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Quantitative

Quantitative. 75 minutes 37 multiple choice questions 22 Problem solving 15 Data Sufficiency Other than the GMAT, you have most likely never seen Data Sufficiency questions. Basic Math Skills Tested. Arithmetic Algebra Number Properties Proportions Statistics Formulas Geometry.

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Quantitative

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  1. Quantitative • 75 minutes • 37 multiple choice questions • 22 Problem solving • 15 Data Sufficiency • Other than the GMAT, you have most likely never seen Data Sufficiency questions

  2. Basic Math Skills Tested • Arithmetic • Algebra • Number Properties • Proportions • Statistics • Formulas • Geometry

  3. Work smart, not hard! • Add the integers from 1 to 100 • Remember, no calculators allowed • Speed is important

  4. Work smart, not hard! • Add the integers from 1 to 100 • One approach • 1+2+3+4+5+…..+100 • Without a calculator, this approach is time consuming and prone to errors

  5. Work smart, not hard! • Another approach • Look for patterns by rearranging numbers • (1+100)+(2+99)+(3+98)…(50+51) • (101)+(101)+(101)+…(101) 50 times • (101) * 50 • 5050

  6. Work smart not hard • At a diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $1.70. What is the price of 2 doughnuts? • $0.55 • $1.00 • $1.10 • $1.30 • $1.80

  7. Work smart not hard • At a diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $1.70. What is the price of 2 doughnuts? • The only difference in the orders is one doughnut, so a doughnut must cost (2.25-1.70) = .55. Therefore 2 doughnuts cost .55 * 2 = $1.10

  8. Pace Yourself • 75 Questions in 37 minutes = ~2 minutes per question • Missing hard questions does not hurt your score very much (remember if you miss a question you are given an easier one next) • Not finishing a section definitely does hurt your score • No Review – You CAN NOT skip a question and go back or return to a question to double check your work

  9. Educated Guess • Eliminate answers you know are wrong • Avoid suspicious answers: • Not logical • Not like any other choices (only choice with a fraction, negative, etc.) • Estimate the answer and select the closest

  10. Data Sufficiency Answer Choices • (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. • (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. • (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. • (D) EACH statement ALONE is sufficient. • (E) Statements (1) and (2) TOGETHER are NOT sufficient.

  11. Data Sufficiency • Consider the information given in the question. • Examine statement 1 alone to determine if it, with the given information, is sufficient to answer the question. • Next FORGET about statement 1 and evaluate the given information and statement 2 to determine if it is sufficient to answer the question. • Evaluate both statements together to determine if combined they are sufficient to answer the question.

  12. Data Sufficiency • What is the value of y? • (1) y-3 = 2 • (2) Y2 = 25

  13. Data Sufficiency • What is the value of y? • (1) y-3 = 2 • (2) Y2 = 25 • (1) tells us that x = 5. Sufficient • (2) tells us that x = +5 or -5. Insufficient. Rule out B,C,D,E • A is correct choice.

  14. Data Sufficiency • If a + b = c what is the value of a? • 1) c-4 = b+10 • 2) b = 6 • (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. • (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. • (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. • (D) EACH statement ALONE is sufficient. • (E) Statements (1) and (2) TOGETHER are NOT sufficient.

  15. Data Sufficiency • If a + b = c what is the value of a? • 1) c-4 = b+10 • 2) b = 6 • (1) re-arrange c-b = 10+4 • c-b = 14 Sufficient alone • (2) B = 6 Insufficient, we still don’t know a & c, 1 equation with 2 unknowns can’t be solved

  16. Basic Math Skills Tested • Arithmetic • Algebra • Number Properties • Proportions • Statistics • Formulas • Geometry

  17. Number Properties • Odd +- Odd = Even • Even +-Even = Even • Odd +-Even = Odd • Odd * Odd = Odd • Even * Even = Even • Odd * Even = Even • Odd positive integer = Odd • Even positive integer = Even

  18. Number Properties • If x is an integer, is x odd? • x + 4 is an odd integer • x/3 is NOT an even integer. • (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. • (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. • (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. • (D) EACH statement ALONE is sufficient. • (E) Statements (1) and (2) TOGETHER are NOT sufficient.

  19. Number Properties • (1) Because 4 is even and only odd + even = odd, we know x must be odd. (1) is sufficient. Eliminate B,C,E • (2) Pick numbers; if x=3(odd), x/3 =1 = not even integer. If x=2(even), x/3 = 2/3 = not even integer. (2) is insufficient, so Choice A is correct.

  20. Arithmetic • Order of Operation (please excuse my dear aunt sally) • Parentheses • Exponents • Multiplication & Division • Addition & Subtraction

  21. Order of Operation Example • 7 + (6 × 52 + 3) = ?

  22. Order of Operation Example • 7 + (6 × 52 + 3) = ? • 7 + (6 × 52 + 3) = ? Parentheses, Exponents • 7 + (6 x 25 + 3)=? Multiplication & Division • 7 + (150 + 3)=? Addition & Subtraction • 7 + (153) = 160

  23. Speed – Answer in 45 seconds • If Joe has 3 times as much as he has now, he would have enough money to buy 2 notepads at $1.23 each and 4 pens at $0.93 each. How much money does Joe have? • $1.23 • $2.06 • $2.46 • $3.72 • $6.16

  24. Speed – Answer in 45 seconds • If Joe has 3 times as much as he has now, he would have enough money to buy 2 notepads at $1.23 each and 4 pens at $0.93 each. How much money does Joe have? • Approximate: • 2(1.25) + 4(1) = 2.50 + 4 = 6.50 • 6.50/3 = 2.17 I rounded up, so the answer is slightly below $2.17  $2.06

