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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. 30-60-90 triangle basic lengths of sides
0.15n + 0.08(5) = 0.1(n+5)
Immediately UNFACTOR or vice versa
Find all prime factors
x(sq. rt 3) - x - 2x

2. Set Problems formula
Sum of digits is multiple of 3 - last two digits multiple of 4.
3 - 6 - 9 - 12
(sum of bases)(height) / 2
(x-n(n)y-n)

3. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
Figure out the probability for each individual event. Multiply the individual probabilities together.
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 9

4. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
______ |m-n|
1 - P(E)
Odd

5. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
2 steps
Sum of digits is multiple of 3
83.3%

6. Odd Factors
Odd numbers only have ___________
1/16
P(E) + P(F) - P(E and F)
principle (interest rate - in decimal form) (time - in years)

7. Gross
The total amount before any deductions
0.15n + 0.08(5) = 0.1(n+5)
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/100 = is/of

8. Sum of consecutive numbers
sum = (average)(number of terms)
gcd(m,n)*lcm(m,n) = mn
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.

9. 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
180(n-2)
n! / (n - r)!
The probability of an event occurring plus the probability of the event not occurring = 1

10. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
Figure out the probability for each individual event. Multiply the individual probabilities together.
P(event NOT occurring) = 1 - P(event occurring)
Principal (1 + interest/number times compounded)^(t)(n)

11. x^r/s = ?
Immediately UNFACTOR or vice versa
180(n-2)
(sum of bases)(height) / 2
s Sq. rt (x^r)

12. Sq. rt(2)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1.4
Immediately try factoring/simplifying when possible
x - x - x(sq. rt 2)

13. How to check whether a number is a multiple of 6
If the outcome of one event affects the outcome of the other event.
Number is a multiple of 3 and 2
x - x - x(sq. rt 2)
(# of favorable outcomes) / (# of possible outcomes)

14. How to find the slope.
The probability of event occurring is...
y2 - y1 / x2 - x1
3-4-5 - 5-12-13 - 9-12-15
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

15. How to check whether a number is a multiple of 4.
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

16. 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.
Odd
Even
1st Rule of Probability: Basic Rule is what?
D or E

17. 4th rule of Probability
(amount of change) / (original amount)
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)
(total A) / (total B)
s Sq. rt (x^r)

18. Dependent events: When are two events said to be dependent events?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
If the outcome of one event affects the outcome of the other event.
Immediately try factoring/simplifying when possible
Divide 4999 by 15 => 333 integers

19. Combined Events: E and F
14 liters
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 3 - last two digits multiple of 4.
P(E)P(F)

20. Average Rate: Average speed
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 - last two digits multiple of 4.
always try to factor
(total distance) / (total time)

21. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
gcd(m,n)*lcm(m,n) = mn
347
principle (interest rate - in decimal form) (time - in years)

22. 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?
s Sq. rt (x^r)
at least 3 steps
Any multiplication involving an even number creates an even product.
14 liters

23. 1/6 = what %
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
12^3
(total distance) / (total time)
16.6%

24. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Balancing
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Sum of digits is multiple of 9

25. Work problem rule
(# of favorable outcomes) / (# of possible outcomes)
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.
0.15n + 0.08(5) = 0.1(n+5)
The total amount before any deductions

26. How to check for a prime number.

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27. Volume of a sphere
p/100 = is/of
The amount after deductions
14 liters
4/3 TT r ^3

28. How to check whether a number is a multiple of 3.
sum = (average)(number of terms)
Sum of digits is multiple of 3
Immediately UNFACTOR or vice versa
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.

29. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
The amount after deductions
Organize into a grid.
n! / (n - r)!

30. Formula for area of a Trapezoid
(n-1)!
P(E) + P(F) - P(E and F)
(sum of bases)(height) / 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.

31. The number of outcomes that result in A divided by the total number of possible outcomes.
83.3%
| A union B| = |A| + |B| - |A intersect B|
gcd(m,n)*lcm(m,n) = mn
The probability of event occurring is...

32. Multiplication principle
14 liters
1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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

33. 2n - 2n+2 - 2n+4
Even
Purchase price
Find all prime factors
Organize into a grid.

34. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Sum of digits is multiple of 9
Divide 4999 by 15 => 333 integers
(# of favorable outcomes) / (# of possible outcomes)
-b +- sq. rt(b^2 - 4ac) / 2a

35. Gross Profit formula
180(n-2)
Any multiplication involving an even number creates an even product.
______ |m-n|
Gross Profit = Selling Price - Cost

36. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
180(n-2)
x(sq. rt 3) - x - 2x
Odd numbers only have ___________

37. In general - difficult questions require how many steps to solve?
at least 3 steps
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
x - x - x(sq. rt 2)

38. How to check whether number is multiple of 9
0.15n + 0.08(5) = 0.1(n+5)
-b +- sq. rt(b^2 - 4ac) / 2a
Sum of digits is multiple of 3 - last two digits multiple of 4.
Sum of digits is multiple of 9

39. Percent increase = ?
x - x - x(sq. rt 2)
(amount of change) / (original amount)
gcd(m,n)*lcm(m,n) = mn
-b +- sq. rt(b^2 - 4ac) / 2a

40. Price purchased for by wholesaler
Figure out the probability for each individual event. Multiply the individual probabilities together.
1st Rule of Probability: Basic Rule is what?
Purchase price
Group 1 + Group 2 + Neither - Both = Total

41. Properties of 0
always try to factor
1/16
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 3

42. Average Rate: Average A per B
P(E) + P(F) - P(E and F)
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.
(# of favorable outcomes) / (# of possible outcomes)
(total A) / (total B)

43. Number added or deleted
16.6%
n! / (n - r)!
D or E
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

44. Trial Problems: look at the probability of NOT OCCURRING
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.
12^3
P(event NOT occurring) = 1 - P(event occurring)

45. Odd and Even rule.
D or E
Divide 4999 by 15 => 333 integers
Any multiplication involving an even number creates an even product.
12^3

46. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
y2 - y1 / x2 - x1
A = P(1 + r) ^n
Odd numbers only have ___________
Immediately UNFACTOR or vice versa

47. Net
The amount after deductions
The probability of event occurring is...
market value
Organize into a grid.

48. Compound interest rule
Find simple interest then look for the answer that is a little bigger
Any multiplication involving an even number creates an even product.
1.7
Sum of digits is multiple of 3 - last two digits multiple of 4.

49. When you see an equation in factored form in a question?
The total amount before any deductions
Immediately UNFACTOR or vice versa
y2 - y1 / x2 - x1
83.3%

50. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(# of favorable outcomes) / (# of possible outcomes)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.