ?
    Can ONLY be ODD or NON-Integer not EVEN
  77. How can you get the average of an evenly spaced set of integers?
    Take the average of the FIRST and LAST integer in the set
  78. How do you calculate the SUM of the terms in an evenly spaced set?
    Multiply the average by the #of terms.
  79. How can you find the #of terms between two integers?
    • Subtract the LOWEST integer from the Highest, divide by the interval b/w each integer in the set and ADD 1.
    • Ex.
    • Set A: 6,7,8,9,10 : 10-6=4 +1 = 5integers
    • Set B: 12,14,16,18,20,22,24 : 24-12=12 /2 = 6 +1 = 7integers
  80. If you have an ODD number of consecutive integers, will the average be an integer?
    YES - always

    • The sum of an ODD number of consecutive integers will also ALWAYS be a multiple of the number of terms
    • ex. 4+5+6+7+8 = 30, a multiple of 5
  81. If you have an EVEN number of consecutive integers, will the average be an integer?
    NO - never
  82. How do you calculate the sum of different parts of a set?
    • Use N as the first integer and add the interval to each consecutive integer starting with N.
    • ex. How much greater is the sum of the last four integers in a set of eight than the first 4
    • (n+4)+(n+5)+(n+6)+(n+7)
    • -[ n +(n+1)+(n+2)+(n+3)]
    • 4 + 4 + 4 + 4 = 16 , the last 4 intergers is 16 more than the first 4 integers
  83. 03
    • 0
    • zero to any power is zero
  84. 16
    • 1
    • 1 to any power is 1
  85. 170
    • 1
    • any number with 0 as the exponent is 1
  86. 1891
    • 189
    • Any number to the exponent of 1 is that number
  87. √(y3)
    √y√y√y = y√y
  88. REMEMBER variables with EVEN exponents always have TWO values, a negative and positive
    Variables with ODD exponents have ONE value, same sign as the base
  89. What is the MASTER RULE?
    If two equations are LINEAR (no squared terms) the equations WILL be sufficient to find the value of the variables unless the two equations are mathematically identical ex. x+y=12 2x+2y=24

    if there are ANY NON-linear terms (X2,Y3,XY,X/Y) there are usually 2 or more values for each variable.
  90. Same base means same exponent
    • ex.
    • (4w)3=32dw-1
    • ((2)2)w)3 = (25)w-1
    • 6W = 5(W-1)
    • W = -5
  91. What is the LINEAR FORMULA used for determining a value in a sequence?
    ex What is the rule for the sequence: 16,20,24,28
    • Sn = kn+x
    • K = the constant interval between integers in a set

    • Sn = 4n+x
    • S1 = 4(1)+x
    • 16 = 4+x
    • x = 12
  92. What is the EXPONENTIAL FORMULA used for determining a value in a sequence?ex What is the rule for the sequence: 20,200,2000,20000
    • Sn = x(kn)
    • K = is the constant that when multiplied by one number in the set yields the next

    • Sn = x(10n)
    • S1 = 20
    • 20 = x(101)
    • x = 2
  93. What is the formulat for LINEAR GROWTH
    • y = mx+b
    • m = constant rate of growth or decay
    • b = y-intercept at time zero
    • x = time
  94. How is Q related to each variable in the below formula:
    Q = 4W/4xz2
    • Q is DIRECTLY proportional to W, if one increases so does the other
    • Q is Inderectly proportional to x and z, if one increases the other decreases
  95. NEVER SUBTRACT OR DIVIDE INEQUALITIES, you can combine through multiplication or addition
  96. 8+LT2
    LT10 or <10
  97. 8-LT2
    GT6 or >6 remember toe FLIP the sign when subtracting extreme values
  98. 8*LT2
    LT16 or <16
  99. -7*LT2
    GT(-14) remember to flip the sign when multiplying NEGATIVE extreme values
  100. 8/LT2
    GT4 or >4 remember to FLIP the sign when DIVIDING extreme values
  101. LT2*LT8
    LT16 or <16
  102. What is the value(s) for X in |x-2|<5?
    |x-2|<5