  25. Percent, Decimal, Fraction • Parts/Whole *100 = % • ¾ = .75 = 75% • 32% = 32/100 • 32% = .32 • 3.2% = .032 • X% of y = x/100 * y

  26. Absolute Value

  27. Absolute Value • Order of operation (treat absolute value, like parentheses, then multiply, then subtract)

  28. Central Tendency • Mean is the average: add all numbers and divide by the number of numbers • Median is the 'middle value' in a list (if there are an even number of numbers “average” the middle two numbers) • Mode is the number that occurs most frequently in a list

  29. Central Tendency • In the list 3,4,5,5,5,5,7,11,21 what fraction of the data is less than the mode? • 2/9 • 1/3 • 2/5 • 2/3 • 7/9

  30. Central Tendency • In the list 3,4,5,5,5,5,7,11,21 what fraction of the data is less than the mode? • Mode is 5 • Total numbers is 9 • Numbers less than mode is 2 • Fraction is 2/9

  31. Central Tendency • If the average of four numbers is 10, how many of the numbers are greater than 10? • (1) Precisely 2 of the numbers are equal to 10. • (2) The largest of the 4 numbers is 10 greater than the smallest of the 4 numbers. • (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. • (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. • (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. • (D) EACH statement ALONE is sufficient. • (E) Statements (1) and (2) TOGETHER are NOT sufficient.

  32. Central Tendency • If the average of four numbers is 10, how many of the numbers are greater than 10? • (1) Precisely 2 of the numbers are equal to 10. • (2) The largest of the 4 numbers is 10 greater than the smallest of the 4 numbers. • If the average is 10, then the sum must be 40. • (1) if 2 numbers are 10, then of the other 2 one must be >10 and the other <10. (1) is sufficient. Rule out B,C,E. • (2) largest must be >10, smallest must be <10. Possibles {5,10,10,15} {4,10,12,14}. (2) is insufficient. • Choice A is correct

  33. Probabilities • Probability = • Probability of event 1 and event 2 happening = (P1) * (P2) • Probability of event 1 or event 2 happening = (P1) + (P2)

  34. Probability • P(coin flip landing heads) = • P (2 coin flips both landing heads) = • P(after 3 flips of the next flip landing heads) = P(coin flip landing heads or tails) =

  35. Probability • P(coin flip landing heads) = ½ = 50% • P (2 coin flips both landing heads) =1/2*1/2 = ¼ = .25 • P(after 3 flips of the next flip landing heads) = ½ = 50% • P(coin flip landing heads or tails) = ½ + ½ = 100%

  36. Probability • A bowl has only 5 apples and 5 bananas. If one piece of fruit is selected from the bowl at random, and a second piece is selected from the bowl without replacing the first, what is the probability that both pieces of fruit chosen are applies? • 1/10 • 1/5 • 2/9 • 2/5 • 1/2

  37. Probability • A bowl has only 5 apples and 5 bananas. If one piece of fruit is selected from the bowl at random, and a second piece is selected from the bowl without replacing the first, what is the probability that both pieces of fruit chosen are applies? • X = =

  38. Isolating a Variable • To solve for D: • = • AD = BC • D =

  39. Algebra • If 1/x + 70/x2 =3, what is the value of 3x2-x • 8 • 5 • 49 • 67 • 70

  40. Algebra • If 1/x + 70/x2 =3, what is the value of 3x2-x • I was not asked to solve for x • 1/x + 70/x2 =3 (x2) multiply both sides by x2 • X + 70 = 3x2 Re-arrange terms • 70 = 3x2 -x

  41. Algebra • If x is not 0, and xy – 5 = -2x – 5 what is y? • -5 • -2 • 0 • 1 • 5

  42. Algebra • If x is not 0, and xy – 5 = -2x – 5 what is y? • Let x = 1 (easy arithmetic) • (1)y – 5 = -2(1) -5 • Y -5 = -2-5 • Y = -2

  43. Algebra • What is the value of x if √(x+7) +√x = √16 +√36 • 5 • 41 • 57 • 64 • 137

  44. Algebra • What is the value of x if √(x+7) +√4 = √16 +√36 • √(x+7) +2 = 4+6 • √(x+7) = 4+6-2 • √(x+7) = 8 Square both sides • X+7 = 64 • X=64-7 • X=57

  45. Algebra • If a-4b=1 and 2a=14b-10 what is the value of b? • 2 • 3 • 5 • 7 • 9

  46. Algebra • If a-4b=1 and 2a=14b-10 what is the value of b? • 2 equations with 2 unknowns – elimination • 2a-14b=-10 rearranged equation 2 • -2a+8b=-2 multiply equation 1 by (-2) • -6b = -12 • B=2

  47. Algebra • What is the value of x if y=5x+36 and y=-4x-36? • -8 • -4 • -2 • 4 • 12

  48. Algebra • What is the value of x if y=5x+36 and y=-4x-36? • Y=5x+36 2 equations 2 unknowns eliminate • Y=-4x-36 subtract eq 2 from eq 1 • 0=9x+72 • -72=9x • -8 = x

  49. Common Formulas • Rate = Quantity A per Quantity B • Speed = • Be careful of units!

  50. Rate & Speed • If Jose reads at a constant rate of 2 pages every 5 minutes, how many seconds will it take him to read N pages? • 2/5 N • 2N • 5/2 N • 24 N • 150 N

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