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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. Simple probability
Odd numbers only have ___________
(# of favorable outcomes) / (# of possible outcomes)
Sum of digits is multiple of 3 - last two digits multiple of 4.
always try to factor

2. Sum of consecutive numbers
1
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.
sum = (average)(number of terms)
0.15n + 0.08(5) = 0.1(n+5)

3. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Exterior angle d is equal to the sum of the two remote interior angles a and b
A = P(1 + r) ^n
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

4. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
The total amount before any deductions
(# of favorable outcomes) / (# of possible outcomes)
Exterior angle d is equal to the sum of the two remote interior angles a and b
22

5. Number added or deleted
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 = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
p/100 = is/of
1 - P(E)

6. How to check whether a number is a multiple of 6
3-4-5 - 5-12-13 - 9-12-15
Number is a multiple of 3 and 2
| A union B| = |A| + |B| - |A intersect B|
0.15n + 0.08(5) = 0.1(n+5)

7. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
s Sq. rt (x^r)
principle (interest rate - in decimal form) (time - in years)
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.

8. Price sold for by retailer (after markup)
Find all prime factors
Even
market value
1.4

9. Formula for area of a Trapezoid
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.
(sum of bases)(height) / 2
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
83.3%

10. How to find all divisors of a number
3-4-5 - 5-12-13 - 9-12-15
3 - 6 - 9 - 12
A = P(1 + r) ^n
Find all prime factors

11. Price purchased for by wholesaler
Purchase price
(amount of change) / (original amount)
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.
Find all prime factors

12. gcd(m,n)*lcm(m,n)
3 - 6 - 9 - 12
gcd(m,n)*lcm(m,n) = mn
0.15n + 0.08(5) = 0.1(n+5)
Immediately UNFACTOR or vice versa

13. 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.
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.
1st Rule of Probability: Basic Rule is what?
1/16
Even

14. Odd Factors
Any multiplication involving an even number creates an even product.
Number is a multiple of 3 and 2
12.5%
Odd numbers only have ___________

15. (1/4)^2
Odd numbers only have ___________
The probability of event occurring is...
Purchase price
1/16

16. 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.
x - x - x(sq. rt 2)
Group 1 + Group 2 + Neither - Both = Total
Organize into a grid.
(sum of bases)(height) / 2

17. 2n - 2n+2 - 2n+4
(total A) / (total B)
1 - P(E)
Even
A = P(1 + r) ^n

18. The number of outcomes that result in A divided by the total number of possible outcomes.
Sum of digits is multiple of 9
P(E)P(F)
Sum of digits is multiple of 3
The probability of event occurring is...

19. Gross Profit formula
3-4-5 - 5-12-13 - 9-12-15
Gross Profit = Selling Price - Cost
Principal (1 + interest/number times compounded)^(t)(n)
Odd numbers only have ___________

20. What to do with equations that have fractions
$11 - 025
Immediately try factoring/simplifying when possible
12^3
22

21. How to check whether a number is a multiple of 3.
at least 3 steps
83.3%
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.

22. Net
Immediately try factoring/simplifying when possible
If the outcome of one event affects the outcome of the other event.
P(E) + P(F) - P(E and F)
The amount after deductions

23. gcd(m,n)
______ |m-n|
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
$11 - 025
1

24. 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.
1
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.
14 liters

25. How to check whether a number is a multiple of 12.
2 steps
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
Sum of digits is multiple of 3 - last two digits multiple of 4.
x - x - x(sq. rt 2)

26. Compound interest rule
n! / (n - r)!
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
Odd
Find simple interest then look for the answer that is a little bigger

27. Properties of 0
16.6%
1/16
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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

28. 0! = ?
gcd(m,n)*lcm(m,n) = mn
always try to factor
Find all prime factors
1

29. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
| A union B| = |A| + |B| - |A intersect B|
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Find simple interest then look for the answer that is a little bigger
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

30. 3^3 x 4^3 = ?
-b +- sq. rt(b^2 - 4ac) / 2a
1st Rule of Probability: Basic Rule is what?
1 - P(E)
12^3

31. When you see an equation in factored form in a question?
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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Immediately UNFACTOR or vice versa
22

32. In general - difficult questions require how many steps to solve?
at least 3 steps
P(E) + P(F) - P(E and F)
14 liters
Immediately UNFACTOR or vice versa

33. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
| A union B| = |A| + |B| - |A intersect B|
p/100 = is/of
$11 - 025
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.

34. 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.
Number is a multiple of 3 and 2
Odd numbers only have ___________
Find all prime factors

35. Work problem rule
1 - P(E)
1st Rule of Probability: Basic Rule is what?
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.
A = P(1 + r) ^n

36. 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
| A union B| = |A| + |B| - |A intersect B|
Balancing
Figure out the probability for each individual event. Multiply the individual probabilities together.
at least 3 steps

37. Multiplication principle
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 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
principle (interest rate - in decimal form) (time - in years)
Exterior angle d is equal to the sum of the two remote interior angles a and b

38. The average of consecutive numbers
(total distance) / (total time)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
14 liters
Find simple interest then look for the answer that is a little bigger

39. Percent Formula
1
p/100 = is/of
1 - P(E)
3-4-5 - 5-12-13 - 9-12-15

40. Probability and Geometry.
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
Exterior angle d is equal to the sum of the two remote interior angles a and b
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.
n! / (n - r)!

41. In general - medium questions require how many steps to solve?
always try to factor
(sum of bases)(height) / 2
2 steps
1.4

42. How do you multiply roots together.
22
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Number is a multiple of 3 and 2
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

43. Sq. rt(3)
D or E
12^3
1.7
Odd numbers only have ___________

44. Combined Events: Not E = P(not E) = ?
1 - P(E)
-b +- sq. rt(b^2 - 4ac) / 2a
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
n! / (n - r)!

45. 2nd Rule of Probability: P(E) = 1 - P(not E)
D or E
(n-1)!
The probability of an event occurring plus the probability of the event not occurring = 1
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.

46. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
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.
(n-1)!
(# of favorable outcomes) / (# of possible outcomes)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

47. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
12^3
Any multiplication involving an even number creates an even product.
4/3 TT r ^3

48. Prime Factorization to find Greatest Common Factor
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
Odd
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)

49. How to find the slope.
x(sq. rt 3) - x - 2x
always try to factor
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
y2 - y1 / x2 - x1

50. Multiples of 3
0.15n + 0.08(5) = 0.1(n+5)
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.
3 - 6 - 9 - 12
always try to factor