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GMAT Quantitative General

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
D or E
______ |m-n|
(x-n(n)y-n)

2. Think of averages as what? The average of 3 - 4 - 5 - and x is 5. What is x? 3 is 2 less than 5 4 is 1 less than 5 - 5 is the average - x = 5 + 3 = 8
Purchase price
If a point is chosen at random within a space with an area - volume - or length of Y and a space with a respective area - volume - or length of X lies within Y - the probability of choosing a random point within Y is the area - volume - or length of
Balancing
The probability of event occurring is...

3. How do you multiply roots together.
if a first object may be chosen in m ways and a second object may be chosen in n ways - then there are mn ways of choosing both objects
Sum of digits is multiple of 3
1/16
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

4. 3rd Rule of Probability: Conditional Probability
14 liters
the probability of event A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
-b +- sq. rt(b^2 - 4ac) / 2a
The probability of an event occurring plus the probability of the event not occurring = 1

5. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
if a first object may be chosen in m ways and a second object may be chosen in n ways - then there are mn ways of choosing both objects
-b +- sq. rt(b^2 - 4ac) / 2a
y2 - y1 / x2 - x1

6. Prime Factorization to find Greatest Common Factor
1. Start by writing each number as product of primes. 2. Write so that each new prime factor begins in the same place. 3. Greatest Common Factor is found by multiplying all factors appearing in BOTH lists
Balancing
Sum of digits is multiple of 9
D or E

7. Gross
y2 - y1 / x2 - x1
The total amount before any deductions
1
0.15n + 0.08(5) = 0.1(n+5)

8. The average of consecutive numbers
Sum of digits is multiple of 9
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
P(E) + P(F) - P(E and F)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

9. x^r/s = ?
Immediately try factoring/simplifying when possible
s Sq. rt (x^r)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The amount after deductions

10. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
Organize into a grid.
Sum of digits is multiple of 3
Even

11. 2nd Rule of Probability: P(E) = 1 - P(not E)
sum = (average)(number of terms)
22
1.4
The probability of an event occurring plus the probability of the event not occurring = 1

12. Properties of 0
If the outcome of one event affects the outcome of the other event.
P(event NOT occurring) = 1 - P(event occurring)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
gcd(m,n)*lcm(m,n) = mn

13. Probability and Geometry.
Group 1 + Group 2 + Neither - Both = Total
1/16
Organize into a grid.
If a point is chosen at random within a space with an area - volume - or length of Y and a space with a respective area - volume - or length of X lies within Y - the probability of choosing a random point within Y is the area - volume - or length of

14. 5/6 = what %
83.3%
at least 3 steps
y2 - y1 / x2 - x1
Figure out the probability for each individual event. Multiply the individual probabilities together.

15. Indistinguishable events how to find the number of permutations

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16. Price sold for by retailer (after markup)
1.7
3 - 6 - 9 - 12
market value
Purchase price

17. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
Immediately try factoring/simplifying when possible
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(total distance) / (total time)

18. Percent Formula
Odd
83.3%
Purchase price
p/100 = is/of

19. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
The probability of event occurring is...
(total A) / (total B)
Principal (1 + interest/number times compounded)^(t)(n)
principle (interest rate - in decimal form) (time - in years)

20. gcd(m,n)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
at least 3 steps
D or E
______ |m-n|

21. Inscribed Angle - Minor Arc
Odd
1
Minor arc = 2(inscribed angle)
22

22. Multiplication principle
1
if a first object may be chosen in m ways and a second object may be chosen in n ways - then there are mn ways of choosing both objects
Exterior angle d is equal to the sum of the two remote interior angles a and b
The probability of event occurring is...

23. 2n - 2n+2 - 2n+4
the probability of event A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
$11 - 025
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Even

24. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
1. Start by writing each number as a product of primes. 2. Write so that each new prime factor begins in the same place. 3. Lowest common multiple is found by multiplying all factors in either list.
3 - 6 - 9 - 12
Even

25. 0! = ?
1st Rule of Probability: Basic Rule is what?
Immediately UNFACTOR or vice versa
1
at least 3 steps

26. Formula for area of a Trapezoid
(sum of bases)(height) / 2
______ |m-n|
p/100 = is/of
Immediately UNFACTOR or vice versa

27. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
always try to factor
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

28. Average Rate: Average A per B
1.7
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(total A) / (total B)
Check each prime number up to the approximate square root of the number. If you haven't found a number less than or equal to the square root of the number - then the number is prime.

29. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Sum of digits is multiple of 3 - last two digits multiple of 4.
16.6%
22
p/100 = is/of

30. 30-60-90 triangle basic lengths of sides
1.7
______ |m-n|
The total amount before any deductions
x(sq. rt 3) - x - 2x

31. How to find all divisors of a number
y2 - y1 / x2 - x1
Find all prime factors
(total distance) / (total time)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

32. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Immediately try factoring/simplifying when possible
Divide 4999 by 15 => 333 integers
P(E)P(F)

33. Sq. rt(2)
1.4
Consider work done in one hour. Inverse of the time it takes everyone working together = Sum of the inverse of the times it would take each person working individually.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
The probability of event occurring is...

34. Some GMAT word problems involve groups with distinct 'either/or' categories (male/female - blue collar/white collar - etc.) The key is to do what with the information? 1. Find total number of possible outcomes. 2. Find the number of desired outcomes.
Sum of digits is multiple of 9
$11 - 025
Organize into a grid.
(x-n(n)y-n)

35. gcd(m,n)*lcm(m,n)
The probability of event A OR B occurring is the probability of event A occurring plus the probability of event B occurring minus the probability of both events occurring. P(A or B) = P(A) +P(B) - P(A and B)
Odd
The amount after deductions
gcd(m,n)*lcm(m,n) = mn

36. 2n+1 - 2n+3 - 2n+5
s Sq. rt (x^r)
Gross Profit = Selling Price - Cost
Odd
1. Start by writing each number as a product of primes. 2. Write so that each new prime factor begins in the same place. 3. Lowest common multiple is found by multiplying all factors in either list.

37. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
p/100 = is/of
3 - 6 - 9 - 12
always try to factor
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

38. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Minor arc = 2(inscribed angle)
Sum of digits is multiple of 3
(sum of bases)(height) / 2

39. Multiples of 3
Sum of digits is multiple of 3
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
3 - 6 - 9 - 12
Odd

40. Lowest Common Multiple 60: 2 x 2 x 3 x 5 - 72: 2 x 2 x 2 x 3 x 3 - LCM: 2 x 2 x 2 x 3 x 3 x 5
(n-1)!
1. Start by writing each number as a product of primes. 2. Write so that each new prime factor begins in the same place. 3. Lowest common multiple is found by multiplying all factors in either list.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
D or E

41. Net
______ |m-n|
180(n-2)
The amount after deductions
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

42. 45-45-90 triangle basic lengths of sides
1. Start by writing each number as a product of primes. 2. Write so that each new prime factor begins in the same place. 3. Lowest common multiple is found by multiplying all factors in either list.
x - x - x(sq. rt 2)
0.15n + 0.08(5) = 0.1(n+5)
Odd

43. Average Rate: Average speed
(total distance) / (total time)
x - x - x(sq. rt 2)
n! / (n - r)!
| A union B| = |A| + |B| - |A intersect B|

44. In general - medium questions require how many steps to solve?
Odd
Minor arc = 2(inscribed angle)
2 steps
(sum of bases)(height) / 2

45. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
347
Last two digits are multiple of 4 or the number can be divided by 2 twice.
the probability of event A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.

46. Sq. rt(3)
Odd numbers only have ___________
3-4-5 - 5-12-13 - 9-12-15
1.7
Number is a multiple of 3 and 2

47. Always try to factor
1 - P(E)
always try to factor
(total distance) / (total time)
if a first object may be chosen in m ways and a second object may be chosen in n ways - then there are mn ways of choosing both objects

48. Combined Events: E or F
P(E) + P(F) - P(E and F)
P(E)P(F)
3 - 6 - 9 - 12
Balancing

49. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
Find simple interest then look for the answer that is a little bigger
n! / (n - r)!
Odd

50. 4th rule of Probability
Principal (1 + interest/number times compounded)^(t)(n)
The probability of event A OR B occurring is the probability of event A occurring plus the probability of event B occurring minus the probability of both events occurring. P(A or B) = P(A) +P(B) - P(A and B)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
x(sq. rt 3) - x - 2x

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GMAT Quantitative General

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