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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. 3^3 x 4^3 = ?
12^3
market value
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

2. 1. A and B < A or B 2. A or B > Individual probabilities of A - B 3. P(A and B) = P(A) x P(B) <-- 'fewer options' 4. P(A or B) = P(A) + P(B) <-- 'more options' - Probability of multiple events rules.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1st Rule of Probability: Basic Rule is what?
Purchase price
gcd(m,n)*lcm(m,n) = mn

3. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
A = P(1 + r) ^n
Immediately try factoring/simplifying when possible
s Sq. rt (x^r)

4. 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.
Balancing
x - x - x(sq. rt 2)
n! / (n - r)!

5. Combined Events: E or F
gcd(m,n)*lcm(m,n) = mn
P(E) + P(F) - P(E and F)
22
(sum of bases)(height) / 2

6. 45-45-90 triangle basic lengths of sides
always try to factor
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
x - x - x(sq. rt 2)
(# of favorable outcomes) / (# of possible outcomes)

7. 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.
Sum of digits is multiple of 9
3 - 6 - 9 - 12
22

8. Probability and Geometry.
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 bases)(height) / 2
market value
83.3%

9. Set Problems formula
Immediately try factoring/simplifying when possible
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
(x-n(n)y-n)
at least 3 steps

10. 2nd Rule of Probability: P(E) = 1 - P(not E)
Minor arc = 2(inscribed angle)
The probability of an event occurring plus the probability of the event not occurring = 1
(amount of change) / (original amount)
sum = (average)(number of terms)

11. To determine the number of integers less than 5000 that are evenly divisible by 15...?
0.15n + 0.08(5) = 0.1(n+5)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately UNFACTOR or vice versa
Divide 4999 by 15 => 333 integers

12. 1/8 = what %
The total amount before any deductions
12.5%
12^3
$11 - 025

13. In general - difficult questions require how many steps to solve?
3-4-5 - 5-12-13 - 9-12-15
D or E
at least 3 steps
(amount of change) / (original amount)

14. 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
Balancing
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
x - x - x(sq. rt 2)
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

15. How to find all divisors of a number
Last two digits are multiple of 4 or the number can be divided by 2 twice.
principle (interest rate - in decimal form) (time - in years)
Find all prime factors
s Sq. rt (x^r)

16. Combined Events: Not E = P(not E) = ?
Sum of digits is multiple of 3
(n-1)!
Sum of digits is multiple of 3 - last two digits multiple of 4.
1 - P(E)

17. Quadratic formula
Sum of digits is multiple of 3
-b +- sq. rt(b^2 - 4ac) / 2a
D or E
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

18. Volume of a sphere
The probability of an event occurring plus the probability of the event not occurring = 1
Gross Profit = Selling Price - Cost
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)
4/3 TT r ^3

19. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Minor arc = 2(inscribed angle)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

20. To determine multiple-event probability where each individual event must occur in a certain way.
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.
Number is a multiple of 3 and 2
y2 - y1 / x2 - x1
Figure out the probability for each individual event. Multiply the individual probabilities together.

21. How do you multiply roots together.
principle (interest rate - in decimal form) (time - in years)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Minor arc = 2(inscribed angle)
Immediately try factoring/simplifying when possible

22. How to check whether a number is a multiple of 12.
Odd numbers only have ___________
Sum of digits is multiple of 3 - last two digits multiple of 4.
1.4
Last two digits are multiple of 4 or the number can be divided by 2 twice.

23. Always try to factor
12.5%
always try to factor
Minor arc = 2(inscribed angle)
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.

24. Percent Formula
Balancing
p/100 = is/of
1
The probability of event occurring is...

25. Sq. rt(3)
347
x - x - x(sq. rt 2)
(n-1)!
1.7

26. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
83.3%
The probability of an event occurring plus the probability of the event not occurring = 1
D or E

27. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
83.3%
Purchase price
Minor arc = 2(inscribed angle)

28. Indistinguishable events how to find the number of permutations

29. How to find the slope.
-b +- sq. rt(b^2 - 4ac) / 2a
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
y2 - y1 / x2 - x1
2 steps

30. (1/4)^2
x - x - x(sq. rt 2)
1/16
-b +- sq. rt(b^2 - 4ac) / 2a
$11 - 025

31. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
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.
(total A) / (total B)
P(event NOT occurring) = 1 - P(event occurring)

32. gcd(m,n)
Divide 4999 by 15 => 333 integers
180(n-2)
-b +- sq. rt(b^2 - 4ac) / 2a
______ |m-n|

33. Prime Factorization to find Greatest Common Factor
(x-n(n)y-n)
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
Immediately try factoring/simplifying when possible
4/3 TT r ^3

34. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Organize into a grid.
Purchase price
D or E

35. 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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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
Organize into a grid.
Balancing

36. How to check whether a number is a multiple of 4.
12^3
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
-b +- sq. rt(b^2 - 4ac) / 2a

37. Sq. rt(2)
12^3
(amount of change) / (original amount)
1.4
x - x - x(sq. rt 2)

38. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
1.4
Sum of digits is multiple of 3
n! / (n - r)!
347

39. In general - medium questions require how many steps to solve?
| A union B| = |A| + |B| - |A intersect B|
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
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
2 steps

40. Gross
(n-1)!
The total amount before any deductions
The probability of an event occurring plus the probability of the event not occurring = 1
The probability of event occurring is...

41. 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
1st Rule of Probability: Basic Rule is what?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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)

42. Price sold for by retailer (after markup)
n! / (n - r)!
market value
sum = (average)(number of terms)
Find all prime factors

43. 1/6 = what %
16.6%
x(sq. rt 3) - x - 2x
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
market value

44. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
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
Any multiplication involving an even number creates an even product.
1.4

45. Trial Problems: look at the probability of NOT 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.
principle (interest rate - in decimal form) (time - in years)
The total amount before any deductions
P(event NOT occurring) = 1 - P(event occurring)

46. Price purchased for by wholesaler
Figure out the probability for each individual event. Multiply the individual probabilities together.
n! / (n - r)!
Purchase price
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

47. gcd(m,n)*lcm(m,n)
Sum of digits is multiple of 3 - last two digits multiple of 4.
gcd(m,n)*lcm(m,n) = mn
1/16
The probability of an event occurring plus the probability of the event not occurring = 1

48. Number added or deleted
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
y2 - y1 / x2 - x1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

49. Compound interest formula
market value
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
14 liters
Principal (1 + interest/number times compounded)^(t)(n)

50. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
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 3
$11 - 025
Odd numbers only have ___________