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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. 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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The probability of event occurring is...
Balancing
The total amount before any deductions

2. 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
83.3%
| A union B| = |A| + |B| - |A intersect B|
4/3 TT r ^3

3. To determine multiple-event probability where each individual event must occur in a certain way.
(x-n(n)y-n)
Find simple interest then look for the answer that is a little bigger
Figure out the probability for each individual event. Multiply the individual probabilities together.
x(sq. rt 3) - x - 2x

4. Sq. rt(2)
market value
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.
1.4
12^3

5. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
12.5%
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Any multiplication involving an even number creates an even product.
Find all prime factors

6. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
| A union B| = |A| + |B| - |A intersect B|
-b +- sq. rt(b^2 - 4ac) / 2a
12^3

7. 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.
| A union B| = |A| + |B| - |A intersect B|
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The probability of an event occurring plus the probability of the event not occurring = 1
1st Rule of Probability: Basic Rule is what?

8. gcd(m,n)*lcm(m,n)
Sum of digits is multiple of 9
1/16
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
gcd(m,n)*lcm(m,n) = mn

9. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
16.6%
Minor arc = 2(inscribed angle)
4/3 TT r ^3

10. 2n - 2n+2 - 2n+4
Even
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.
Odd
n! / (n - r)!

11. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
12.5%
| 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

12. How to find all divisors of a number
Sum of digits is multiple of 9
Find all prime factors
1 - P(E)
(total distance) / (total time)

13. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Exterior angle d is equal to the sum of the two remote interior angles a and b
347
Sum of digits is multiple of 9
The total amount before any deductions

14. Sum of consecutive numbers
sum = (average)(number of terms)
p/100 = is/of
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 numbers only have ___________

15. 2nd Rule of Probability: P(E) = 1 - P(not E)
Sum of digits is multiple of 3 - last two digits multiple of 4.
The probability of an event occurring plus the probability of the event not occurring = 1
3-4-5 - 5-12-13 - 9-12-15
Last two digits are multiple of 4 or the number can be divided by 2 twice.

16. x^r/s = ?
Divide 4999 by 15 => 333 integers
at least 3 steps
347
s Sq. rt (x^r)

17. Combined Events: Not E = P(not E) = ?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(# of favorable outcomes) / (# of possible outcomes)
x - x - x(sq. rt 2)
1 - P(E)

18. Formula for Mixed Group problems (involving Both/Neither)
P(E) + P(F) - P(E and F)
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.
Group 1 + Group 2 + Neither - Both = Total

19. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
(total A) / (total B)
$11 - 025
sum = (average)(number of terms)
Balancing

20. Odd and Even rule.
Any multiplication involving an even number creates an even product.
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 = (average)(number of terms)
(total distance) / (total time)

21. 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
Sum of digits is multiple of 3
P(E)P(F)
3-4-5 - 5-12-13 - 9-12-15

22. 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?
Balancing
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.
1.4
0.15n + 0.08(5) = 0.1(n+5)

23. The number of ways independent events can occur together.
p/100 = is/of
P(E)P(F)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Balancing

24. In general - medium questions require how many steps to solve?
Number is a multiple of 3 and 2
Group 1 + Group 2 + Neither - Both = Total
2 steps
Figure out the probability for each individual event. Multiply the individual probabilities together.

25. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
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.
principle (interest rate - in decimal form) (time - in years)
(n-1)!
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

26. How to check whether a number is a multiple of 4.
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
Balancing
Last two digits are multiple of 4 or the number can be divided by 2 twice.
2 steps

27. Gross
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
The total amount before any deductions
If the outcome of one event affects the outcome of the other event.
(total A) / (total B)

28. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(total distance) / (total time)
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
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)

29. 3^3 x 4^3 = ?
y2 - y1 / x2 - x1
12^3
$11 - 025
Last two digits are multiple of 4 or the number can be divided by 2 twice.

30. (1/4)^2
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
s Sq. rt (x^r)
-b +- sq. rt(b^2 - 4ac) / 2a
1/16

31. 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.
Organize into a grid.
Figure out the probability for each individual event. Multiply the individual probabilities together.
p/100 = is/of

32. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Group 1 + Group 2 + Neither - Both = Total
A = P(1 + r) ^n
(n-1)!
x(sq. rt 3) - x - 2x

33. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Find all prime factors
D or E
Principal (1 + interest/number times compounded)^(t)(n)
1 - P(E)

34. 1/6 = what %
14 liters
4/3 TT r ^3
Organize into a grid.
16.6%

35. Set Problems formula
Odd numbers only have ___________
Any multiplication involving an even number creates an even product.
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-n(n)y-n)

36. Percent increase = ?
x(sq. rt 3) - x - 2x
Divide 4999 by 15 => 333 integers
(amount of change) / (original amount)
(n-1)!

37. gcd(m,n)
The probability of event occurring is...
-b +- sq. rt(b^2 - 4ac) / 2a
______ |m-n|
4/3 TT r ^3

38. Volume of a sphere
14 liters
4/3 TT r ^3
A = P(1 + r) ^n
3-4-5 - 5-12-13 - 9-12-15

39. 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
D or E
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

40. What to do with equations that have fractions
0.15n + 0.08(5) = 0.1(n+5)
(total A) / (total B)
______ |m-n|
Immediately try factoring/simplifying when possible

41. The number of outcomes that result in A divided by the total number of possible outcomes.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Even
Balancing
The probability of event occurring is...

42. Always try to factor
always try to factor
1.4
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
P(E)P(F)

43. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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 = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

44. Net
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
principle (interest rate - in decimal form) (time - in years)
The amount after deductions

45. 1/8 = what %
Balancing
at least 3 steps
12.5%
Principal (1 + interest/number times compounded)^(t)(n)

46. Quadratic formula
market value
3 - 6 - 9 - 12
______ |m-n|
-b +- sq. rt(b^2 - 4ac) / 2a

47. 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
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.
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.
A = P(1 + r) ^n

48. Average Rate: Average A per B
y2 - y1 / x2 - x1
Number is a multiple of 3 and 2
22
(total A) / (total B)

49. How to check whether a number is a multiple of 12.
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.

50. How to check for a prime number.

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