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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. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
| A union B| = |A| + |B| - |A intersect B|
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
A = P(1 + r) ^n
principle (interest rate - in decimal form) (time - in years)

2. Net
22
(x-n(n)y-n)
12.5%
The amount after deductions

3. The number of outcomes that result in A divided by the total number of possible outcomes.
x(sq. rt 3) - x - 2x
Gross Profit = Selling Price - Cost
1
The probability of event occurring is...

4. Quadratic formula
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
(# of favorable outcomes) / (# of possible outcomes)
The amount after deductions
-b +- sq. rt(b^2 - 4ac) / 2a

5. Simple probability
-b +- sq. rt(b^2 - 4ac) / 2a
s Sq. rt (x^r)
(# of favorable outcomes) / (# of possible outcomes)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

6. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
83.3%
(n-1)!
1/16
347

7. Prime Factorization to find Greatest Common Factor
180(n-2)
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
Sum of digits is multiple of 3

8. 1/6 = what %
The probability of event occurring is...
16.6%
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

9. Permutations: Order Matters
n! / (n - r)!
1/16
(amount of change) / (original amount)
Exterior angle d is equal to the sum of the two remote interior angles a and b

10. When you see an equation in factored form in a question?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Divide 4999 by 15 => 333 integers
Immediately UNFACTOR or vice versa
Odd numbers only have ___________

11. How do you multiply roots together.
D or E
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Balancing
Exterior angle d is equal to the sum of the two remote interior angles a and b

12. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
P(event NOT occurring) = 1 - P(event occurring)
market value
The amount after deductions

13. 3rd Rule of Probability: Conditional Probability
(total A) / (total B)
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.
Gross Profit = Selling Price - Cost
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.

14. Gross Profit formula
(total distance) / (total time)
P(E)P(F)
3-4-5 - 5-12-13 - 9-12-15
Gross Profit = Selling Price - Cost

15. Three triangle length patterns
0.15n + 0.08(5) = 0.1(n+5)
3-4-5 - 5-12-13 - 9-12-15
P(E)P(F)
Sum of digits is multiple of 3 - last two digits multiple of 4.

16. How to check for a prime number.

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17. gcd(m,n)*lcm(m,n)
always try to factor
x(sq. rt 3) - x - 2x
Find simple interest then look for the answer that is a little bigger
gcd(m,n)*lcm(m,n) = mn

18. 0! = ?
1
Sum of digits is multiple of 9
p/100 = is/of
The amount after deductions

19. Gross
The total amount before any deductions
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(total distance) / (total time)
1.4

20. How to check whether a number is a multiple of 4.
$11 - 025
If the outcome of one event affects the outcome of the other event.
Find simple interest then look for the answer that is a little bigger
Last two digits are multiple of 4 or the number can be divided by 2 twice.

21. 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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
gcd(m,n)*lcm(m,n) = mn
(sum of bases)(height) / 2
1st Rule of Probability: Basic Rule is what?

22. gcd(m,n)
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.
gcd(m,n)*lcm(m,n) = mn
______ |m-n|
3 - 6 - 9 - 12

23. How to check whether a number is a multiple of 12.
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 3
Sum of digits is multiple of 3 - last two digits multiple of 4.
16.6%

24. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
(# of favorable outcomes) / (# of possible outcomes)
Immediately try factoring/simplifying when possible
22
3 - 6 - 9 - 12

25. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
p/100 = is/of
Find all prime factors

26. 1/8 = what %
Any multiplication involving an even number creates an even product.
12.5%
Purchase price
If the outcome of one event affects the outcome of the other event.

27. Combined Events: Not E = P(not E) = ?
1 - P(E)
Group 1 + Group 2 + Neither - Both = Total
347
Odd numbers only have ___________

28. Multiplication principle
| A union B| = |A| + |B| - |A intersect B|
Purchase price
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
______ |m-n|

29. Indistinguishable events how to find the number of permutations

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30. 45-45-90 triangle basic lengths of sides
n! / (n - r)!
x - x - x(sq. rt 2)
1 - P(E)
3-4-5 - 5-12-13 - 9-12-15

31. How to find all divisors of a number
2 steps
0.15n + 0.08(5) = 0.1(n+5)
Find all prime factors
The amount after deductions

32. In general - medium questions require how many steps to solve?
2 steps
(total distance) / (total time)
P(event NOT occurring) = 1 - P(event occurring)
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 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?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
0.15n + 0.08(5) = 0.1(n+5)
347
gcd(m,n)*lcm(m,n) = mn

34. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
83.3%
P(event NOT occurring) = 1 - P(event occurring)
If the outcome of one event affects the outcome of the other event.

35. Average Rate: Average speed
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
| A union B| = |A| + |B| - |A intersect B|
(total distance) / (total time)

36. The number of ways independent events can occur together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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.
| A union B| = |A| + |B| - |A intersect B|
The total amount before any deductions

37. How to check whether a number is a multiple of 6
Figure out the probability for each individual event. Multiply the individual probabilities together.
Balancing
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
Number is a multiple of 3 and 2

38. Multiples of 3
P(E)P(F)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
83.3%
3 - 6 - 9 - 12

39. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
3-4-5 - 5-12-13 - 9-12-15
1 - P(E)
Exterior angle d is equal to the sum of the two remote interior angles a and b

40. x^r/s = ?
s Sq. rt (x^r)
Figure out the probability for each individual event. Multiply the individual probabilities together.
(total A) / (total B)
Find simple interest then look for the answer that is a little bigger

41. 4th rule of Probability
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%
sum = (average)(number of terms)
P(E)P(F)

42. Compound interest formula
(total distance) / (total time)
P(event NOT occurring) = 1 - P(event occurring)
Principal (1 + interest/number times compounded)^(t)(n)
Odd numbers only have ___________

43. How to check whether number is multiple of 9
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 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 probability of an event occurring plus the probability of the event not occurring = 1
Sum of digits is multiple of 9

44. Trial Problems: look at the probability of NOT OCCURRING
P(E) + P(F) - P(E and F)
180(n-2)
P(event NOT occurring) = 1 - P(event occurring)
2 steps

45. Odd and Even rule.
Sum of digits is multiple of 3
D or E
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Any multiplication involving an even number creates an even product.

46. 3^3 x 4^3 = ?
(total distance) / (total time)
16.6%
12^3
P(E) + P(F) - P(E and F)

47. Percent increase = ?
The probability of an event occurring plus the probability of the event not occurring = 1
(amount of change) / (original amount)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Immediately try factoring/simplifying when possible

48. 2n+1 - 2n+3 - 2n+5
83.3%
y2 - y1 / x2 - x1
3-4-5 - 5-12-13 - 9-12-15
Odd

49. Volume of a sphere
principle (interest rate - in decimal form) (time - in years)
3 - 6 - 9 - 12
4/3 TT r ^3
Sum of digits is multiple of 3

50. 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
at least 3 steps
Principal (1 + interest/number times compounded)^(t)(n)
A = P(1 + r) ^n
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.