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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
1.4
y2 - y1 / x2 - x1
Balancing
D or E

2. Price purchased for by wholesaler
Purchase price
1.4
Any multiplication involving an even number creates an even product.
3-4-5 - 5-12-13 - 9-12-15

3. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
4/3 TT r ^3
The total amount before any deductions
Find simple interest then look for the answer that is a little bigger
principle (interest rate - in decimal form) (time - in years)

4. Prime Factorization to find Greatest Common Factor
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
12^3
0.15n + 0.08(5) = 0.1(n+5)
x - x - x(sq. rt 2)

5. How to check for a prime number.

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6. Sum of consecutive numbers
______ |m-n|
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)
sum = (average)(number of terms)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

7. Combined Events: Not E = P(not E) = ?
Balancing
1 - P(E)
1/16
The probability of an event occurring plus the probability of the event not occurring = 1

8. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
(total distance) / (total time)
A = P(1 + r) ^n
22
(amount of change) / (original amount)

9. 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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Find all prime factors
The amount after deductions
Organize into a grid.

10. Triangle abc with d on the outside with a line. What does d = ?
Immediately UNFACTOR or vice versa
22
Exterior angle d is equal to the sum of the two remote interior angles a and b
x(sq. rt 3) - x - 2x

11. How to check whether a number is a multiple of 3.
x - x - x(sq. rt 2)
Immediately UNFACTOR or vice versa
Sum of digits is multiple of 3
3 - 6 - 9 - 12

12. Properties of 0
Group 1 + Group 2 + Neither - Both = Total
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
y2 - y1 / x2 - x1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

13. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
1.7
Organize into a grid.
14 liters

14. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
-b +- sq. rt(b^2 - 4ac) / 2a
3 - 6 - 9 - 12
(n-1)!
Any multiplication involving an even number creates an even product.

15. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
1
Even
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.

16. Probability and Geometry.
14 liters
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
Any multiplication involving an even number creates an even product.
market value

17. Percent Formula
The total amount before any deductions
P(event NOT occurring) = 1 - P(event occurring)
p/100 = is/of
at least 3 steps

18. 2nd Rule of Probability: P(E) = 1 - P(not E)
12^3
Find all prime factors
The probability of an event occurring plus the probability of the event not occurring = 1
3 - 6 - 9 - 12

19. Always try to factor
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
always try to factor
Exterior angle d is equal to the sum of the two remote interior angles a and b
(sum of bases)(height) / 2

20. Work problem rule
P(E) + P(F) - P(E and F)
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.
(# of favorable outcomes) / (# of possible outcomes)
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.

21. 30-60-90 triangle basic lengths of sides
Odd numbers only have ___________
Figure out the probability for each individual event. Multiply the individual probabilities together.
x(sq. rt 3) - x - 2x
(total distance) / (total time)

22. Combined Events: E and F
Figure out the probability for each individual event. Multiply the individual probabilities together.
Immediately UNFACTOR or vice versa
Number is a multiple of 3 and 2
P(E)P(F)

23. Gross Profit formula
Gross Profit = Selling Price - Cost
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
22
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)

24. How to check whether number is multiple of 9
P(E) + P(F) - P(E and F)
Sum of digits is multiple of 9
0.15n + 0.08(5) = 0.1(n+5)
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.

25. Combined Events: E or F
22
P(E) + P(F) - P(E and F)
Balancing
sum = (average)(number of terms)

26. 2n+1 - 2n+3 - 2n+5
Odd
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(x-n(n)y-n)
12^3

27. To determine the number of integers less than 5000 that are evenly divisible by 15...?
1
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)
Divide 4999 by 15 => 333 integers

28. Formula for Mixed Group problems (involving Both/Neither)
sum = (average)(number of terms)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Group 1 + Group 2 + Neither - Both = Total
market value

29. 5/6 = what %
Exterior angle d is equal to the sum of the two remote interior angles a and b
83.3%
(n-1)!
n! / (n - r)!

30. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
22
1.4
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.

31. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
market value
Organize into a grid.
(amount of change) / (original amount)

32. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
83.3%
at least 3 steps
principle (interest rate - in decimal form) (time - in years)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

33. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1.7
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
347

34. 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?
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
14 liters
always try to factor
sum = (average)(number of terms)

35. How to find all divisors of a number
n! / (n - r)!
Number is a multiple of 3 and 2
principle (interest rate - in decimal form) (time - in years)
Find all prime factors

36. Multiples of 3
3 - 6 - 9 - 12
Balancing
1 - P(E)
Odd numbers only have ___________

37. Gross
Sum of digits is multiple of 3 - last two digits multiple of 4.
Gross Profit = Selling Price - Cost
x(sq. rt 3) - x - 2x
The total amount before any deductions

38. When you see an equation in factored form in a question?
1
If the outcome of one event affects the outcome of the other event.
______ |m-n|
Immediately UNFACTOR or vice versa

39. gcd(m,n)*lcm(m,n)
83.3%
gcd(m,n)*lcm(m,n) = mn
Minor arc = 2(inscribed angle)
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.

40. How do you multiply roots together.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(n-1)!

41. Inscribed Angle - Minor Arc
x(sq. rt 3) - x - 2x
Minor arc = 2(inscribed angle)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

42. The number of outcomes that result in A divided by the total number of possible outcomes.
Any multiplication involving an even number creates an even product.
The probability of event occurring is...
1/16
Immediately UNFACTOR or vice versa

43. Multiplication principle
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
P(E) + P(F) - P(E and F)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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

44. Dependent events: When are two events said to be dependent events?
p/100 = is/of
market value
347
If the outcome of one event affects the outcome of the other event.

45. The number of ways independent events can occur together.
2 steps
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.
principle (interest rate - in decimal form) (time - in years)

46. How to find the slope.
12^3
y2 - y1 / x2 - x1
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

47. Odd and Even rule.
1.4
(total distance) / (total time)
-b +- sq. rt(b^2 - 4ac) / 2a
Any multiplication involving an even number creates an even product.

48. Quadratic formula
gcd(m,n)*lcm(m,n) = mn
Principal (1 + interest/number times compounded)^(t)(n)
12^3
-b +- sq. rt(b^2 - 4ac) / 2a

49. Price sold for by retailer (after markup)
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 distance) / (total time)
-b +- sq. rt(b^2 - 4ac) / 2a
market value

50. Odd Factors
Odd numbers only have ___________
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
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 amount after deductions