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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. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
4/3 TT r ^3
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)
Balancing
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

2. Indistinguishable events how to find the number of permutations
(total distance) / (total time)
gcd(m,n)*lcm(m,n) = mn
To find the number of distinct permutations of a set of items with indistinguishable ('repeat') items - divide the factorial of the items in the set by the product of the factorials of the number of indistinguishable elements.
The total amount before any deductions

3. Properties of 0
P(E)P(F)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
2 steps
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

4. To determine the number of integers less than 5000 that are evenly divisible by 15...?
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.
1st Rule of Probability: Basic Rule is what?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Divide 4999 by 15 => 333 integers

5. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Odd numbers only have ___________
12.5%
$11 - 025
| A union B| = |A| + |B| - |A intersect B|

6. Percent Formula
p/100 = is/of
2 steps
The total amount before any deductions
Group 1 + Group 2 + Neither - Both = Total

7. Simple probability
Immediately try factoring/simplifying when possible
(# of favorable outcomes) / (# of possible outcomes)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Odd

8. How do you multiply roots together.
Immediately try factoring/simplifying when possible
Figure out the probability for each individual event. Multiply the individual probabilities together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
3-4-5 - 5-12-13 - 9-12-15

9. To determine multiple-event probability where each individual event must occur in a certain way.
n! / (n - r)!
Figure out the probability for each individual event. Multiply the individual probabilities together.
1st Rule of Probability: Basic Rule is what?
12.5%

10. 4th rule of Probability
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)
s Sq. rt (x^r)
To find the number of distinct permutations of a set of items with indistinguishable ('repeat') items - divide the factorial of the items in the set by the product of the factorials of the number of indistinguishable elements.
D or E

11. Number added or deleted
Divide 4999 by 15 => 333 integers
Sum of digits is multiple of 3 - last two digits multiple of 4.
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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

12. How many liters of a solution that is 15% salt must be added to 5 liters of a solution that is 8% salt so that the resulting mixture is 10% salt?
Exterior angle d is equal to the sum of the two remote interior angles a and b
0.15n + 0.08(5) = 0.1(n+5)
| A union B| = |A| + |B| - |A intersect B|
always try to factor

13. How to check whether number is multiple of 9
1.4
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
Sum of digits is multiple of 9
Minor arc = 2(inscribed angle)

14. 0! = ?
180(n-2)
3-4-5 - 5-12-13 - 9-12-15
| A union B| = |A| + |B| - |A intersect B|
1

15. Sum of consecutive numbers
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)
Organize into a grid.
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
sum = (average)(number of terms)

16. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Any multiplication involving an even number creates an even product.
Number is a multiple of 3 and 2
principle (interest rate - in decimal form) (time - in years)
Immediately UNFACTOR or vice versa

17. Inscribed Angle - Minor Arc
x - x - x(sq. rt 2)
Minor arc = 2(inscribed angle)
1/16
Even

18. Dependent events: When are two events said to be dependent events?
market value
If the outcome of one event affects the outcome of the other event.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Odd

19. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
principle (interest rate - in decimal form) (time - in years)
(n-1)!
1

20. 1/6 = what %
22
Figure out the probability for each individual event. Multiply the individual probabilities together.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
16.6%

21. How to check whether a number is a multiple of 12.
gcd(m,n)*lcm(m,n) = mn
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
Sum of digits is multiple of 3 - last two digits multiple of 4.
The probability of an event occurring plus the probability of the event not occurring = 1

22. 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
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
P(event NOT occurring) = 1 - P(event occurring)

23. Formula for area of a Trapezoid
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Any multiplication involving an even number creates an even product.
(sum of bases)(height) / 2
Gross Profit = Selling Price - Cost

24. Set Problems formula
(x-n(n)y-n)
Odd numbers only have ___________
| A union B| = |A| + |B| - |A intersect B|
The total amount before any deductions

25. 3^3 x 4^3 = ?
12^3
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
n! / (n - r)!
The amount after deductions

26. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
market value
Group 1 + Group 2 + Neither - Both = Total
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
347

27. (1/4)^2
1/16
D or E
Purchase price
(amount of change) / (original amount)

28. Compound interest rule
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)
If the outcome of one event affects the outcome of the other event.
A = P(1 + r) ^n
Find simple interest then look for the answer that is a little bigger

29. Sq. rt(3)
1.4
1.7
Principal (1 + interest/number times compounded)^(t)(n)
always try to factor

30. 3rd Rule of Probability: Conditional Probability
22
(amount of change) / (original amount)
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.
The probability of event occurring is...

31. Triangle abc with d on the outside with a line. What does d = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
Odd
Group 1 + Group 2 + Neither - Both = Total
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.

32. Odd Factors
p/100 = is/of
Organize into a grid.
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
Odd numbers only have ___________

33. 2n+1 - 2n+3 - 2n+5
16.6%
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1.4
Odd

34. The number of ways independent events can occur together.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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.
(n-1)!

35. Percent increase = ?
(total distance) / (total time)
(amount of change) / (original amount)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
n! / (n - r)!

36. 30-60-90 triangle basic lengths of sides
(amount of change) / (original amount)
principle (interest rate - in decimal form) (time - in years)
x(sq. rt 3) - x - 2x
Purchase price

37. Multiplication principle
(total A) / (total B)
1
gcd(m,n)*lcm(m,n) = mn
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

38. Multiples of 3
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
P(E) + P(F) - P(E and F)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
3 - 6 - 9 - 12

39. Sq. rt(2)
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
1.4
12.5%
$11 - 025

40. 2n - 2n+2 - 2n+4
12^3
1.7
Number is a multiple of 3 and 2
Even

41. In general - difficult questions require how many steps to solve?
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
347
at least 3 steps
(amount of change) / (original amount)

42. Combined Events: E and F
Sum of digits is multiple of 9
16.6%
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.
P(E)P(F)

43. Probability and Geometry.
1st Rule of Probability: Basic Rule is what?
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
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
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

44. Permutations: Order Matters
n! / (n - r)!
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)
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
2 steps

45. How to find the slope.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(E) + P(F) - P(E and F)
The probability of an event occurring plus the probability of the event not occurring = 1
y2 - y1 / x2 - x1

46. Combined Events: E or F
1.7
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
Immediately try factoring/simplifying when possible
P(E) + P(F) - P(E and F)

47. When you see an equation in factored form in a question?
gcd(m,n)*lcm(m,n) = mn
Immediately UNFACTOR or vice versa
Sum of digits is multiple of 9
Gross Profit = Selling Price - Cost

48. Trial Problems: look at the probability of NOT OCCURRING
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.
14 liters
P(event NOT occurring) = 1 - P(event occurring)
Find all prime factors

49. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
Odd
The probability of event occurring is...
D or E

50. Quadratic formula
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)
Odd numbers only have ___________
-b +- sq. rt(b^2 - 4ac) / 2a

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