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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. How to check whether a number is a multiple of 4.
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
A = P(1 + r) ^n
22
Last two digits are multiple of 4 or the number can be divided by 2 twice.

2. 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.
Sum of digits is multiple of 9
1st Rule of Probability: Basic Rule is what?
sum = (average)(number of terms)
Divide 4999 by 15 => 333 integers

3. Average Rate: Average A per B
(total A) / (total B)
3-4-5 - 5-12-13 - 9-12-15
x(sq. rt 3) - x - 2x
2 steps

4. 4th rule of Probability
Principal (1 + interest/number times compounded)^(t)(n)
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)
12.5%
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

5. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
(x-n(n)y-n)
market value
Any multiplication involving an even number creates an even product.

6. Trial Problems: look at the probability of NOT OCCURRING
83.3%
Divide 4999 by 15 => 333 integers
P(event NOT occurring) = 1 - P(event occurring)
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.

7. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Number is a multiple of 3 and 2
(n-1)!
Odd
P(E) + P(F) - P(E and F)

8. In general - medium questions require how many steps to solve?
-b +- sq. rt(b^2 - 4ac) / 2a
2 steps
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Odd

9. Gross Profit formula
Immediately UNFACTOR or vice versa
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Gross Profit = Selling Price - Cost
Divide 4999 by 15 => 333 integers

10. Combined Events: Not E = P(not E) = ?
1 - P(E)
market value
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Sum of digits is multiple of 9

11. How to check whether a number is a multiple of 12.
14 liters
1.7
Sum of digits is multiple of 3 - last two digits multiple of 4.
______ |m-n|

12. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
(total distance) / (total time)
-b +- sq. rt(b^2 - 4ac) / 2a
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

13. Sum of consecutive numbers
Any multiplication involving an even number creates an even product.
n! / (n - r)!
sum = (average)(number of terms)
p/100 = is/of

14. 2n - 2n+2 - 2n+4
Even
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
y2 - y1 / x2 - x1
Immediately try factoring/simplifying when possible

15. Gross
(total distance) / (total time)
Principal (1 + interest/number times compounded)^(t)(n)
The total amount before any deductions
y2 - y1 / x2 - x1

16. The number of outcomes that result in A divided by the total number of possible outcomes.
gcd(m,n)*lcm(m,n) = mn
Divide 4999 by 15 => 333 integers
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.
The probability of event occurring is...

17. 5/6 = what %
12.5%
347
Odd numbers only have ___________
83.3%

18. Triangle abc with d on the outside with a line. What does d = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
The probability of event occurring is...
(total A) / (total B)
Organize into a grid.

19. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
Balancing
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
16.6%

20. Combined Events: E or F
P(event NOT occurring) = 1 - P(event occurring)
P(E) + P(F) - P(E and F)
x - x - x(sq. rt 2)
Odd

21. What to do with equations that have fractions
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
D or E
A = P(1 + r) ^n
Immediately try factoring/simplifying when possible

22. How to check whether a number is a multiple of 6
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
y2 - y1 / x2 - x1
Number is a multiple of 3 and 2

23. Sq. rt(3)
1.7
(total distance) / (total time)
Organize into a grid.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

24. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
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
Purchase price
Figure out the probability for each individual event. Multiply the individual probabilities together.

25. How to find all divisors of a number
Find all prime factors
x - x - x(sq. rt 2)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 9

26. Simple probability
A = P(1 + r) ^n
(# of favorable outcomes) / (# of possible outcomes)
Even
0.15n + 0.08(5) = 0.1(n+5)

27. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The probability of event occurring is...
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.
Odd numbers only have ___________

28. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1 - P(E)
83.3%

29. Permutations: Order Matters
n! / (n - r)!
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 9
14 liters

30. 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.
Organize into a grid.
1st Rule of Probability: Basic Rule is what?
Group 1 + Group 2 + Neither - Both = Total
Odd

31. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
x(sq. rt 3) - x - 2x
0.15n + 0.08(5) = 0.1(n+5)
(sum of bases)(height) / 2

32. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Principal (1 + interest/number times compounded)^(t)(n)
D or E
p/100 = is/of

33. The average of consecutive numbers
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 3 - last two digits multiple of 4.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1

34. Multiplication principle
12.5%
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.
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
Organize into a grid.

35. How to check for a prime number.

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36. Prime Factorization to find Greatest Common Factor
180(n-2)
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
The amount after deductions
Even

37. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
n! / (n - r)!
Purchase price
A = P(1 + r) ^n
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

38. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Sum of digits is multiple of 3
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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)!

39. Price purchased for by wholesaler
Odd numbers only have ___________
______ |m-n|
Find all prime factors
Purchase price

40. Net
The amount after deductions
sum = (average)(number of terms)
-b +- sq. rt(b^2 - 4ac) / 2a
(total A) / (total B)

41. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
The probability of an event occurring plus the probability of the event not occurring = 1
p/100 = is/of
y2 - y1 / x2 - x1
$11 - 025

42. Formula for area of a Trapezoid
Minor arc = 2(inscribed angle)
(sum of bases)(height) / 2
22
s Sq. rt (x^r)

43. x^r/s = ?
(# of favorable outcomes) / (# of possible outcomes)
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)
P(E) + P(F) - P(E and F)
s Sq. rt (x^r)

44. Average Rate: Average speed
(total distance) / (total time)
Find simple interest then look for the answer that is a little bigger
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.
P(E) + P(F) - P(E and F)

45. 3rd Rule of Probability: Conditional Probability
(amount of change) / (original amount)
1
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.
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

46. 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)
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.
y2 - y1 / x2 - x1
Immediately try factoring/simplifying when possible

47. Probability and Geometry.
Sum of digits is multiple of 3
D or E
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%

48. (1/4)^2
principle (interest rate - in decimal form) (time - in years)
16.6%
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1/16

49. 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?
347
0.15n + 0.08(5) = 0.1(n+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.
(# of favorable outcomes) / (# of possible outcomes)

50. 45-45-90 triangle basic lengths of sides
(sum of bases)(height) / 2
x - x - x(sq. rt 2)
principle (interest rate - in decimal form) (time - in years)
1 - P(E)