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GMAT Quantitative General

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
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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. Average Rate: Average speed
(amount of change) / (original amount)
Figure out the probability for each individual event. Multiply the individual probabilities together.
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.
(total distance) / (total time)

2. Sum of consecutive numbers
Odd numbers only have ___________
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.
sum = (average)(number of terms)
P(E)P(F)

3. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
gcd(m,n)*lcm(m,n) = mn
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
p/100 = is/of

4. 1/8 = what %
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.
1
1st Rule of Probability: Basic Rule is what?
12.5%

5. 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
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.
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-1)!
Sum of digits is multiple of 9

6. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
P(E)P(F)
Odd
principle (interest rate - in decimal form) (time - in years)
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)

7. Gross
0.15n + 0.08(5) = 0.1(n+5)
Immediately UNFACTOR or vice versa
market value
The total amount before any deductions

8. 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.
D or E
gcd(m,n)*lcm(m,n) = mn
P(event NOT occurring) = 1 - P(event occurring)

9. Set Problems formula
(x-n(n)y-n)
22
1
Figure out the probability for each individual event. Multiply the individual probabilities together.

10. Multiples of 3
If the outcome of one event affects the outcome of the other event.
Balancing
x - x - x(sq. rt 2)
3 - 6 - 9 - 12

11. 3^3 x 4^3 = ?
12^3
The probability of an event occurring plus the probability of the event not occurring = 1
Gross Profit = Selling Price - Cost
P(E) + P(F) - P(E and F)

12. How to find the slope.
at least 3 steps
y2 - y1 / x2 - x1
16.6%
0.15n + 0.08(5) = 0.1(n+5)

13. Volume of a sphere
Find simple interest then look for the answer that is a little bigger
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
4/3 TT r ^3
y2 - y1 / x2 - x1

14. In general - difficult questions require how many steps to solve?
1
$11 - 025
Group 1 + Group 2 + Neither - Both = Total
at least 3 steps

15. Odd Factors
P(event NOT occurring) = 1 - P(event occurring)
The probability of event occurring is...
Purchase price
Odd numbers only have ___________

16. Combined Events: Not E = P(not E) = ?
Divide 4999 by 15 => 333 integers
16.6%
Exterior angle d is equal to the sum of the two remote interior angles a and b
1 - P(E)

17. Odd and Even rule.
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
Any multiplication involving an even number creates an even product.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

18. (1/4)^2
1/16
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
1
Find all prime factors

19. How to check whether a number is a multiple of 4.
If the outcome of one event affects the outcome of the other event.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Principal (1 + interest/number times compounded)^(t)(n)
1st Rule of Probability: Basic Rule is what?

20. Probability and Geometry.
0.15n + 0.08(5) = 0.1(n+5)
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
3 - 6 - 9 - 12
1.7

21. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Even
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Purchase price

22. Prime Factorization to find Greatest Common Factor
Purchase price
1
Principal (1 + interest/number times compounded)^(t)(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

23. How to check whether number is multiple of 9
180(n-2)
Odd
______ |m-n|
Sum of digits is multiple of 9

24. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
3 - 6 - 9 - 12
1st Rule of Probability: Basic Rule is what?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

25. Indistinguishable events how to find the number of permutations
83.3%
3 - 6 - 9 - 12
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.
always try to factor

26. x^r/s = ?
12^3
1/16
s Sq. rt (x^r)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

27. How to find all divisors of a number
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
$11 - 025
Immediately UNFACTOR or vice versa
Find all prime factors

28. Compound interest rule
Find simple interest then look for the answer that is a little bigger
sum = (average)(number of terms)
D or E
1/16

29. How to check whether a number is a multiple of 12.
Divide 4999 by 15 => 333 integers
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 3 - last two digits multiple of 4.
x - x - x(sq. rt 2)

30. Sq. rt(2)
Purchase price
347
Odd numbers only have ___________
1.4

31. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
n! / (n - r)!
2 steps
s Sq. rt (x^r)

32. 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?
Group 1 + Group 2 + Neither - Both = Total
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 9
14 liters

33. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
______ |m-n|
Any multiplication involving an even number creates an even product.
3 - 6 - 9 - 12

34. How to check whether a number is a multiple of 3.
Odd numbers only have ___________
x - x - x(sq. rt 2)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Sum of digits is multiple of 3

35. Combined Events: E and F
Number is a multiple of 3 and 2
always try to factor
P(E)P(F)
A = P(1 + r) ^n

36. 1/6 = what %
1.4
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)
16.6%
x - x - x(sq. rt 2)

37. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Sum of digits is multiple of 9
gcd(m,n)*lcm(m,n) = mn

38. 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.
P(event NOT occurring) = 1 - P(event occurring)
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)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

39. Percent Formula
p/100 = is/of
(total distance) / (total time)
market value
The total amount before any deductions

40. Average Rate: Average A per B
(total A) / (total B)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately try factoring/simplifying when possible
D or E

41. 4th rule of Probability
2 steps
4/3 TT r ^3
Odd numbers only have ___________
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)

42. Price sold for by retailer (after markup)
market value
If the outcome of one event affects the outcome of the other event.
$11 - 025
12^3

43. Percent increase = ?
Organize into a grid.
at least 3 steps
market value
(amount of change) / (original amount)

44. When you see an equation in factored form in a question?
2 steps
Immediately UNFACTOR or vice versa
x(sq. rt 3) - x - 2x
Purchase price

45. Inscribed Angle - Minor Arc
Sum of digits is multiple of 3 - last two digits multiple of 4.
Balancing
Minor arc = 2(inscribed angle)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

46. 2nd Rule of Probability: P(E) = 1 - P(not E)
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
If the outcome of one event affects the outcome of the other event.
The probability of an event occurring plus the probability of the event not occurring = 1
12.5%

47. The average of consecutive numbers
Immediately try factoring/simplifying when possible
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
at least 3 steps
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.

48. To determine multiple-event probability where each individual event must occur in a certain way.
A = P(1 + r) ^n
Immediately try factoring/simplifying when possible
Figure out the probability for each individual event. Multiply the individual probabilities together.
14 liters

49. Formula for area of a Trapezoid
Find simple interest then look for the answer that is a little bigger
Number is a multiple of 3 and 2
(x-n(n)y-n)
(sum of bases)(height) / 2

50. 5/6 = what %
Gross Profit = Selling Price - Cost
Even
1st Rule of Probability: Basic Rule is what?
83.3%

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GMAT Quantitative General

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