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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. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
gcd(m,n)*lcm(m,n) = mn
P(E)P(F)
347

2. Quadratic formula
x(sq. rt 3) - x - 2x
-b +- sq. rt(b^2 - 4ac) / 2a
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.
A = P(1 + r) ^n

3. 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.
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.
n! / (n - r)!
0.15n + 0.08(5) = 0.1(n+5)

4. 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
Purchase price
(total distance) / (total time)
-b +- sq. rt(b^2 - 4ac) / 2a

5. gcd(m,n)
(amount of change) / (original amount)
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|
Even

6. Probability and Geometry.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
12^3
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.
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

7. (1/4)^2
1/16
12^3
-b +- sq. rt(b^2 - 4ac) / 2a
D or E

8. How to check whether a number is a multiple of 4.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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)
y2 - y1 / x2 - x1
Figure out the probability for each individual event. Multiply the individual probabilities together.

9. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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.
D or E
The probability of event occurring is...
Find all prime factors

10. Multiplication principle
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
x - x - x(sq. rt 2)
3-4-5 - 5-12-13 - 9-12-15
1/16

11. 2nd Rule of Probability: P(E) = 1 - P(not E)
P(E) + P(F) - P(E and F)
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.
The probability of an event occurring plus the probability of the event not occurring = 1
4/3 TT r ^3

12. How many liters of a solution that is 10% alcohol by volume must be added to 2 liters of a solution that is 50% alcohol by volume to create a solution that is 15% alcohol by volume?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
14 liters
16.6%
x - x - x(sq. rt 2)

13. 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.
(total distance) / (total time)
P(E) + P(F) - P(E and F)
12.5%

14. Odd and Even rule.
always try to factor
principle (interest rate - in decimal form) (time - in years)
Any multiplication involving an even number creates an even product.
(total distance) / (total time)

15. Permutations: Order Matters
(sum of bases)(height) / 2
n! / (n - r)!
4/3 TT r ^3
Figure out the probability for each individual event. Multiply the individual probabilities together.

16. Percent increase = ?
22
(amount of change) / (original amount)
12.5%
x(sq. rt 3) - x - 2x

17. When you see an equation in factored form in a question?
1/16
Immediately UNFACTOR or vice versa
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.
(x-n(n)y-n)

18. Odd Factors
Divide 4999 by 15 => 333 integers
Odd numbers only have ___________
Organize into a grid.
4/3 TT r ^3

19. Sum of consecutive numbers
83.3%
sum = (average)(number of terms)
The amount after deductions
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.

20. How to check whether a number is a multiple of 12.
Odd numbers only have ___________
(total distance) / (total time)
Sum of digits is multiple of 3 - last two digits multiple of 4.
y2 - y1 / x2 - x1

21. 5/6 = what %
83.3%
p/100 = is/of
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)
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.

22. In general - medium questions require how many steps to solve?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
2 steps
Find simple interest then look for the answer that is a little bigger
1.4

23. How do you multiply roots together.
s Sq. rt (x^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)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
-b +- sq. rt(b^2 - 4ac) / 2a

24. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
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
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

25. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
p/100 = is/of
market value
gcd(m,n)*lcm(m,n) = mn

26. Combined Events: E or F
P(E) + P(F) - P(E and F)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
83.3%
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

27. 4th rule of Probability
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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)
22
y2 - y1 / x2 - x1

28. Gross
P(E)P(F)
The total amount before any deductions
always try to factor
(amount of change) / (original amount)

29. 1/6 = what %
Odd
16.6%
1st Rule of Probability: Basic Rule is what?
A = P(1 + r) ^n

30. In general - difficult questions require how many steps to solve?
sum = (average)(number of terms)
Sum of digits is multiple of 3 - last two digits multiple of 4.
at least 3 steps
-b +- sq. rt(b^2 - 4ac) / 2a

31. Properties of 0
12.5%
Sum of digits is multiple of 3 - last two digits multiple of 4.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Any multiplication involving an even number creates an even product.

32. Volume of a sphere
The amount after deductions
The probability of an event occurring plus the probability of the event not occurring = 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
4/3 TT r ^3

33. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
The amount after deductions
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Exterior angle d is equal to the sum of the two remote interior angles a and b

34. 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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Purchase price
1st Rule of Probability: Basic Rule is what?
x - x - x(sq. rt 2)

35. 2n+1 - 2n+3 - 2n+5
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Odd
gcd(m,n)*lcm(m,n) = mn
(sum of bases)(height) / 2

36. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
D or E
22
The amount after deductions
3 - 6 - 9 - 12

37. Percent Formula
P(E) + P(F) - P(E and F)
p/100 = is/of
A = P(1 + r) ^n
principle (interest rate - in decimal form) (time - in years)

38. 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
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
Principal (1 + interest/number times compounded)^(t)(n)
Balancing
The probability of an event occurring plus the probability of the event not occurring = 1

39. Set Problems formula
(amount of change) / (original amount)
3 - 6 - 9 - 12
(x-n(n)y-n)
1/16

40. 1/8 = what %
12.5%
n! / (n - r)!
1 - P(E)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

41. x^r/s = ?
Odd
s Sq. rt (x^r)
14 liters
(total distance) / (total time)

42. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
22
12^3
sum = (average)(number of terms)

43. Average Rate: Average speed
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.
(total distance) / (total time)
4/3 TT r ^3
Sum of digits is multiple of 3

44. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(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.
D or E
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.

45. Simple probability
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Any multiplication involving an even number creates an even product.
(# of favorable outcomes) / (# of possible outcomes)
always try to factor

46. Sq. rt(2)
Exterior angle d is equal to the sum of the two remote interior angles a and b
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)
(amount of change) / (original amount)
1.4

47. 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 probability of an event occurring plus the probability of the event not occurring = 1
$11 - 025
The amount after deductions

48. How to find all divisors of a number
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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
3 - 6 - 9 - 12
Find all prime factors

49. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
Figure out the probability for each individual event. Multiply the individual probabilities together.
(n-1)!
(total A) / (total B)

50. Number added or deleted
Any multiplication involving an even number creates an even product.
n! / (n - r)!
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The total amount before any deductions