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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. Combined Events: Not E = P(not E) = ?
| A union B| = |A| + |B| - |A intersect B|
The total amount before any deductions
1 - P(E)
22

2. 1/6 = what %
16.6%
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.
(amount of change) / (original amount)
Figure out the probability for each individual event. Multiply the individual probabilities together.

3. Permutations: Order Matters
Exterior angle d is equal to the sum of the two remote interior angles a and b
Odd
180(n-2)
n! / (n - r)!

4. 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.
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
Immediately try factoring/simplifying when possible
p/100 = is/of

5. x^r/s = ?
P(event NOT occurring) = 1 - P(event occurring)
s Sq. rt (x^r)
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.
Group 1 + Group 2 + Neither - Both = Total

6. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
(amount of change) / (original amount)
1/16
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.

7. Odd Factors
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.
1.7
market value
Odd numbers only have ___________

8. Simple probability
D or E
0.15n + 0.08(5) = 0.1(n+5)
(# of favorable outcomes) / (# of possible outcomes)
12.5%

9. 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
Principal (1 + interest/number times compounded)^(t)(n)
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.
The total amount before any deductions
Odd numbers only have ___________

10. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1 - P(E)
The total amount before any deductions
market value

11. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
sum = (average)(number of terms)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Even

12. How to check whether number is multiple of 9
3-4-5 - 5-12-13 - 9-12-15
Sum of digits is multiple of 9
16.6%
12^3

13. 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
Figure out the probability for each individual event. Multiply the individual probabilities together.
sum = (average)(number of terms)
n! / (n - r)!

14. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Immediately try factoring/simplifying when possible
(n-1)!
always try to factor

15. 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.
Number is a multiple of 3 and 2
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.
Gross Profit = Selling Price - Cost
Organize into a grid.

16. Percent increase = ?
The total amount before any deductions
1/16
(amount of change) / (original amount)
A = P(1 + r) ^n

17. Sq. rt(2)
P(E)P(F)
$11 - 025
1.4
(sum of bases)(height) / 2

18. Quadratic formula
22
-b +- sq. rt(b^2 - 4ac) / 2a
1 - P(E)
Find simple interest then look for the answer that is a little bigger

19. How to find all divisors of a number
Find all prime factors
Divide 4999 by 15 => 333 integers
-b +- sq. rt(b^2 - 4ac) / 2a
Number is a multiple of 3 and 2

20. Average Rate: Average speed
(total distance) / (total time)
12.5%
Balancing
p/100 = is/of

21. 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
Balancing
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.
Gross Profit = Selling Price - Cost
gcd(m,n)*lcm(m,n) = mn

22. Price sold for by retailer (after markup)
market value
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
Balancing

23. Volume of a sphere
83.3%
4/3 TT r ^3
0.15n + 0.08(5) = 0.1(n+5)
1.7

24. Set Problems formula
1.7
(x-n(n)y-n)
180(n-2)
principle (interest rate - in decimal form) (time - in years)

25. 0! = ?
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)
1
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.
at least 3 steps

26. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Sum of digits is multiple of 3 - last two digits multiple of 4.
347
Sum of digits is multiple of 3
at least 3 steps

27. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
Divide 4999 by 15 => 333 integers
-b +- sq. rt(b^2 - 4ac) / 2a
Find all prime factors

28. 5/6 = what %
Sum of digits is multiple of 3 - last two digits multiple of 4.
Balancing
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
83.3%

29. 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)
x - x - x(sq. rt 2)
1.4
12^3

30. Formula for area of a Trapezoid
| A union B| = |A| + |B| - |A intersect B|
(sum of bases)(height) / 2
22
(# of favorable outcomes) / (# of possible outcomes)

31. Indistinguishable events how to find the number of permutations

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32. Always try to factor
always try to factor
P(event NOT occurring) = 1 - P(event occurring)
Odd numbers only have ___________
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

33. How to check for a prime number.

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34. How to check whether a number is a multiple of 12.
4/3 TT r ^3
Sum of digits is multiple of 3 - last two digits multiple of 4.
Divide 4999 by 15 => 333 integers
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

35. Gross Profit formula
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
n! / (n - r)!
Gross Profit = Selling Price - Cost
12.5%

36. The number of outcomes that result in A divided by the total number of possible outcomes.
Number is a multiple of 3 and 2
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)
The probability of event occurring is...

37. Combined Events: E and F
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
P(E)P(F)
Immediately UNFACTOR or vice versa
(n-1)!

38. 30-60-90 triangle basic lengths of sides
(# of favorable outcomes) / (# of possible outcomes)
gcd(m,n)*lcm(m,n) = mn
x(sq. rt 3) - x - 2x
12^3

39. Number added or deleted
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
1 - P(E)
3-4-5 - 5-12-13 - 9-12-15

40. 2n+1 - 2n+3 - 2n+5
P(event NOT occurring) = 1 - P(event occurring)
Odd
A = P(1 + r) ^n
at least 3 steps

41. Compound interest rule
Purchase price
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
Find simple interest then look for the answer that is a little bigger

42. Multiples of 3
3 - 6 - 9 - 12
gcd(m,n)*lcm(m,n) = mn
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
______ |m-n|

43. 2n - 2n+2 - 2n+4
Find all prime factors
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.
-b +- sq. rt(b^2 - 4ac) / 2a
Even

44. How to find the slope.
12^3
y2 - y1 / x2 - x1
-b +- sq. rt(b^2 - 4ac) / 2a
Find simple interest then look for the answer that is a little bigger

45. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
(# of favorable outcomes) / (# of possible outcomes)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
s Sq. rt (x^r)

46. How to check whether a number is a multiple of 6
If the outcome of one event affects the outcome of the other event.
s Sq. rt (x^r)
Odd
Number is a multiple of 3 and 2

47. To determine multiple-event probability where each individual event must occur in a certain way.
Find all prime factors
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)
347
Figure out the probability for each individual event. Multiply the individual probabilities together.

48. Dependent events: When are two events said to be dependent events?
x - x - x(sq. rt 2)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
If the outcome of one event affects the outcome of the other event.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

49. In general - difficult questions require how many steps to solve?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The amount after deductions
at least 3 steps
Find all prime factors

50. Triangle abc with d on the outside with a line. What does d = ?
Sum of digits is multiple of 3
| A union B| = |A| + |B| - |A intersect B|
Minor arc = 2(inscribed angle)
Exterior angle d is equal to the sum of the two remote interior angles a and b