    • absolute value formulas have 2 possible values, when the absolute value is negative or positive
    • x-2<5 -(x-2)<5
    • x<7 -x+2<5
    • x>-3
    • -3<x<7 is the range
  103. What are the rules for picking numbers?
    • Avoid using 1 or 0
    • Use Different numbers for each value
    • Use primes
    • Avoid picking numbers that appear as coefficients in the answer choices
  104. What is the formula for 'x' percent of y?
    • 'x' percent = x/100
    • (x/100)y = xy/100
  105. What is the formula for 'y' percent less than z?
    z-z(y/100) = z=(1-y/100)
  106. What is a Premise?
    STATED piece of information that generally provides support for a given conclusion (facts,opinions,claims-NOT the final claim/conclusion)
  107. What is an Assumption?
    UNSTATED parts of the argument neccessary to reach a conclusion
  108. What are the basic CONCLUSION signal words.
    • Therefore So
    • As a result Consequently
    • Suggests Thus
    • Indicates Hence
    • Accordingly It follows that
  109. What are the rules for determining a claim?
    • 1. Predict the future; will,should,can expect to, are likely to
    • 2. Subjective Opinion
    • 3. Cause and Effect; if there is more than one claim which claim leads to the other(final claim)
    • X therefore Y test
  110. When describing/using a period in time, what relative pronoun must be used WHICH or WHEN?
    • WHEN
    • ..at a time when
    • ..on the weekend when
  111. What preposition needs to be used when explaining HOW something is done?
    • BY
    • ..by doing X, Y can be accomplished
  112. What is the formula for WEIGHTED AVERAGE?
    ex. What is the WA of two 20s and 3 30s
    • WA = weight/sum of weights(data point) + weight/sum of weights(data point)....
    • ex. [2(20)+3(30)]/(2+3) = 26
  113. When is LIKE used?
    To compare objects, people, or things.
  114. When is AS used?
    To compare clauses, actions, verbs
  115. When is SUCH AS used
    used as in "for example"
  116. If two situations CANNOT occur together, what is the probability of one OR the other occurring separately?
    Simply add the probability of each situation together.
  117. If two situations CAN occur together, what is the probability of ONE happening and NOT the other?
    P(AorB) = P(A)+P(B)-P(A+B)
  118. How do you calculate the COMBINED work of people WORKING TOGETHER?
    Simply add the rates of each person. Only when one person is UNDOING the work do you subtract
  119. How do you calculate average rate?
    • If given the individual rates and distances, calculate each individual time and add.
    • Rate * Time = Distance
    • going 4mph 3 12
    • returning 6mph 2 24
    • 4.8 5 24
    • If ONLY given the rates, PICK distances that have a multiple of those rates
  120. When "WHICH" follows a comma, the word "WHICH" is referring to is the subject closest to it before the comma.
    We like the store, which is large. CORRECT

    We liked the rugs in the store, which were fur INCORRECTLY STATING STORE IS MADE OF FUR
  121. What are the 3 rules of READING COMPREHENSION?
    Justify EVERY word in the answer choice.

    Avoid answer choices with EXTREME words.

    Choose teh answer choice that infers as LITTLE as possible.
  122. What is the formula for RATE?
    • Rate * Time = Work
    • Rate * Time = Distance
  123. How do you combine the rates of 2 objects that are driving TOWARD each other?
    Add the rates of the two objects. (same if driving AWAY from each other)
  124. At what rate with CAR A catch up to CAR B?
    Rate A - Rate B
  125. How do you calculate the rate of Car A if it is chasing Car B and falling behind?
    Rate B - Rate A
  126. 1.42
    ~2
  127. 1.72
    ~3
  128. 2.252
    ~5
  129. 112
    121
  130. 122
    144
  131. 132
    169
  132. 142
    196
  133. 152
    225
  134. 162
    256
  135. 252
    625

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