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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. Formula for Mixed Group problems (involving Both/Neither)
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
(total distance) / (total time)
3 - 6 - 9 - 12

2. Formula for area of a Trapezoid
1.7
Figure out the probability for each individual event. Multiply the individual probabilities together.
Any multiplication involving an even number creates an even product.
(sum of bases)(height) / 2

3. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
| A union B| = |A| + |B| - |A intersect B|
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)
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

4. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
Minor arc = 2(inscribed angle)
Divide 4999 by 15 => 333 integers
Sum of digits is multiple of 3 - last two digits multiple of 4.

5. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Principal (1 + interest/number times compounded)^(t)(n)
principle (interest rate - in decimal form) (time - in years)
Group 1 + Group 2 + Neither - Both = Total
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.

6. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
16.6%
Any multiplication involving an even number creates an even product.
The total amount before any deductions

7. 3rd Rule of Probability: Conditional Probability
2 steps
4/3 TT r ^3
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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

8. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
A = P(1 + r) ^n
y2 - y1 / x2 - x1
$11 - 025

9. Always try to factor
gcd(m,n)*lcm(m,n) = mn
1/16
always try to factor
D or E

10. What to do with equations that have fractions
Exterior angle d is equal to the sum of the two remote interior angles a and b
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.
Immediately try factoring/simplifying when possible

11. Properties of 0
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 multiple of 4.
| A union B| = |A| + |B| - |A intersect B|
The amount after deductions

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.
Divide 4999 by 15 => 333 integers
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1st Rule of Probability: Basic Rule is what?
22

13. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
$11 - 025
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.

14. How to check whether number is multiple of 9
Purchase price
Sum of digits is multiple of 9
Exterior angle d is equal to the sum of the two remote interior angles a and b
3-4-5 - 5-12-13 - 9-12-15

15. To determine multiple-event probability where each individual event must occur in a certain way.
(x-n(n)y-n)
Figure out the probability for each individual event. Multiply the individual probabilities together.
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
347

16. Indistinguishable events how to find the number of permutations

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17. 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
P(E)P(F)
22
(# of favorable outcomes) / (# of possible outcomes)

18. Average Rate: Average speed
(total distance) / (total time)
Odd
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.
16.6%

19. 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)
(x-n(n)y-n)
Sum of digits is multiple of 3 - last two digits multiple of 4.
at least 3 steps

20. How to check whether a number is a multiple of 12.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
4/3 TT r ^3
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.
Sum of digits is multiple of 3 - last two digits multiple of 4.

21. Percent Formula
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The amount after deductions
p/100 = is/of
1.4

22. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Find all prime factors
(total distance) / (total time)
P(event NOT occurring) = 1 - P(event occurring)

23. Sq. rt(3)
1.7
14 liters
Find simple interest then look for the answer that is a little bigger
12^3

24. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
347
2 steps
22
The probability of an event occurring plus the probability of the event not occurring = 1

25. 2n+1 - 2n+3 - 2n+5
Odd
$11 - 025
16.6%
Gross Profit = Selling Price - Cost

26. Inscribed Angle - Minor Arc
Gross Profit = Selling Price - Cost
1.7
principle (interest rate - in decimal form) (time - in years)
Minor arc = 2(inscribed angle)

27. Odd and Even rule.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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 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.

28. How to check whether a number is a multiple of 4.
Immediately try factoring/simplifying when possible
p/100 = is/of
1st Rule of Probability: Basic Rule is what?
Last two digits are multiple of 4 or the number can be divided by 2 twice.

29. Dependent events: When are two events said to be dependent events?
Purchase price
n! / (n - r)!
If the outcome of one event affects the outcome of the other event.
0.15n + 0.08(5) = 0.1(n+5)

30. Volume of a sphere
4/3 TT r ^3
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(# of favorable outcomes) / (# of possible outcomes)
(sum of bases)(height) / 2

31. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
always try to factor
(n-1)!
3-4-5 - 5-12-13 - 9-12-15
Exterior angle d is equal to the sum of the two remote interior angles a and b

32. Percent increase = ?
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 3 - last two digits multiple of 4.
(amount of change) / (original amount)
y2 - y1 / x2 - x1

33. What does the Sum of the angles in a Regular Polygon formula look like?
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 9
180(n-2)
(# of favorable outcomes) / (# of possible outcomes)

34. Gross
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 total amount before any deductions
4/3 TT r ^3
(total distance) / (total time)

35. Sum of consecutive numbers
sum = (average)(number of terms)
Principal (1 + interest/number times compounded)^(t)(n)
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.
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

36. 30-60-90 triangle basic lengths of sides
Divide 4999 by 15 => 333 integers
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The amount after deductions
x(sq. rt 3) - x - 2x

37. Average Rate: Average A per B
3-4-5 - 5-12-13 - 9-12-15
(total A) / (total B)
gcd(m,n)*lcm(m,n) = mn
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.

38. 1/6 = what %
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
3 - 6 - 9 - 12
p/100 = is/of
16.6%

39. gcd(m,n)*lcm(m,n)
3 - 6 - 9 - 12
gcd(m,n)*lcm(m,n) = mn
Immediately UNFACTOR or vice versa
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.

40. How to find all divisors of a number
Immediately try factoring/simplifying when possible
Find all prime factors
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
The probability of an event occurring plus the probability of the event not occurring = 1

41. 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
Even
(n-1)!
3-4-5 - 5-12-13 - 9-12-15

42. (1/4)^2
16.6%
1/16
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.
Minor arc = 2(inscribed angle)

43. Combined Events: E and F
(# of favorable outcomes) / (# of possible outcomes)
12^3
1.4
P(E)P(F)

44. In general - medium questions require how many steps to solve?
2 steps
Find all prime factors
at least 3 steps
(amount of change) / (original amount)

45. Gross Profit formula
Gross Profit = Selling Price - Cost
1/16
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.

46. Sq. rt(2)
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.
Immediately try factoring/simplifying when possible
1.4
14 liters

47. 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.
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 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

48. The number of outcomes that result in A divided by the total number of possible outcomes.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The probability of event occurring is...
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.
market value

49. Compound interest rule
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.
Find simple interest then look for the answer that is a little bigger
1.4

50. x^r/s = ?
Immediately UNFACTOR or vice versa
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.
s Sq. rt (x^r)