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GMAT Quantitative General

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Properties of 0
always try to factor
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
sum = (average)(number of terms)
at least 3 steps

2. 2n - 2n+2 - 2n+4
x - x - x(sq. rt 2)
Even
The total amount before any deductions
-b +- sq. rt(b^2 - 4ac) / 2a

3. Combined Events: E or F
Purchase price
always try to factor
P(E) + P(F) - P(E and F)
at least 3 steps

4. Average Rate: Average speed
(total distance) / (total time)
If the outcome of one event affects the outcome of the other event.
3 - 6 - 9 - 12
4/3 TT r ^3

5. Set Problems formula
1.4
Organize into a grid.
Group 1 + Group 2 + Neither - Both = Total
(x-n(n)y-n)

6. Formula for area of a Trapezoid
1 - P(E)
16.6%
(sum of bases)(height) / 2
always try to factor

7. Intersecting Sets
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
Find all prime factors
Odd
| A union B| = |A| + |B| - |A intersect B|

8. Sq. rt(3)
Sum of digits is multiple of 3
1.7
12.5%
always try to factor

9. 30-60-90 triangle basic lengths of sides
Balancing
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
y2 - y1 / x2 - x1
x(sq. rt 3) - x - 2x

10. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
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
| A union B| = |A| + |B| - |A intersect B|
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

11. Combined Events: E and F
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
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
______ |m-n|
P(E)P(F)

12. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
1/16
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
D or E

13. gcd(m,n)
| A union B| = |A| + |B| - |A intersect B|
Sum of digits is multiple of 3
______ |m-n|
If the outcome of one event affects the outcome of the other event.

14. To determine the number of integers less than 5000 that are evenly divisible by 15...?
1
Principal (1 + interest/number times compounded)^(t)(n)
(sum of bases)(height) / 2
Divide 4999 by 15 => 333 integers

15. The average of consecutive numbers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
market value
83.3%
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.

16. Compound interest formula
Even
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)
Principal (1 + interest/number times compounded)^(t)(n)
principle (interest rate - in decimal form) (time - in years)

17. What does the Sum of the angles in a Regular Polygon formula look like?
1
$11 - 025
Immediately UNFACTOR or vice versa
180(n-2)

18. Volume of a sphere
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Even
4/3 TT r ^3

19. Probability and Geometry.
Immediately try factoring/simplifying when possible
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
Number is a multiple of 3 and 2
Principal (1 + interest/number times compounded)^(t)(n)

20. When you see an equation in factored form in a question?
If the outcome of one event affects the outcome of the other event.
Immediately UNFACTOR or vice versa
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
22

21. Indistinguishable events how to find the number of permutations

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22. What to do with equations that have fractions
sum = (average)(number of terms)
(total distance) / (total time)
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 9

23. Price sold for by retailer (after markup)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Odd
14 liters
market value

24. Gross Profit formula
always try to factor
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Gross Profit = Selling Price - Cost
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

25. Trial Problems: look at the probability of NOT OCCURRING
180(n-2)
n! / (n - r)!
P(event NOT occurring) = 1 - P(event occurring)
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.

26. In general - difficult questions require how many steps to solve?
Odd numbers only have ___________
P(E)P(F)
principle (interest rate - in decimal form) (time - in years)
at least 3 steps

27. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Sum of digits is multiple of 3
1.4
Gross Profit = Selling Price - Cost

28. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Number is a multiple of 3 and 2
sum = (average)(number of terms)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
P(E) + P(F) - P(E and F)

29. gcd(m,n)*lcm(m,n)
P(E)P(F)
3 - 6 - 9 - 12
gcd(m,n)*lcm(m,n) = mn
3-4-5 - 5-12-13 - 9-12-15

30. Multiples of 3
If the outcome of one event affects the outcome of the other event.
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
3 - 6 - 9 - 12
83.3%

31. Quadratic formula
The total amount before any deductions
market value
at least 3 steps
-b +- sq. rt(b^2 - 4ac) / 2a

32. 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
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(n-1)!
347

33. Work problem rule
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Divide 4999 by 15 => 333 integers
P(E)P(F)

34. 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.
Odd
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.
1

35. 4th rule of Probability
Purchase price
(# of favorable outcomes) / (# of possible outcomes)
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)
Gross Profit = Selling Price - Cost

36. 5/6 = what %
(n-1)!
Sum of digits is multiple of 9
83.3%
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

37. Gross
Find all prime factors
4/3 TT r ^3
The total amount before any deductions
at least 3 steps

38. 1/8 = what %
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.
| A union B| = |A| + |B| - |A intersect B|
3 - 6 - 9 - 12
12.5%

39. 45-45-90 triangle basic lengths of sides
Odd numbers only have ___________
x - x - x(sq. rt 2)
12^3
Number is a multiple of 3 and 2

40. The number of ways independent events can occur together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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
347

41. Odd and Even rule.
Odd numbers only have ___________
Figure out the probability for each individual event. Multiply the individual probabilities together.
Find all prime factors
Any multiplication involving an even number creates an even product.

42. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Figure out the probability for each individual event. Multiply the individual probabilities together.
3-4-5 - 5-12-13 - 9-12-15
Organize into a grid.
22

43. Percent increase = ?
The amount after deductions
(amount of change) / (original amount)
Number is a multiple of 3 and 2
Purchase price

44. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
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.
A = P(1 + r) ^n
Number is a multiple of 3 and 2
Organize into a grid.

45. Always try to factor
(# of favorable outcomes) / (# of possible outcomes)
always try to factor
22
1.4

46. 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.
p/100 = is/of
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Organize into a grid.
at least 3 steps

47. How to check for a prime number.

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48. Sq. rt(2)
1.4
D or E
market value
(# of favorable outcomes) / (# of possible outcomes)

49. x^r/s = ?
s Sq. rt (x^r)
at least 3 steps
Find simple interest then look for the answer that is a little bigger
2 steps

50. 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
$11 - 025
x(sq. rt 3) - x - 2x
Balancing
A = P(1 + r) ^n