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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. Average Rate: Average A per B
1.7
(total A) / (total B)
22
3 - 6 - 9 - 12

2. 2n - 2n+2 - 2n+4
(# of favorable outcomes) / (# of possible outcomes)
Even
Sum of digits is multiple of 9
y2 - y1 / x2 - x1

3. Combined Events: E and F
P(E)P(F)
The amount after deductions
Sum of digits is multiple of 3
180(n-2)

4. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
| A union B| = |A| + |B| - |A intersect B|
14 liters
$11 - 025

5. How to find the slope.
The probability of an event occurring plus the probability of the event not occurring = 1
Minor arc = 2(inscribed angle)
Exterior angle d is equal to the sum of the two remote interior angles a and b
y2 - y1 / x2 - x1

6. Multiples of 3
3 - 6 - 9 - 12
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
Immediately try factoring/simplifying when possible
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

7. Set Problems formula
347
(x-n(n)y-n)
(sum of bases)(height) / 2
0.15n + 0.08(5) = 0.1(n+5)

8. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
The probability of event occurring is...
1.4
Gross Profit = Selling Price - Cost

9. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(event NOT occurring) = 1 - P(event occurring)
A = P(1 + r) ^n
Exterior angle d is equal to the sum of the two remote interior angles a and b

10. Net
______ |m-n|
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 amount after deductions
Immediately UNFACTOR or vice versa

11. Prime Factorization to find Greatest Common Factor
n! / (n - r)!
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
The probability of an event occurring plus the probability of the event not occurring = 1

12. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
principle (interest rate - in decimal form) (time - in years)
347
Exterior angle d is equal to the sum of the two remote interior angles a and b
sum = (average)(number of terms)

13. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Even
Sum of digits is multiple of 3
22
1.4

14. How to check for a prime number.

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15. Work problem rule
(x-n(n)y-n)
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.
gcd(m,n)*lcm(m,n) = mn
P(E) + P(F) - P(E and F)

16. 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?
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
14 liters
Any multiplication involving an even number creates an even product.
market value

17. 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.
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
Odd
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

18. How do you multiply roots together.
347
Divide 4999 by 15 => 333 integers
1.4
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

19. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
sum = (average)(number of terms)
Group 1 + Group 2 + Neither - Both = Total
principle (interest rate - in decimal form) (time - in years)

20. Compound interest rule
Find simple interest then look for the answer that is a little bigger
Sum of digits is multiple of 9
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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

21. 3rd Rule of Probability: Conditional Probability
The probability of an event occurring plus the probability of the event not occurring = 1
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 event A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
3 - 6 - 9 - 12

22. 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.
Organize into a grid.
1st Rule of Probability: Basic Rule is what?
Group 1 + Group 2 + Neither - Both = Total
Immediately UNFACTOR or vice versa

23. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
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.
x(sq. rt 3) - x - 2x

24. Odd Factors
(# 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
Odd numbers only have ___________
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

25. gcd(m,n)*lcm(m,n)
(n-1)!
1/16
gcd(m,n)*lcm(m,n) = mn
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

26. Dependent events: When are two events said to be dependent events?
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.
4/3 TT r ^3
Minor arc = 2(inscribed angle)

27. Number added or deleted
180(n-2)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Sum of digits is multiple of 3

28. Odd and Even rule.
1/16
Odd
Find simple interest then look for the answer that is a little bigger
Any multiplication involving an even number creates an even product.

29. Sq. rt(3)
3-4-5 - 5-12-13 - 9-12-15
s Sq. rt (x^r)
Figure out the probability for each individual event. Multiply the individual probabilities together.
1.7

30. 1/6 = what %
16.6%
sum = (average)(number of terms)
Balancing
(total distance) / (total time)

31. Indistinguishable events how to find the number of permutations

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32. The number of ways independent events can occur together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
always try to factor
s Sq. rt (x^r)
The total amount before any deductions

33. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
If the outcome of one event affects the outcome of the other event.
12^3
sum = (average)(number of terms)

34. Some GMAT word problems involve groups with distinct 'either/or' categories (male/female - blue collar/white collar - etc.) The key is to do what with the information? 1. Find total number of possible outcomes. 2. Find the number of desired outcomes.
14 liters
0.15n + 0.08(5) = 0.1(n+5)
market value
Organize into a grid.

35. To determine multiple-event probability where each individual event must occur in a certain way.
Divide 4999 by 15 => 333 integers
1.7
4/3 TT r ^3
Figure out the probability for each individual event. Multiply the individual probabilities together.

36. Combined Events: Not E = P(not E) = ?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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
16.6%
1 - P(E)

37. Combined Events: E or F
Gross Profit = Selling Price - Cost
A = P(1 + r) ^n
P(E) + P(F) - P(E and F)
22

38. 30-60-90 triangle basic lengths of sides
1.7
x(sq. rt 3) - x - 2x
Sum of digits is multiple of 9
2 steps

39. Formula for Mixed Group problems (involving Both/Neither)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1.4
12^3
Group 1 + Group 2 + Neither - Both = Total

40. Always try to factor
22
Any multiplication involving an even number creates an even product.
(total distance) / (total time)
always try to factor

41. 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
______ |m-n|
Minor arc = 2(inscribed angle)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.

42. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
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
If the outcome of one event affects the outcome of the other event.
$11 - 025

43. How to check whether a number is a multiple of 3.
83.3%
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
180(n-2)
Sum of digits is multiple of 3

44. Percent increase = ?
Sum of digits is multiple of 3 - last two digits multiple of 4.
(amount of change) / (original amount)
n! / (n - r)!
Even

45. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
3-4-5 - 5-12-13 - 9-12-15
22
______ |m-n|

46. 3^3 x 4^3 = ?
12^3
2 steps
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
$11 - 025

47. How to check whether number is multiple of 9
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1/16
Sum of digits is multiple of 9
0.15n + 0.08(5) = 0.1(n+5)

48. Three triangle length patterns
(sum of bases)(height) / 2
Organize into a grid.
3-4-5 - 5-12-13 - 9-12-15
Sum of digits is multiple of 3

49. Multiplication principle
Gross Profit = Selling Price - Cost
n! / (n - r)!
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
Organize into a grid.

50. 4th rule of Probability
1.7
12^3
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)
(total A) / (total B)