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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. In general - medium questions require how many steps to solve?
12^3
at least 3 steps
(# of favorable outcomes) / (# of possible outcomes)
2 steps

2. 1/8 = what %
12.5%
The probability of event occurring is...
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
| A union B| = |A| + |B| - |A intersect B|

3. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
Odd numbers only have ___________
22
1.7

4. Sum of consecutive numbers
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 = (average)(number of terms)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
______ |m-n|

5. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
Find all prime factors
The amount after deductions
12^3

6. 0! = ?
Sum of digits is multiple of 3
Balancing
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
1

7. Average Rate: Average A per B
Gross Profit = Selling Price - Cost
(total A) / (total B)
If the outcome of one event affects the outcome of the other event.
4/3 TT r ^3

8. 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
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 9
Balancing
-b +- sq. rt(b^2 - 4ac) / 2a

9. How to check whether a number is a multiple of 12.
x - x - x(sq. rt 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.
-b +- sq. rt(b^2 - 4ac) / 2a
Sum of digits is multiple of 3 - last two digits multiple of 4.

10. 3^3 x 4^3 = ?
Odd
347
y2 - y1 / x2 - x1
12^3

11. Intersecting Sets
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
1/16
| A union B| = |A| + |B| - |A intersect B|

12. Net
The amount after deductions
1.4
n! / (n - r)!
(x-n(n)y-n)

13. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.

14. Prime Factorization to find Greatest Common Factor
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Organize into a grid.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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

15. Odd Factors
3 - 6 - 9 - 12
(total distance) / (total time)
Principal (1 + interest/number times compounded)^(t)(n)
Odd numbers only have ___________

16. Combined Events: E and F
Find all prime factors
always try to factor
P(E)P(F)
Find simple interest then look for the answer that is a little bigger

17. 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
x(sq. rt 3) - x - 2x
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.
14 liters
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.

18. Volume of a sphere
4/3 TT r ^3
1st Rule of Probability: Basic Rule is what?
1/16
Number is a multiple of 3 and 2

19. Trial Problems: look at the probability of NOT OCCURRING
(sum of bases)(height) / 2
12^3
always try to factor
P(event NOT occurring) = 1 - P(event occurring)

20. How to check whether a number is a multiple of 6
P(E)P(F)
Number is a multiple of 3 and 2
(total A) / (total B)
at least 3 steps

21. 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.
Exterior angle d is equal to the sum of the two remote interior angles a and b
2 steps
Even

22. Properties of 0
1.4
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
gcd(m,n)*lcm(m,n) = mn
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

23. 30-60-90 triangle basic lengths of sides
The total amount before any deductions
x(sq. rt 3) - x - 2x
D or E
Purchase price

24. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
3-4-5 - 5-12-13 - 9-12-15
Odd
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)

25. Sq. rt(3)
1.7
0.15n + 0.08(5) = 0.1(n+5)
P(E)P(F)
A = P(1 + r) ^n

26. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
(amount of change) / (original amount)
principle (interest rate - in decimal form) (time - in years)
If the outcome of one event affects the outcome of the other event.
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.

27. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
at least 3 steps
Any multiplication involving an even number creates an even product.
1.7

28. 2nd Rule of Probability: P(E) = 1 - P(not E)
Find simple interest then look for the answer that is a little bigger
1.7
The probability of an event occurring plus the probability of the event not occurring = 1
Sum of digits is multiple of 3

29. Combined Events: Not E = P(not E) = ?
1 - P(E)
s Sq. rt (x^r)
-b +- sq. rt(b^2 - 4ac) / 2a
(# of favorable outcomes) / (# of possible outcomes)

30. Formula for area of a Trapezoid
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)
1st Rule of Probability: Basic Rule is what?
(sum of bases)(height) / 2
Divide 4999 by 15 => 333 integers

31. How to check for a prime number.

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32. Quadratic formula
Principal (1 + interest/number times compounded)^(t)(n)
-b +- sq. rt(b^2 - 4ac) / 2a
Any multiplication involving an even number creates an even product.
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.

33. How to check whether a number is a multiple of 3.
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.
The probability of event occurring is...
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Sum of digits is multiple of 3

34. How to check whether number is multiple of 9
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
3-4-5 - 5-12-13 - 9-12-15
(n-1)!
Sum of digits is multiple of 9

35. Average Rate: Average speed
Group 1 + Group 2 + Neither - Both = Total
gcd(m,n)*lcm(m,n) = mn
14 liters
(total distance) / (total time)

36. 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?
If the outcome of one event affects the outcome of the other event.
14 liters
Even
1st Rule of Probability: Basic Rule is what?

37. Indistinguishable events how to find the number of permutations

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38. Number added or deleted
P(event NOT occurring) = 1 - P(event occurring)
at least 3 steps
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Figure out the probability for each individual event. Multiply the individual probabilities together.

39. Set Problems formula
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(x-n(n)y-n)
4/3 TT r ^3

40. Always try to factor
always try to factor
(# of favorable outcomes) / (# of possible outcomes)
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.
The probability of an event occurring plus the probability of the event not occurring = 1

41. Combined Events: E or F
Organize into a grid.
Group 1 + Group 2 + Neither - Both = Total
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(E) + P(F) - P(E and F)

42. (1/4)^2
3 - 6 - 9 - 12
Any multiplication involving an even number creates an even product.
(n-1)!
1/16

43. 45-45-90 triangle basic lengths of sides
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
x - x - x(sq. rt 2)
Gross Profit = Selling Price - Cost
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

44. How to find all divisors of a number
1
Purchase price
347
Find all prime factors

45. 3rd Rule of Probability: Conditional Probability
1
If the outcome of one event affects the outcome of the other event.
Number is a multiple of 3 and 2
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.

46. Permutations: Order Matters
p/100 = is/of
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)
n! / (n - r)!
Group 1 + Group 2 + Neither - Both = Total

47. 1/6 = what %
16.6%
Organize into a grid.
Gross Profit = Selling Price - Cost
Find all prime factors

48. Price sold for by retailer (after markup)
market value
P(event NOT occurring) = 1 - P(event occurring)
Organize into a grid.
22

49. Probability and Geometry.
market value
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
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)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

50. Gross Profit formula
(total distance) / (total time)
(total A) / (total B)
______ |m-n|
Gross Profit = Selling Price - Cost