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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. 3rd Rule of Probability: Conditional Probability
sum = (average)(number of terms)
(x-n(n)y-n)
P(E) + P(F) - P(E and F)
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.

2. 0! = ?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
$11 - 025

3. How to check whether a number is a multiple of 3.
x - x - x(sq. rt 2)
Sum of digits is multiple of 3
sum = (average)(number of terms)
| A union B| = |A| + |B| - |A intersect B|

4. 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
(# of favorable outcomes) / (# of possible outcomes)
P(E)P(F)
Find all prime factors
Balancing

5. What to do with equations that have fractions
(sum of bases)(height) / 2
p/100 = is/of
n! / (n - r)!
Immediately try factoring/simplifying when possible

6. 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?
0.15n + 0.08(5) = 0.1(n+5)
Number is a multiple of 3 and 2
1.7
14 liters

7. How to check whether a number is a multiple of 6
P(E)P(F)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Number is a multiple of 3 and 2
at least 3 steps

8. Average Rate: Average A per 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.
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.
(total A) / (total B)

9. Formula for area of a Trapezoid
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
Principal (1 + interest/number times compounded)^(t)(n)
(sum of bases)(height) / 2
Balancing

10. Sq. rt(3)
y2 - y1 / x2 - x1
1.7
0.15n + 0.08(5) = 0.1(n+5)
1/16

11. 45-45-90 triangle basic lengths of sides
(x-n(n)y-n)
3 - 6 - 9 - 12
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
x - x - x(sq. rt 2)

12. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
1.7
P(E) + P(F) - P(E and F)
The total amount before any deductions

13. The average of consecutive numbers
2 steps
(x-n(n)y-n)
3 - 6 - 9 - 12
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

14. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
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.
Exterior angle d is equal to the sum of the two remote interior angles a and b
(n-1)!

15. x^r/s = ?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Odd numbers only have ___________
Last two digits are multiple of 4 or the number can be divided by 2 twice.
s Sq. rt (x^r)

16. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
| A union B| = |A| + |B| - |A intersect B|
Immediately UNFACTOR or vice versa
Gross Profit = Selling Price - Cost

17. How to find the slope.
(x-n(n)y-n)
y2 - y1 / x2 - x1
always try to factor
The total amount before any deductions

18. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
(total A) / (total B)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
180(n-2)

19. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
3 - 6 - 9 - 12
2 steps
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.
347

20. Prime Factorization to find Greatest Common Factor
Number is a multiple of 3 and 2
(n-1)!
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
1.4

21. How to check for a prime number.

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22. Formula for Mixed Group problems (involving Both/Neither)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Sum of digits is multiple of 3
Group 1 + Group 2 + Neither - Both = Total
(# of favorable outcomes) / (# of possible outcomes)

23. 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?
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
market value
Sum of digits is multiple of 9

24. Set Problems formula
3 - 6 - 9 - 12
(x-n(n)y-n)
14 liters
gcd(m,n)*lcm(m,n) = mn

25. Three triangle length patterns
p/100 = is/of
3-4-5 - 5-12-13 - 9-12-15
(total A) / (total B)
Sum of digits is multiple of 3 - last two digits multiple of 4.

26. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
347
market value
(x-n(n)y-n)

27. 4th rule of Probability
(x-n(n)y-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)
Odd numbers only have ___________
If the outcome of one event affects the outcome of the other event.

28. 2n - 2n+2 - 2n+4
3-4-5 - 5-12-13 - 9-12-15
12.5%
P(E) + P(F) - P(E and F)
Even

29. 3^3 x 4^3 = ?
The probability of an event occurring plus the probability of the event not occurring = 1
at least 3 steps
12^3
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.

30. Percent Formula
-b +- sq. rt(b^2 - 4ac) / 2a
______ |m-n|
347
p/100 = is/of

31. Sq. rt(2)
Sum of digits is multiple of 9
1.4
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.
(total distance) / (total time)

32. The number of ways independent events can occur together.
p/100 = is/of
Divide 4999 by 15 => 333 integers
The amount after deductions
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

33. Work problem rule
16.6%
Even
1 - P(E)
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.

34. Probability and Geometry.
The probability of an event occurring plus the probability of the event not occurring = 1
(total A) / (total B)
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
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. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Sum of digits is multiple of 3
1.4

36. 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
P(event NOT occurring) = 1 - P(event occurring)
180(n-2)
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.
at least 3 steps

37. 2nd Rule of Probability: P(E) = 1 - P(not 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
(n-1)!
The probability of an event occurring plus the probability of the event not occurring = 1
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

38. Compound interest rule
(amount of change) / (original amount)
Minor arc = 2(inscribed angle)
Find simple interest then look for the answer that is a little bigger
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)

39. 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
4/3 TT r ^3
y2 - y1 / x2 - x1
347

40. Average Rate: Average speed
22
always try to factor
(total distance) / (total time)
1

41. Number added or deleted
83.3%
D or E
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
sum = (average)(number of terms)

42. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
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
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

43. Sum of consecutive numbers
Purchase price
P(E) + P(F) - P(E and F)
3-4-5 - 5-12-13 - 9-12-15
sum = (average)(number of terms)

44. Compound interest formula
16.6%
x(sq. rt 3) - x - 2x
Principal (1 + interest/number times compounded)^(t)(n)
Group 1 + Group 2 + Neither - Both = Total

45. Permutations: Order Matters
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.
Figure out the probability for each individual event. Multiply the individual probabilities together.
n! / (n - r)!
347

46. Net
Principal (1 + interest/number times compounded)^(t)(n)
The amount after deductions
1 - P(E)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

47. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Sum of digits 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.

48. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
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
0.15n + 0.08(5) = 0.1(n+5)
Principal (1 + interest/number times compounded)^(t)(n)

49. Combined Events: E or F
P(E) + P(F) - P(E and F)
(total distance) / (total time)
12.5%
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

50. How to check whether a number is a multiple of 4.
Odd
Organize into a grid.
market value
Last two digits are multiple of 4 or the number can be divided by 2 twice.