Test your basic knowledge |

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. Average Rate: Average speed
Figure out the probability for each individual event. Multiply the individual probabilities together.
(total distance) / (total time)
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
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.

2. Formula for area of a Trapezoid
Odd
(sum of bases)(height) / 2
3-4-5 - 5-12-13 - 9-12-15
y2 - y1 / x2 - x1

3. Formula for Mixed Group problems (involving Both/Neither)
1.7
Group 1 + Group 2 + Neither - Both = Total
3 - 6 - 9 - 12
P(event NOT occurring) = 1 - P(event occurring)

4. Triangle abc with d on the outside with a line. What does d = ?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Gross Profit = Selling Price - Cost
4/3 TT r ^3
Exterior angle d is equal to the sum of the two remote interior angles a and b

5. 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.
3 - 6 - 9 - 12
1 - P(E)
Exterior angle d is equal to the sum of the two remote interior angles a and b

6. Trial Problems: look at the probability of NOT OCCURRING
1.4
Odd
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.
P(event NOT occurring) = 1 - P(event occurring)

7. Prime Factorization to find Greatest Common Factor
1 - P(E)
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 amount after deductions
Immediately UNFACTOR or vice versa

8. 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.
Find all prime factors
principle (interest rate - in decimal form) (time - in years)
always try to factor

9. 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
1.4
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.
Find simple interest then look for the answer that is a little bigger
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.

10. Probability and Geometry.
y2 - y1 / x2 - x1
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
12^3
347

11. Gross Profit formula
(# of favorable outcomes) / (# of possible outcomes)
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.
Gross Profit = Selling Price - Cost
sum = (average)(number of terms)

12. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Organize into a grid.
The probability of an event occurring plus the probability of the event not occurring = 1
P(event NOT occurring) = 1 - P(event occurring)
principle (interest rate - in decimal form) (time - in years)

13. Percent Formula
3 - 6 - 9 - 12
Any multiplication involving an even number creates an even product.
y2 - y1 / x2 - x1
p/100 = is/of

14. Gross
Exterior angle d is equal to the sum of the two remote interior angles a and b
The total amount before any deductions
| A union B| = |A| + |B| - |A intersect B|
sum = (average)(number of terms)

15. 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
Balancing
2 steps
0.15n + 0.08(5) = 0.1(n+5)

16. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
2 steps
D or E
| A union B| = |A| + |B| - |A intersect B|
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

17. What does the Sum of the angles in a Regular Polygon formula look like?
Find simple interest then look for the answer that is a little bigger
180(n-2)
Immediately UNFACTOR or vice versa
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.

18. 3rd Rule of Probability: Conditional Probability
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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Balancing
1/16

19. 0! = ?
(amount of change) / (original amount)
1
The probability of an event occurring plus the probability of the event not occurring = 1
s Sq. rt (x^r)

20. How to check whether a number is a multiple of 12.
$11 - 025
y2 - y1 / x2 - x1
Sum of digits is multiple of 3 - last two digits multiple of 4.
2 steps

21. How to find the slope.
83.3%
Principal (1 + interest/number times compounded)^(t)(n)
y2 - y1 / x2 - x1
Immediately UNFACTOR or vice versa

22. Net
The amount after deductions
Figure out the probability for each individual event. Multiply the individual probabilities together.
4/3 TT r ^3
16.6%

23. Multiplication principle
The probability of event occurring is...
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.
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
Group 1 + Group 2 + Neither - Both = Total

24. 2nd Rule of Probability: P(E) = 1 - P(not E)
1
(# of favorable outcomes) / (# of possible outcomes)
22
The probability of an event occurring plus the probability of the event not occurring = 1

25. 2n - 2n+2 - 2n+4
22
p/100 = is/of
The probability of an event occurring plus the probability of the event not occurring = 1
Even

26. Properties of 0
3 - 6 - 9 - 12
(total A) / (total B)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
gcd(m,n)*lcm(m,n) = mn

27. Sum of consecutive numbers
gcd(m,n)*lcm(m,n) = mn
______ |m-n|
Even
sum = (average)(number of terms)

28. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
(n-1)!
(amount of change) / (original amount)
Number is a multiple of 3 and 2

29. Combined Events: E or F
sum = (average)(number of terms)
P(E) + P(F) - P(E and F)
P(event NOT occurring) = 1 - P(event occurring)
1

30. 1/8 = what %
4/3 TT r ^3
12.5%
(n-1)!
If the outcome of one event affects the outcome of the other event.

31. How to check whether a number is a multiple of 4.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 3
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The probability of event occurring is...

32. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
The amount after deductions
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)
principle (interest rate - in decimal form) (time - in years)
A = P(1 + r) ^n

33. Multiples of 3
n! / (n - r)!
The probability of an event occurring plus the probability of the event not occurring = 1
Exterior angle d is equal to the sum of the two remote interior angles a and b
3 - 6 - 9 - 12

34. Volume of a sphere
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
4/3 TT r ^3
at least 3 steps

35. How to check for a prime number.

36. Quadratic formula
347
16.6%
-b +- sq. rt(b^2 - 4ac) / 2a
principle (interest rate - in decimal form) (time - in years)

37. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
x - x - x(sq. rt 2)
347
$11 - 025
16.6%

38. Dependent events: When are two events said to be dependent events?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
16.6%
12^3
If the outcome of one event affects the outcome of the other event.

39. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
-b +- sq. rt(b^2 - 4ac) / 2a
If the outcome of one event affects the outcome of the other event.
______ |m-n|

40. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 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.
x - x - x(sq. rt 2)
P(E) + P(F) - P(E and F)

41. Odd Factors
Odd numbers only have ___________
(x-n(n)y-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.
The probability of event occurring is...

42. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Purchase price
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.

43. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
at least 3 steps
n! / (n - r)!
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
12^3

44. Odd and Even 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.
Any multiplication involving an even number creates an even product.
______ |m-n|
Divide 4999 by 15 => 333 integers

45. Average Rate: Average A per B
Group 1 + Group 2 + Neither - Both = Total
1
(n-1)!
(total A) / (total B)

46. 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)
If the outcome of one event affects the outcome of the other event.
14 liters
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

47. 45-45-90 triangle basic lengths of sides
always try to factor
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.
x - x - x(sq. rt 2)
180(n-2)

48. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Gross Profit = Selling Price - Cost
22
Group 1 + Group 2 + Neither - Both = Total

49. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
22
D or E
16.6%

50. How to check whether a number is a multiple of 6
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
at least 3 steps
Number is a multiple of 3 and 2
1.7