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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. How to check whether a number is a multiple of 3.
If the outcome of one event affects the outcome of the other event.
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 3
P(event NOT occurring) = 1 - P(event occurring)

2. Work problem rule
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.
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)
market value

3. Sq. rt(3)
1.7
______ |m-n|
Odd numbers only have ___________
Immediately try factoring/simplifying when possible

4. x^r/s = ?
Balancing
s Sq. rt (x^r)
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
at least 3 steps

5. Sum of consecutive numbers
1
Odd numbers only have ___________
Any multiplication involving an even number creates an even product.
sum = (average)(number of terms)

6. When you see an equation in factored form in a question?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Immediately UNFACTOR or vice versa
Sum of digits is multiple of 3 - last two digits multiple of 4.
A = P(1 + r) ^n

7. 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.
Odd
always try to factor
Figure out the probability for each individual event. Multiply the individual probabilities together.

8. Price purchased for by wholesaler
Purchase price
2 steps
P(E)P(F)
Odd

9. Odd and Even rule.
Any multiplication involving an even number creates an even product.
$11 - 025
sum = (average)(number of terms)
180(n-2)

10. Combined Events: E or F
2 steps
Immediately try factoring/simplifying when possible
Organize into a grid.
P(E) + P(F) - P(E and F)

11. 1/6 = what %
| A union B| = |A| + |B| - |A intersect B|
16.6%
-b +- sq. rt(b^2 - 4ac) / 2a
The amount after deductions

12. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
(x-n(n)y-n)
always try to factor
A = P(1 + r) ^n
P(E) + P(F) - P(E and F)

13. 0! = ?
Sum of digits is multiple of 3
A = P(1 + r) ^n
-b +- sq. rt(b^2 - 4ac) / 2a
1

14. Formula for Mixed Group problems (involving Both/Neither)
Minor arc = 2(inscribed angle)
(amount of change) / (original amount)
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

15. How to check for a prime number.

16. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
1.4
Odd numbers only have ___________
x(sq. rt 3) - x - 2x

17. Indistinguishable events how to find the number of permutations

18. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
1
P(E)P(F)
p/100 = is/of

19. The average of consecutive numbers
______ |m-n|
(amount of change) / (original amount)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
2 steps

20. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
principle (interest rate - in decimal form) (time - in years)
347
12^3
Any multiplication involving an even number creates an even product.

21. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 9
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
principle (interest rate - in decimal form) (time - in years)

22. How to check whether number is multiple of 9
1 - P(E)
Sum of digits is multiple of 9
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)
$11 - 025

23. 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?
14 liters
Exterior angle d is equal to the sum of the two remote interior angles a and b
3 - 6 - 9 - 12
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

24. Permutations: Order Matters
n! / (n - r)!
gcd(m,n)*lcm(m,n) = mn
180(n-2)
If the outcome of one event affects the outcome of the other event.

25. The number of outcomes that result in A divided by the total number of possible outcomes.
Even
The probability of event occurring is...
-b +- sq. rt(b^2 - 4ac) / 2a
1.7

26. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 9
(n-1)!
Purchase price

27. Number added or deleted
______ |m-n|
sum = (average)(number of terms)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

28. Average Rate: Average speed
4/3 TT r ^3
Any multiplication involving an even number creates an even product.
(total distance) / (total time)
Odd

29. 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
0.15n + 0.08(5) = 0.1(n+5)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Balancing
Immediately UNFACTOR or vice versa

30. Percent increase = ?
(amount of change) / (original amount)
Balancing
0.15n + 0.08(5) = 0.1(n+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)

31. 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
Find all prime factors
______ |m-n|
Principal (1 + interest/number times compounded)^(t)(n)

32. 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.
s Sq. rt (x^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.
1.7

33. Combined Events: Not E = P(not E) = ?
Find all prime factors
$11 - 025
1 - P(E)
Immediately UNFACTOR or vice versa

34. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
(total A) / (total B)
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 3 - last two digits multiple of 4.

35. Percent Formula
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
p/100 = is/of
Divide 4999 by 15 => 333 integers
2 steps

36. 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
(x-n(n)y-n)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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.
always try to factor

37. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
1.4
22
Any multiplication involving an even number creates an even product.

38. 30-60-90 triangle basic lengths of sides
at least 3 steps
(amount of change) / (original amount)
x(sq. rt 3) - x - 2x
Divide 4999 by 15 => 333 integers

39. Gross Profit formula
Gross Profit = Selling Price - Cost
(# of favorable outcomes) / (# of possible outcomes)
A = P(1 + r) ^n
(amount of change) / (original amount)

40. Set Problems formula
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.
sum = (average)(number of terms)
P(E) + P(F) - P(E and F)
(x-n(n)y-n)

41. The number of ways independent events can occur together.
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
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(total A) / (total B)
x(sq. rt 3) - x - 2x

42. 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.
always try to factor
Exterior angle d is equal to the sum of the two remote interior angles a and b
83.3%

43. Always try to factor
Principal (1 + interest/number times compounded)^(t)(n)
Minor arc = 2(inscribed angle)
always try to factor
The probability of event occurring is...

44. How to check whether a number is a multiple of 6
Group 1 + Group 2 + Neither - Both = Total
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
Number is a multiple of 3 and 2
n! / (n - r)!

45. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
p/100 = is/of
sum = (average)(number of terms)
16.6%

46. 2n+1 - 2n+3 - 2n+5
Odd
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
______ |m-n|
The total amount before any deductions

47. How do you multiply roots together.
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)
x(sq. rt 3) - x - 2x
12.5%
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

48. How to check whether a number is a multiple of 12.
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)
0.15n + 0.08(5) = 0.1(n+5)
1.4
Sum of digits is multiple of 3 - last two digits multiple of 4.

49. 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)
Even
4/3 TT r ^3
sum = (average)(number of terms)

50. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
______ |m-n|
Group 1 + Group 2 + Neither - Both = Total
Immediately UNFACTOR or vice versa
347