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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. 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
Balancing
(total distance) / (total time)
always try to factor
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.

2. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
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
22
1/16
4/3 TT r ^3

3. Average Rate: Average A per B
Find simple interest then look for the answer that is a little bigger
(total A) / (total B)
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
Last two digits are multiple of 4 or the number can be divided by 2 twice.

4. Formula for area of a Trapezoid
The probability of event occurring is...
Minor arc = 2(inscribed angle)
(sum of bases)(height) / 2
(total distance) / (total time)

5. How to check whether a number is a multiple of 4.
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
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(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)

6. Price purchased for by wholesaler
Purchase price
market value
Odd
Sum of digits is multiple of 9

7. gcd(m,n)*lcm(m,n)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
gcd(m,n)*lcm(m,n) = mn
Find all prime factors
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.

8. Percent Formula
(# of favorable outcomes) / (# of possible outcomes)
Figure out the probability for each individual event. Multiply the individual probabilities together.
1 - P(E)
p/100 = is/of

9. Probability and Geometry.
2 steps
If the outcome of one event affects the outcome of the other event.
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
1/16

10. Work problem rule
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.
(total A) / (total B)
Organize into a grid.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

11. Combined Events: E and F
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
1 - P(E)
P(E)P(F)
If the outcome of one event affects the outcome of the other event.

12. x^r/s = ?
The probability of an event occurring plus the probability of the event not occurring = 1
Immediately UNFACTOR or vice versa
s Sq. rt (x^r)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

13. Average Rate: Average speed
n! / (n - r)!
1 - P(E)
P(E) + P(F) - P(E and F)
(total distance) / (total time)

14. Sq. rt(2)
(amount of change) / (original amount)
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.
1.4

15. Multiplication principle
(x-n(n)y-n)
-b +- sq. rt(b^2 - 4ac) / 2a
s Sq. rt (x^r)
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

16. Sq. rt(3)
180(n-2)
(# of favorable outcomes) / (# of possible outcomes)
n! / (n - r)!
1.7

17. Number added or deleted
-b +- sq. rt(b^2 - 4ac) / 2a
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The probability of an event occurring plus the probability of the event not occurring = 1
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

18. What does the Sum of the angles in a Regular Polygon formula look like?
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.
The probability of event occurring is...
180(n-2)
If the outcome of one event affects the outcome of the other event.

19. Dependent events: When are two events said to be dependent events?
D or E
(sum of bases)(height) / 2
If the outcome of one event affects the outcome of the other event.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

20. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
at least 3 steps
Exterior angle d is equal to the sum of the two remote interior angles a and b
The probability of an event occurring plus the probability of the event not occurring = 1

21. When you see an equation in factored form in a question?
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.
Immediately UNFACTOR or vice versa
3-4-5 - 5-12-13 - 9-12-15
83.3%

22. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
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)
Purchase price
12.5%

23. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
gcd(m,n)*lcm(m,n) = mn
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
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
D or E

24. Percent increase = ?
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
Balancing
(amount of change) / (original amount)
D or E

25. 1/8 = what %
2 steps
Principal (1 + interest/number times compounded)^(t)(n)
12.5%
Group 1 + Group 2 + Neither - Both = Total

26. Gross
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
22
The total amount before any deductions

27. 2n+1 - 2n+3 - 2n+5
The probability of an event occurring plus the probability of the event not occurring = 1
(sum of bases)(height) / 2
12^3
Odd

28. 3^3 x 4^3 = ?
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.
always try to factor
12^3
(sum of bases)(height) / 2

29. gcd(m,n)
A = P(1 + r) ^n
p/100 = is/of
______ |m-n|
(total A) / (total B)

30. 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.
1 - P(E)
Principal (1 + interest/number times compounded)^(t)(n)
12^3
1st Rule of Probability: Basic Rule is what?

31. Trial Problems: look at the probability of NOT OCCURRING
gcd(m,n)*lcm(m,n) = mn
P(event NOT occurring) = 1 - P(event occurring)
(total distance) / (total time)
180(n-2)

32. Permutations: Order Matters
14 liters
p/100 = is/of
n! / (n - r)!
83.3%

33. How to find all divisors of a number
Organize into a grid.
Find all prime factors
Even
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

34. How to check whether a number is a multiple of 6
1.4
$11 - 025
Number is a multiple of 3 and 2
Even

35. Indistinguishable events how to find the number of permutations

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36. Set Problems formula
(x-n(n)y-n)
347
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.

37. 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.
The amount after deductions
3 - 6 - 9 - 12
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.

38. 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
s Sq. rt (x^r)
180(n-2)
______ |m-n|
Balancing

39. Triangle abc with d on the outside with a line. What does d = ?
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
Exterior angle d is equal to the sum of the two remote interior angles a and b
Divide 4999 by 15 => 333 integers
1st Rule of Probability: Basic Rule is what?

40. Intersecting Sets
3 - 6 - 9 - 12
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.
The probability of an event occurring plus the probability of the event not occurring = 1
| A union B| = |A| + |B| - |A intersect B|

41. How to find the slope.
Even
3 - 6 - 9 - 12
y2 - y1 / x2 - x1
83.3%

42. How to check whether number is multiple of 9
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.
(total distance) / (total time)
Sum of digits is multiple of 9
2 steps

43. 5/6 = what %
(total distance) / (total time)
83.3%
Divide 4999 by 15 => 333 integers
1 - P(E)

44. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Group 1 + Group 2 + Neither - Both = Total
Minor arc = 2(inscribed angle)
A = P(1 + r) ^n

45. In general - difficult questions require how many steps to solve?
(amount of change) / (original amount)
1/16
at least 3 steps
gcd(m,n)*lcm(m,n) = mn

46. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
P(E)P(F)
s Sq. rt (x^r)
at least 3 steps

47. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Minor arc = 2(inscribed angle)
$11 - 025
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
347

48. Properties of 0
If the outcome of one event affects the outcome of the other event.
at least 3 steps
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
principle (interest rate - in decimal form) (time - in years)

49. Sum of consecutive numbers
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 3
0.15n + 0.08(5) = 0.1(n+5)
sum = (average)(number of terms)

50. Multiples of 3
The amount after deductions
3 - 6 - 9 - 12
1.7
(# of favorable outcomes) / (# of possible outcomes)