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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. Triangle abc with d on the outside with a line. What does d = ?
Sum of digits is multiple of 3 - last two digits multiple of 4.
Exterior angle d is equal to the sum of the two remote interior angles a and b
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)
83.3%

2. Sum of consecutive numbers
180(n-2)
sum = (average)(number of terms)
(sum of bases)(height) / 2
______ |m-n|

3. Permutations: Order Matters
n! / (n - r)!
1st Rule of Probability: Basic Rule is what?
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)

4. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
P(E) + P(F) - P(E and F)
(total distance) / (total time)

5. Multiples of 3
(sum of bases)(height) / 2
0.15n + 0.08(5) = 0.1(n+5)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
3 - 6 - 9 - 12

6. 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
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
Balancing
1
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

7. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The probability of an event occurring plus the probability of the event not occurring = 1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(x-n(n)y-n)

8. Sq. rt(2)
Immediately UNFACTOR or vice versa
market value
1.7
1.4

9. Always try to factor
(x-n(n)y-n)
347
always try to factor
Minor arc = 2(inscribed angle)

10. 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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Find all prime factors
at least 3 steps

11. How to check whether a number is a multiple of 6
A = P(1 + r) ^n
1
Number is a multiple of 3 and 2
(amount of change) / (original amount)

12. Percent Formula
p/100 = is/of
2 steps
(# of favorable outcomes) / (# of possible outcomes)
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.

13. To determine the number of integers less than 5000 that are evenly divisible by 15...?
at least 3 steps
Organize into a grid.
Divide 4999 by 15 => 333 integers
Number is a multiple of 3 and 2

14. Odd Factors
Principal (1 + interest/number times compounded)^(t)(n)
gcd(m,n)*lcm(m,n) = mn
Odd numbers only have ___________
(# of favorable outcomes) / (# of possible outcomes)

15. In general - difficult questions require how many steps to solve?
83.3%
at least 3 steps
3-4-5 - 5-12-13 - 9-12-15
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.

16. x^r/s = ?
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)
(total A) / (total B)
3-4-5 - 5-12-13 - 9-12-15
s Sq. rt (x^r)

17. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
Find simple interest then look for the answer that is a little bigger
1.4
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

18. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Gross Profit = Selling Price - Cost
market value
A = P(1 + r) ^n
3-4-5 - 5-12-13 - 9-12-15

19. Volume of a sphere
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
(sum of bases)(height) / 2
4/3 TT r ^3
x(sq. rt 3) - x - 2x

20. Price purchased for by wholesaler
(sum of bases)(height) / 2
Purchase price
| A union B| = |A| + |B| - |A intersect B|
2 steps

21. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
1st Rule of Probability: Basic Rule is what?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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

22. Average Rate: Average A per B
4/3 TT r ^3
Divide 4999 by 15 => 333 integers
1.7
(total A) / (total B)

23. Combined Events: Not E = P(not E) = ?
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)
(sum of bases)(height) / 2
Even

24. Gross Profit formula
Sum of digits is multiple of 3
Purchase price
12.5%
Gross Profit = Selling Price - Cost

25. The number of outcomes that result in A divided by the total number of possible outcomes.
3 - 6 - 9 - 12
Divide 4999 by 15 => 333 integers
The probability of event occurring is...
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

26. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1
The total amount before any deductions

27. How to find all divisors of a number
The probability of event occurring is...
Find all prime factors
Immediately try factoring/simplifying when possible
principle (interest rate - in decimal form) (time - in years)

28. 30-60-90 triangle basic lengths of sides
$11 - 025
x(sq. rt 3) - x - 2x
Exterior angle d is equal to the sum of the two remote interior angles a and 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

29. Probability and Geometry.
1/16
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 number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

30. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
market value
Immediately try factoring/simplifying when possible
Balancing
$11 - 025

31. How to find the slope.
P(event NOT occurring) = 1 - P(event occurring)
y2 - y1 / x2 - x1
Balancing
A = P(1 + r) ^n

32. Prime Factorization to find Greatest Common Factor
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
D or E
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
(# of favorable outcomes) / (# of possible outcomes)

33. 1/8 = what %
Balancing
Figure out the probability for each individual event. Multiply the individual probabilities together.
1.4
12.5%

34. Combined Events: E or F
P(E) + P(F) - P(E and F)
Odd numbers only have ___________
p/100 = is/of
Sum of digits is multiple of 3

35. Intersecting Sets
Immediately try factoring/simplifying when possible
Figure out the probability for each individual event. Multiply the individual probabilities together.
| A union B| = |A| + |B| - |A intersect B|
Last two digits are multiple of 4 or the number can be divided by 2 twice.

36. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
1 - P(E)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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.
Odd

37. gcd(m,n)
(total distance) / (total time)
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 number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
______ |m-n|

38. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Odd numbers only have ___________
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
x(sq. rt 3) - x - 2x
principle (interest rate - in decimal form) (time - in years)

39. How many liters of a solution that is 10% alcohol by volume must be added to 2 liters of a solution that is 50% alcohol by volume to create a solution that is 15% alcohol by volume?
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
The total amount before any deductions
(sum of bases)(height) / 2
14 liters

40. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
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 the outcome of one event affects the outcome of the other event.
x - x - x(sq. rt 2)

41. How to check whether a number is a multiple of 4.
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.
at least 3 steps
market value

42. Set Problems formula
n! / (n - r)!
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(x-n(n)y-n)
0.15n + 0.08(5) = 0.1(n+5)

43. Indistinguishable events how to find the number of permutations

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44. Inscribed Angle - Minor Arc
16.6%
The probability of event occurring is...
Gross Profit = Selling Price - Cost
Minor arc = 2(inscribed angle)

45. Net
Divide 4999 by 15 => 333 integers
Even
If the outcome of one event affects the outcome of the other event.
The amount after deductions

46. 2n+1 - 2n+3 - 2n+5
gcd(m,n)*lcm(m,n) = mn
Odd
Number is a multiple of 3 and 2
(total distance) / (total time)

47. Combined Events: E and F
Sum of digits is multiple of 9
P(E)P(F)
22
1.7

48. 2nd Rule of Probability: P(E) = 1 - P(not E)
Principal (1 + interest/number times compounded)^(t)(n)
Number is a multiple of 3 and 2
The probability of an event occurring plus the probability of the event not occurring = 1
p/100 = is/of

49. To determine multiple-event probability where each individual event must occur in a certain way.
x(sq. rt 3) - x - 2x
347
$11 - 025
Figure out the probability for each individual event. Multiply the individual probabilities together.

50. Three triangle length patterns
180(n-2)
Exterior angle d is equal to the sum of the two remote interior angles a and b
22
3-4-5 - 5-12-13 - 9-12-15