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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. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
| A union B| = |A| + |B| - |A intersect B|
83.3%

2. Volume of a sphere
4/3 TT r ^3
(total A) / (total B)
(total distance) / (total time)
at least 3 steps

3. Price purchased for by wholesaler
Purchase price
gcd(m,n)*lcm(m,n) = mn
Find simple interest then look for the answer that is a little bigger
at least 3 steps

4. Formula for Mixed Group problems (involving Both/Neither)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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)
Group 1 + Group 2 + Neither - Both = Total
2 steps

5. 4th rule of Probability
Sum of digits is multiple of 3 - last two digits multiple of 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)
$11 - 025
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

6. Sum of consecutive numbers
sum = (average)(number of terms)
Minor arc = 2(inscribed angle)
1 - P(E)
(amount of change) / (original amount)

7. To determine multiple-event probability where each individual event must occur in a certain way.
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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Figure out the probability for each individual event. Multiply the individual probabilities together.
3-4-5 - 5-12-13 - 9-12-15

8. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
1.7
Number is a multiple of 3 and 2
22

9. 45-45-90 triangle basic lengths of sides
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.
Divide 4999 by 15 => 333 integers
x - x - x(sq. rt 2)

10. Properties of 0
Odd
Sum of digits is multiple of 9
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
p/100 = is/of

11. Permutations: Order Matters
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
n! / (n - r)!
(x-n(n)y-n)
A = P(1 + r) ^n

12. 2nd Rule of Probability: P(E) = 1 - P(not E)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Find simple interest then look for the answer that is a little bigger
The probability of an event occurring plus the probability of the event not occurring = 1
1 - P(E)

13. Odd Factors
0.15n + 0.08(5) = 0.1(n+5)
Odd numbers only have ___________
Minor arc = 2(inscribed angle)
14 liters

14. Inscribed Angle - Minor Arc
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
Find simple interest then look for the answer that is a little bigger
12.5%
Minor arc = 2(inscribed angle)

15. Gross
Even
14 liters
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The total amount before any deductions

16. gcd(m,n)*lcm(m,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
14 liters
gcd(m,n)*lcm(m,n) = mn
(total A) / (total B)

17. When you see an equation in factored form in a question?
| A union B| = |A| + |B| - |A intersect B|
Minor arc = 2(inscribed angle)
(# of favorable outcomes) / (# of possible outcomes)
Immediately UNFACTOR or vice versa

18. In general - difficult questions require how many steps to solve?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
at least 3 steps
Sum of digits is multiple of 3 - last two digits multiple of 4.
(n-1)!

19. How to find all divisors of a number
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Find all prime factors

20. 3^3 x 4^3 = ?
12^3
The total amount before any deductions
sum = (average)(number of terms)
Odd numbers only have ___________

21. 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?
The amount after deductions
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.

22. Three triangle length patterns
Immediately UNFACTOR or vice versa
Principal (1 + interest/number times compounded)^(t)(n)
Minor arc = 2(inscribed angle)
3-4-5 - 5-12-13 - 9-12-15

23. Simple probability
Exterior angle d is equal to the sum of the two remote interior angles a and b
If the outcome of one event affects the outcome of the other event.
(# of favorable outcomes) / (# of possible outcomes)
Figure out the probability for each individual event. Multiply the individual probabilities together.

24. Percent Formula
p/100 = is/of
If the outcome of one event affects the outcome of the other event.
(x-n(n)y-n)
347

25. How to check whether number is multiple of 9
Sum of digits is multiple of 9
Purchase price
at least 3 steps
Exterior angle d is equal to the sum of the two remote interior angles a and b

26. 2n+1 - 2n+3 - 2n+5
| A union B| = |A| + |B| - |A intersect B|
Odd
A = P(1 + r) ^n
Find simple interest then look for the answer that is a little bigger

27. 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
The probability of event occurring is...
Divide 4999 by 15 => 333 integers
3 - 6 - 9 - 12

28. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
22
(total A) / (total B)
A = P(1 + r) ^n
market value

29. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
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
(n-1)!
1 - P(E)
$11 - 025

30. 2n - 2n+2 - 2n+4
If the outcome of one event affects the outcome of the other event.
Even
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

31. Price sold for by retailer (after markup)
Balancing
Any multiplication involving an even number creates an even product.
market value
Last two digits are multiple of 4 or the number can be divided by 2 twice.

32. Triangle abc with d on the outside with a line. What does d = ?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
180(n-2)
Minor arc = 2(inscribed angle)
Exterior angle d is equal to the sum of the two remote interior angles a and b

33. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
principle (interest rate - in decimal form) (time - in years)
Group 1 + Group 2 + Neither - Both = Total
12.5%
$11 - 025

34. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
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.
(total A) / (total B)
(amount of change) / (original amount)

35. Net
The amount after deductions
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
83.3%
Sum of digits is multiple of 9

36. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
y2 - y1 / x2 - x1
s Sq. rt (x^r)
P(E) + P(F) - P(E and F)

37. How to check whether a number is a multiple of 4.
| A union B| = |A| + |B| - |A intersect B|
22
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.

38. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Number is a multiple of 3 and 2
A = P(1 + r) ^n
347
P(E) + P(F) - P(E and F)

39. In general - medium questions require how many steps to solve?
Sum of digits is multiple of 3 - last two digits multiple of 4.
sum = (average)(number of terms)
principle (interest rate - in decimal form) (time - in years)
2 steps

40. 0! = ?
1 - P(E)
D or E
1
1.7

41. 5/6 = what %
83.3%
y2 - y1 / x2 - x1
(total A) / (total B)
Sum of digits is multiple of 9

42. Trial Problems: look at the probability of NOT OCCURRING
A = P(1 + r) ^n
P(event NOT occurring) = 1 - P(event occurring)
Balancing
3 - 6 - 9 - 12

43. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
1/16
The probability of event occurring is...
Immediately try factoring/simplifying when possible
D or E

44. Prime Factorization to find Greatest Common Factor
sum = (average)(number of terms)
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
______ |m-n|
1 - P(E)

45. Set Problems formula
3 - 6 - 9 - 12
at least 3 steps
1st Rule of Probability: Basic Rule is what?
(x-n(n)y-n)

46. Combined Events: E and F
(total distance) / (total time)
P(E)P(F)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
gcd(m,n)*lcm(m,n) = mn

47. How do you multiply roots together.
(n-1)!
12^3
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Find all prime factors

48. Average Rate: Average speed
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(total distance) / (total time)
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.
Sum of digits is multiple of 3

49. 1/6 = what %
1st Rule of Probability: Basic Rule is what?
(amount of change) / (original amount)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
16.6%

50. Multiplication principle
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 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
Purchase price
Sum of digits is multiple of 3

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