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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. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
If the outcome of one event affects the outcome of the other event.
2 steps
Organize into a grid.

2. 1/6 = what %
16.6%
principle (interest rate - in decimal form) (time - in years)
-b +- sq. rt(b^2 - 4ac) / 2a
Exterior angle d is equal to the sum of the two remote interior angles a and b

3. 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.
-b +- sq. rt(b^2 - 4ac) / 2a
1.4
Even

4. Average Rate: Average A per B
(total A) / (total B)
Principal (1 + interest/number times compounded)^(t)(n)
x - x - x(sq. rt 2)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

5. Multiples of 3
always try to factor
3 - 6 - 9 - 12
Balancing
1 - P(E)

6. 1/8 = what %
Purchase price
12.5%
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

7. 2nd Rule of Probability: P(E) = 1 - P(not E)
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.
The probability of an event occurring plus the probability of the event not occurring = 1
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
market value

8. Triangle abc with d on the outside with a line. What does d = ?
P(E)P(F)
x - x - x(sq. rt 2)
Exterior angle d is equal to the sum of the two remote interior angles a and b
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.

9. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
22
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.
Purchase price

10. How to find the slope.
y2 - y1 / x2 - x1
12.5%
x(sq. rt 3) - x - 2x
Divide 4999 by 15 => 333 integers

11. 3^3 x 4^3 = ?
12^3
Organize into a grid.
22
Odd numbers only have ___________

12. Compound interest formula
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.
Principal (1 + interest/number times compounded)^(t)(n)
Sum of digits is multiple of 9
Figure out the probability for each individual event. Multiply the individual probabilities together.

13. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
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.
______ |m-n|
always try to factor

14. Combined Events: Not E = P(not E) = ?
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
Odd
-b +- sq. rt(b^2 - 4ac) / 2a

15. Formula for area of a Trapezoid
Group 1 + Group 2 + Neither - Both = Total
Even
Minor arc = 2(inscribed angle)
(sum of bases)(height) / 2

16. Sq. rt(3)
1.7
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Immediately UNFACTOR or vice versa
180(n-2)

17. gcd(m,n)
Balancing
The probability of an event occurring plus the probability of the event not occurring = 1
______ |m-n|
(n-1)!

18. Combined Events: E and F
P(E)P(F)
Immediately try factoring/simplifying when possible
x(sq. rt 3) - x - 2x
A = P(1 + r) ^n

19. Sq. rt(2)
1.4
Odd
P(E)P(F)
Sum of digits is multiple of 3

20. What does the Sum of the angles in a Regular Polygon formula look like?
s Sq. rt (x^r)
180(n-2)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any 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

21. Inscribed Angle - Minor Arc
Number is a multiple of 3 and 2
Minor arc = 2(inscribed angle)
180(n-2)
347

22. The number of ways independent events can occur together.
x - x - x(sq. rt 2)
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 3 - last two digits multiple of 4.
(amount of change) / (original amount)

23. 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.
at least 3 steps
Organize into a grid.
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.
1st Rule of Probability: Basic Rule is what?

24. Set Problems formula
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
1.4
(x-n(n)y-n)

25. To determine multiple-event probability where each individual event must occur in a certain way.
s Sq. rt (x^r)
Figure out the probability for each individual event. Multiply the individual probabilities together.
| A union B| = |A| + |B| - |A intersect B|
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

26. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
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
180(n-2)
Sum of digits is multiple of 3

27. In general - difficult questions require how many steps to solve?
1 - P(E)
Immediately UNFACTOR or vice versa
at least 3 steps
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

28. Odd Factors
Odd numbers only have ___________
(n-1)!
The amount after deductions
(amount of change) / (original amount)

29. (1/4)^2
D or E
1/16
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.
0.15n + 0.08(5) = 0.1(n+5)

30. How to check for a prime number.

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31. Combined Events: E or F
Purchase price
(sum of bases)(height) / 2
Organize into a grid.
P(E) + P(F) - P(E and F)

32. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
P(E)P(F)
Minor arc = 2(inscribed angle)
s Sq. rt (x^r)

33. 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?
Find all prime factors
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)
1/16
0.15n + 0.08(5) = 0.1(n+5)

34. Simple probability
12.5%
Balancing
y2 - y1 / x2 - x1
(# of favorable outcomes) / (# of possible outcomes)

35. Permutations: Order Matters
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
n! / (n - r)!
y2 - y1 / x2 - x1
1.4

36. In general - medium questions require how many steps to solve?
Sum of digits is multiple of 3
2 steps
x(sq. rt 3) - x - 2x
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

37. 0! = ?
Sum of digits is multiple of 3
1
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)
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.

38. gcd(m,n)*lcm(m,n)
180(n-2)
| A union B| = |A| + |B| - |A intersect B|
Balancing
gcd(m,n)*lcm(m,n) = mn

39. Number added or deleted
(x-n(n)y-n)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
y2 - y1 / x2 - x1
Any multiplication involving an even number creates an even product.

40. 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?
D or E
1/16
14 liters
16.6%

41. 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)
1
at least 3 steps
Balancing

42. Quadratic formula
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(n-1)!
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

43. Formula for Mixed Group problems (involving Both/Neither)
(total distance) / (total time)
Sum of digits is multiple of 9
12^3
Group 1 + Group 2 + Neither - Both = Total

44. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
22
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
If the outcome of one event affects the outcome of the other event.

45. How do you multiply roots together.
Sum of digits is multiple of 3
The probability of event occurring is...
sum = (average)(number of terms)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

46. Indistinguishable events how to find the number of permutations

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47. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Sum of digits is multiple of 3
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Group 1 + Group 2 + Neither - Both = Total
12.5%

48. Always try to factor
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
sum = (average)(number of terms)
always try to factor
The probability of an event occurring plus the probability of the event not occurring = 1

49. Gross
The total amount before any deductions
Sum of digits is multiple of 3
x(sq. rt 3) - x - 2x
at least 3 steps

50. 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.
market value
Even
gcd(m,n)*lcm(m,n) = mn