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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. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
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
(# of favorable outcomes) / (# of possible outcomes)
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

2. To determine the number of integers less than 5000 that are evenly divisible by 15...?
x - x - x(sq. rt 2)
Divide 4999 by 15 => 333 integers
-b +- sq. rt(b^2 - 4ac) / 2a
1/16

3. The average of consecutive numbers
p/100 = is/of
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
3 - 6 - 9 - 12
always try to factor

4. gcd(m,n)*lcm(m,n)
Group 1 + Group 2 + Neither - Both = Total
gcd(m,n)*lcm(m,n) = mn
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.

5. 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?
0.15n + 0.08(5) = 0.1(n+5)
Find simple interest then look for the answer that is a little bigger
1.4
1/16

6. Prime Factorization to find Greatest Common Factor
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(amount of change) / (original amount)
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

7. How to check whether a number is a multiple of 3.
Minor arc = 2(inscribed angle)
Sum of digits is multiple of 3
2 steps
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)

8. 4th rule of Probability
Divide 4999 by 15 => 333 integers
D or E
y2 - y1 / x2 - x1
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)

9. How do you multiply roots together.
| A union B| = |A| + |B| - |A intersect B|
Organize into a grid.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
P(event NOT occurring) = 1 - P(event occurring)

10. Set Problems formula
(x-n(n)y-n)
A = P(1 + r) ^n
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
-b +- sq. rt(b^2 - 4ac) / 2a

11. Dependent events: When are two events said to be dependent events?
Sum of digits is multiple of 3 - last two digits multiple of 4.
Odd numbers only have ___________
If the outcome of one event affects the outcome of the other event.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

12. 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.
3-4-5 - 5-12-13 - 9-12-15
1st Rule of Probability: Basic Rule is what?
Any multiplication involving an even number creates an even product.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

13. 3rd Rule of Probability: Conditional Probability
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. 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 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.
(amount of change) / (original amount)

14. 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?
(sum of bases)(height) / 2
1.4
14 liters
Immediately UNFACTOR or vice versa

15. How to find all divisors of a number
1/16
Find all prime factors
4/3 TT r ^3
3 - 6 - 9 - 12

16. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
Number is a multiple of 3 and 2
The probability of event occurring is...
______ |m-n|

17. Quadratic formula
Organize into a grid.
Number is a multiple of 3 and 2
22
-b +- sq. rt(b^2 - 4ac) / 2a

18. Inscribed Angle - Minor Arc
$11 - 025
(amount of change) / (original amount)
Minor arc = 2(inscribed angle)
12^3

19. How to check for a prime number.

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20. 2n - 2n+2 - 2n+4
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
83.3%
Even
Odd

21. How to check whether a number is a multiple of 6
y2 - y1 / x2 - x1
180(n-2)
-b +- sq. rt(b^2 - 4ac) / 2a
Number is a multiple of 3 and 2

22. Combined Events: Not E = P(not E) = ?
1 - P(E)
Gross Profit = Selling Price - Cost
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.
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

23. Three triangle length patterns
sum = (average)(number of terms)
3-4-5 - 5-12-13 - 9-12-15
(total A) / (total 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

24. Odd and Even rule.
Any multiplication involving an even number creates an even product.
1st Rule of Probability: Basic Rule is what?
$11 - 025
Sum of digits is multiple of 9

25. Net
Number is a multiple of 3 and 2
The amount after deductions
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)

26. Combined Events: E and F
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Sum of digits is multiple of 9
Group 1 + Group 2 + Neither - Both = Total
P(E)P(F)

27. Compound interest rule
16.6%
Last two digits are multiple of 4 or the number can be divided by 2 twice.
y2 - y1 / x2 - x1
Find simple interest then look for the answer that is a little bigger

28. The number of ways independent events can occur together.
at least 3 steps
sum = (average)(number of terms)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
4/3 TT r ^3

29. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
market value
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)
P(E)P(F)

30. Sum of consecutive numbers
x(sq. rt 3) - x - 2x
sum = (average)(number of terms)
3 - 6 - 9 - 12
(total distance) / (total time)

31. Price sold for by retailer (after markup)
16.6%
Any multiplication involving an even number creates an even product.
market value
Even

32. 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 occurring is...
P(E) + P(F) - P(E and F)
347

33. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
If the outcome of one event affects the outcome of the other event.
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.
3 - 6 - 9 - 12

34. 3^3 x 4^3 = ?
12^3
Any multiplication involving an even number creates an even product.
4/3 TT r ^3
s Sq. rt (x^r)

35. To determine multiple-event probability where each individual event must occur in a certain way.
83.3%
Figure out the probability for each individual event. Multiply the individual probabilities together.
180(n-2)
3 - 6 - 9 - 12

36. Probability and Geometry.
The amount after deductions
83.3%
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)

37. Compound interest formula
(# of favorable outcomes) / (# of possible outcomes)
Principal (1 + interest/number times compounded)^(t)(n)
s Sq. rt (x^r)
Organize into a grid.

38. How to find the slope.
The probability of an event occurring plus the probability of the event not occurring = 1
x(sq. rt 3) - x - 2x
y2 - y1 / x2 - x1
Sum of digits is multiple of 9

39. Sq. rt(2)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1.4
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.
-b +- sq. rt(b^2 - 4ac) / 2a

40. (1/4)^2
-b +- sq. rt(b^2 - 4ac) / 2a
| A union B| = |A| + |B| - |A intersect B|
Balancing
1/16

41. Properties of 0
Figure out the probability for each individual event. Multiply the individual probabilities together.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
347
(n-1)!

42. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
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
s Sq. rt (x^r)

43. Sq. rt(3)
1.7
(n-1)!
1.4
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

44. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Sum of digits is multiple of 9
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1

45. How to check whether number is multiple of 9
n! / (n - r)!
Sum of digits is multiple of 9
The probability of an event occurring plus the probability of the event not occurring = 1
Figure out the probability for each individual event. Multiply the individual probabilities together.

46. Indistinguishable events how to find the number of permutations

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47. Odd Factors
Odd numbers only have ___________
12.5%
______ |m-n|
Figure out the probability for each individual event. Multiply the individual probabilities together.

48. Always try to factor
p/100 = is/of
P(E)P(F)
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
always try to factor

49. 0! = ?
1
Minor arc = 2(inscribed angle)
Figure out the probability for each individual event. Multiply the individual probabilities together.
Odd numbers only have ___________

50. Average Rate: Average speed
180(n-2)
1 - P(E)
(total distance) / (total time)
market value