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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. Permutations: Order Matters
If the outcome of one event affects the outcome of the other event.
1
n! / (n - r)!
3 - 6 - 9 - 12

2. How to check whether a number is a multiple of 3.
Find all prime factors
Purchase price
Sum of digits is multiple of 3
Even

3. Volume of a sphere
principle (interest rate - in decimal form) (time - in years)
D or E
4/3 TT r ^3
Balancing

4. (1/4)^2
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1/16
always try to factor
The probability of an event occurring plus the probability of the event not occurring = 1

5. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
always try to factor
Even
at least 3 steps

6. The number of outcomes that result in A divided by the total number of possible outcomes.
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
2 steps
s Sq. rt (x^r)
The probability of event occurring is...

7. Sum of consecutive numbers
sum = (average)(number of terms)
(total distance) / (total time)
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.
1 - P(E)

8. Average Rate: Average speed
Divide 4999 by 15 => 333 integers
(total distance) / (total time)
2 steps
1

9. Percent increase = ?
(amount of change) / (original amount)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Find all prime factors
A = P(1 + r) ^n

10. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
If the outcome of one event affects the outcome of the other event.
P(E) + P(F) - P(E and F)
sum = (average)(number of terms)

11. 3^3 x 4^3 = ?
22
(# of favorable outcomes) / (# of possible outcomes)
12^3
The probability of an event occurring plus the probability of the event not occurring = 1

12. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
12^3
$11 - 025
A = P(1 + r) ^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)

13. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
(amount of change) / (original amount)
22
Immediately UNFACTOR or vice versa
16.6%

14. How to find all divisors of a number
The total amount before any deductions
Divide 4999 by 15 => 333 integers
Find all prime factors
Number is a multiple of 3 and 2

15. In general - medium questions require how many steps to solve?
2 steps
Odd numbers only have ___________
Sum of digits is multiple of 3
If the outcome of one event affects the outcome of the other event.

16. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
p/100 = is/of
1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(sum of bases)(height) / 2

17. Compound interest rule
Find simple interest then look for the answer that is a little bigger
at least 3 steps
Odd numbers only have ___________
| A union B| = |A| + |B| - |A intersect B|

18. Set Problems formula
at least 3 steps
(x-n(n)y-n)
(n-1)!
The amount after deductions

19. Compound interest formula
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
1
Principal (1 + interest/number times compounded)^(t)(n)
n! / (n - r)!

20. How to check whether number is multiple of 9
Principal (1 + interest/number times compounded)^(t)(n)
(x-n(n)y-n)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 9

21. Properties of 0
Even
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1
______ |m-n|

22. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
14 liters
347
Balancing
Gross Profit = Selling Price - Cost

23. How to find the slope.
180(n-2)
y2 - y1 / x2 - x1
Purchase price
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

24. 2n - 2n+2 - 2n+4
Even
14 liters
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)
-b +- sq. rt(b^2 - 4ac) / 2a

25. 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
Odd
Find all prime factors
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.
Number is a multiple of 3 and 2

26. Sq. rt(2)
The probability of event occurring is...
22
Immediately UNFACTOR or vice versa
1.4

27. Multiplication principle
s Sq. rt (x^r)
1/16
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
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.

28. Net
s Sq. rt (x^r)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The amount after deductions
The probability of an event occurring plus the probability of the event not occurring = 1

29. Prime Factorization to find Greatest Common Factor
(sum of bases)(height) / 2
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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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

30. Formula for Mixed Group problems (involving Both/Neither)
347
(sum of bases)(height) / 2
Group 1 + Group 2 + Neither - Both = Total
(x-n(n)y-n)

31. gcd(m,n)*lcm(m,n)
Odd numbers only have ___________
Minor arc = 2(inscribed angle)
22
gcd(m,n)*lcm(m,n) = mn

32. To determine the number of integers less than 5000 that are evenly divisible by 15...?
4/3 TT r ^3
Immediately UNFACTOR or vice versa
Divide 4999 by 15 => 333 integers
Sum of digits is multiple of 9

33. 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.
gcd(m,n)*lcm(m,n) = mn
P(E) + P(F) - P(E and F)
16.6%

34. How to check whether a number is a multiple of 6
16.6%
p/100 = is/of
Number is a multiple of 3 and 2
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

35. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
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)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
$11 - 025

36. What to do with equations that have fractions
Balancing
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Immediately try factoring/simplifying when possible
(total A) / (total B)

37. Percent Formula
The probability of an event occurring plus the probability of the event not occurring = 1
Figure out the probability for each individual event. Multiply the individual probabilities together.
p/100 = is/of
1.7

38. Price sold for by retailer (after markup)
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.
market value
4/3 TT r ^3

39. Odd and Even rule.
| A union B| = |A| + |B| - |A intersect B|
market value
Any multiplication involving an even number creates an even product.
-b +- sq. rt(b^2 - 4ac) / 2a

40. The average of consecutive numbers
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
12.5%
Even

41. Dependent events: When are two events said to be dependent events?
Minor arc = 2(inscribed angle)
If the outcome of one event affects the outcome of the other event.
12.5%
P(event NOT occurring) = 1 - P(event occurring)

42. 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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
always try to factor
______ |m-n|

43. 1/8 = what %
(x-n(n)y-n)
1/16
12.5%
Last two digits are multiple of 4 or the number can be divided by 2 twice.

44. 4th rule of Probability
y2 - y1 / x2 - x1
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)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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.

45. What does the Sum of the angles in a Regular Polygon formula look like?
A = P(1 + r) ^n
180(n-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.
y2 - y1 / x2 - x1

46. Odd Factors
Number is a multiple of 3 and 2
Immediately UNFACTOR or vice versa
Odd numbers only have ___________
Last two digits are multiple of 4 or the number can be divided by 2 twice.

47. 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.
1st Rule of Probability: Basic Rule is what?
(x-n(n)y-n)
1/16
(n-1)!

48. 5/6 = what %
83.3%
D or E
2 steps
Immediately UNFACTOR or vice versa

49. 45-45-90 triangle basic lengths of sides
1
x - x - x(sq. rt 2)
Immediately try factoring/simplifying when possible
The amount after deductions

50. Inscribed Angle - Minor Arc
P(event NOT occurring) = 1 - P(event occurring)
y2 - y1 / x2 - x1
Minor arc = 2(inscribed angle)
principle (interest rate - in decimal form) (time - in years)