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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. 1/8 = what %
(total distance) / (total time)
12.5%
Number is a multiple of 3 and 2
at least 3 steps

2. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
p/100 = is/of
Sum of digits is multiple of 3
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
22

3. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
P(E)P(F)
1st Rule of Probability: Basic Rule is what?
______ |m-n|
D or E

4. Formula for Mixed Group problems (involving Both/Neither)
Figure out the probability for each individual event. Multiply the individual probabilities together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
| A union B| = |A| + |B| - |A intersect B|
Group 1 + Group 2 + Neither - Both = Total

5. How to find all divisors of a number
Find simple interest then look for the answer that is a little bigger
Any multiplication involving an even number creates an even product.
Odd numbers only have ___________
Find all prime factors

6. 2n - 2n+2 - 2n+4
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.
Even
Organize into a grid.
A = P(1 + r) ^n

7. Net
Number is a multiple of 3 and 2
The amount after deductions
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

8. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
1 - P(E)
12.5%
gcd(m,n)*lcm(m,n) = mn

9. Gross Profit formula
Immediately UNFACTOR or vice versa
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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Gross Profit = Selling Price - Cost

10. Combined Events: E or F
P(E) + P(F) - P(E and F)
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.
83.3%
Figure out the probability for each individual event. Multiply the individual probabilities together.

11. Probability and Geometry.
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
gcd(m,n)*lcm(m,n) = mn
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.

12. Price sold for by retailer (after markup)
market value
12.5%
Exterior angle d is equal to the sum of the two remote interior angles a and b
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

13. 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?
principle (interest rate - in decimal form) (time - in years)
180(n-2)
(n-1)!
0.15n + 0.08(5) = 0.1(n+5)

14. 4th rule of Probability
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 of digits is multiple of 3
The total amount before any deductions
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

15. 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
x(sq. rt 3) - x - 2x
-b +- sq. rt(b^2 - 4ac) / 2a
(total distance) / (total time)

16. gcd(m,n)
P(E) + P(F) - P(E and F)
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.
Any multiplication involving an even number creates an even product.
______ |m-n|

17. What does the Sum of the angles in a Regular Polygon formula look like?
sum = (average)(number of terms)
principle (interest rate - in decimal form) (time - in years)
(total distance) / (total time)
180(n-2)

18. Odd and Even rule.
Any multiplication involving an even number creates an even product.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(n-1)!
4/3 TT r ^3

19. x^r/s = ?
1.7
x - x - x(sq. rt 2)
s Sq. rt (x^r)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

20. Volume of a sphere
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
Group 1 + Group 2 + Neither - Both = Total
Figure out the probability for each individual event. Multiply the individual probabilities together.
4/3 TT r ^3

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

22. 3^3 x 4^3 = ?
Odd
12^3
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.
Group 1 + Group 2 + Neither - Both = Total

23. Odd Factors
Odd numbers only have ___________
12^3
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Minor arc = 2(inscribed angle)

24. How to check whether a number is a multiple of 6
The amount after deductions
Principal (1 + interest/number times compounded)^(t)(n)
Number is a multiple of 3 and 2
1 - P(E)

25. Sq. rt(3)
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
1/16
1.7
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.

26. 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.
P(E)P(F)
4/3 TT r ^3
y2 - y1 / x2 - x1

27. 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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1st Rule of Probability: Basic Rule is what?
A = P(1 + r) ^n
always try to factor

28. 45-45-90 triangle basic lengths of sides
Immediately try factoring/simplifying when possible
Any multiplication involving an even number creates an even product.
0.15n + 0.08(5) = 0.1(n+5)
x - x - x(sq. rt 2)

29. How to check whether a number is a multiple of 12.
1.7
y2 - y1 / x2 - x1
Sum of digits is multiple of 3 - last two digits multiple of 4.
at least 3 steps

30. 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.
Organize into a grid.
Find simple interest then look for the answer that is a little bigger
sum = (average)(number of terms)
n! / (n - r)!

31. How to check whether number is multiple of 9
Odd numbers only have ___________
Sum of digits is multiple of 9
Figure out the probability for each individual event. Multiply the individual probabilities together.
Sum of digits is multiple of 3

32. Average Rate: Average A per B
(# of favorable outcomes) / (# of possible outcomes)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The probability of an event occurring plus the probability of the event not occurring = 1
(total A) / (total B)

33. How to check whether a number is a multiple of 3.
12.5%
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
Sum of digits is multiple of 3
1

34. Trial Problems: look at the probability of NOT OCCURRING
gcd(m,n)*lcm(m,n) = mn
P(event NOT occurring) = 1 - P(event occurring)
22
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

35. Triangle abc with d on the outside with a line. What does d = ?
Odd numbers only have ___________
2 steps
x - x - x(sq. rt 2)
Exterior angle d is equal to the sum of the two remote interior angles a and b

36. Gross
The total amount before any deductions
3-4-5 - 5-12-13 - 9-12-15
sum = (average)(number of terms)
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.

37. Combined Events: Not E = P(not E) = ?
83.3%
1 - P(E)
P(E) + P(F) - P(E and F)
Even

38. Price purchased for by wholesaler
Purchase price
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.
P(E)P(F)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

39. Three triangle length patterns
83.3%
3-4-5 - 5-12-13 - 9-12-15
(x-n(n)y-n)
(total A) / (total B)

40. 5/6 = what %
1
(# of favorable outcomes) / (# of possible outcomes)
principle (interest rate - in decimal form) (time - in years)
83.3%

41. Combined Events: E and F
P(E)P(F)
Sum of digits is multiple of 9
p/100 = is/of
principle (interest rate - in decimal form) (time - in years)

42. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
0.15n + 0.08(5) = 0.1(n+5)
(total distance) / (total time)
Find all prime factors

43. 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.
Odd
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

44. 2n+1 - 2n+3 - 2n+5
P(E)P(F)
x(sq. rt 3) - x - 2x
Odd
The probability of event occurring is...

45. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Minor arc = 2(inscribed angle)
principle (interest rate - in decimal form) (time - in years)
A = P(1 + r) ^n
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

46. Permutations: Order Matters
P(E) + P(F) - P(E and F)
Divide 4999 by 15 => 333 integers
n! / (n - r)!
x - x - x(sq. rt 2)

47. The average of consecutive numbers
(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.
s Sq. rt (x^r)
market value

48. (1/4)^2
(total A) / (total B)
180(n-2)
sum = (average)(number of terms)
1/16

49. Sum of consecutive numbers
Number is a multiple of 3 and 2
principle (interest rate - in decimal form) (time - in years)
sum = (average)(number of terms)
347

50. Dependent events: When are two events said to be dependent events?
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.
(total distance) / (total time)
If the outcome of one event affects the outcome of the other event.
p/100 = is/of