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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. Sq. rt(3)
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
x(sq. rt 3) - x - 2x
Number is a multiple of 3 and 2
1.7

2. Formula for Mixed Group problems (involving Both/Neither)
p/100 = is/of
Group 1 + Group 2 + Neither - Both = Total
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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.

3. x^r/s = ?
Purchase price
1.7
s Sq. rt (x^r)
______ |m-n|

4. Price sold for by retailer (after markup)
market value
D or 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.
| A union B| = |A| + |B| - |A intersect B|

5. 2nd Rule of Probability: P(E) = 1 - P(not E)
Sum of digits is multiple of 3 - last two digits multiple of 4.
The probability of an event occurring plus the probability of the event not occurring = 1
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(# of favorable outcomes) / (# of possible outcomes)

6. Compound interest rule
Any multiplication involving an even number creates an even product.
$11 - 025
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
Find simple interest then look for the answer that is a little bigger

7. Average Rate: Average speed
Sum of digits is multiple of 3 - last two digits multiple of 4.
(# of favorable outcomes) / (# of possible outcomes)
(total distance) / (total time)
at least 3 steps

8. Three triangle length patterns
$11 - 025
Immediately try factoring/simplifying when possible
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
3-4-5 - 5-12-13 - 9-12-15

9. 2n+1 - 2n+3 - 2n+5
(amount of change) / (original amount)
y2 - y1 / x2 - x1
Odd
3 - 6 - 9 - 12

10. Always try to factor
always try to factor
Immediately try factoring/simplifying when possible
P(E)P(F)
Sum of digits is multiple of 3 - last two digits multiple of 4.

11. Set Problems formula
Principal (1 + interest/number times compounded)^(t)(n)
3 - 6 - 9 - 12
(x-n(n)y-n)
P(E) + P(F) - P(E and F)

12. How to check whether a number is a multiple of 3.
(# of favorable outcomes) / (# of possible outcomes)
Sum of digits is multiple of 3
always try to factor
x(sq. rt 3) - x - 2x

13. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Find all prime factors
(n-1)!
Exterior angle d is equal to the sum of the two remote interior angles a and b
(total A) / (total B)

14. How do you multiply roots together.
The probability of an event occurring plus the probability of the event not occurring = 1
sum = (average)(number of terms)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.

15. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
P(event NOT occurring) = 1 - P(event occurring)
If the outcome of one event affects the outcome of the other event.
16.6%

16. When you see an equation in factored form in a question?
Exterior angle d is equal to the sum of the two remote interior angles a and b
Immediately UNFACTOR or vice versa
(total A) / (total B)
Purchase price

17. In general - difficult questions require how many steps to solve?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
at least 3 steps
14 liters
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

18. Compound interest formula
(total A) / (total B)
x - x - x(sq. rt 2)
Principal (1 + interest/number times compounded)^(t)(n)
Odd

19. Inscribed Angle - Minor Arc
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.
Minor arc = 2(inscribed angle)
1
Number is a multiple of 3 and 2

20. Gross
A = P(1 + r) ^n
The total amount before any deductions
The probability of event occurring is...
22

21. Intersecting Sets
Purchase price
| A union B| = |A| + |B| - |A intersect B|
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 3 - last two digits multiple of 4.

22. Combined Events: E and F
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
P(E)P(F)
sum = (average)(number of terms)
D or E

23. 1/8 = what %
$11 - 025
______ |m-n|
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.
12.5%

24. 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
83.3%
The amount after deductions
Balancing
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.

25. 3rd Rule of Probability: Conditional Probability
180(n-2)
22
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

26. Sq. rt(2)
1.4
Odd numbers only have ___________
x(sq. rt 3) - x - 2x
Divide 4999 by 15 => 333 integers

27. Formula for area of a Trapezoid
0.15n + 0.08(5) = 0.1(n+5)
(sum of bases)(height) / 2
1st Rule of Probability: Basic Rule is what?
n! / (n - r)!

28. 5/6 = what %
22
(# of favorable outcomes) / (# of possible outcomes)
83.3%
Find all prime factors

29. Odd and Even rule.
Any multiplication involving an even number creates an even product.
Principal (1 + interest/number times compounded)^(t)(n)
16.6%
0.15n + 0.08(5) = 0.1(n+5)

30. To determine the number of integers less than 5000 that are evenly divisible by 15...?
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)
Divide 4999 by 15 => 333 integers
Sum of digits is multiple of 3
at least 3 steps

31. Permutations: Order Matters
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
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)
n! / (n - r)!

32. Properties of 0
3 - 6 - 9 - 12
(total A) / (total B)
sum = (average)(number of terms)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

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?
A = P(1 + r) ^n
0.15n + 0.08(5) = 0.1(n+5)
1
If the outcome of one event affects the outcome of the other event.

34. Dependent events: When are two events said to be dependent events?
P(event NOT occurring) = 1 - P(event occurring)
If the outcome of one event affects the outcome of the other event.
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)
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.

35. Quadratic formula
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.
1/16
1.4
-b +- sq. rt(b^2 - 4ac) / 2a

36. Net
The amount after deductions
Find simple interest then look for the answer that is a little bigger
Odd numbers only have ___________
1.7

37. Simple probability
Find simple interest then look for the answer that is a little bigger
(# of favorable outcomes) / (# of possible outcomes)
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. 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.

38. Some GMAT word problems involve groups with distinct 'either/or' categories (male/female - blue collar/white collar - etc.) The key is to do what with the information? 1. Find total number of possible outcomes. 2. Find the number of desired outcomes.
16.6%
Organize into a grid.
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 A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.

39. Gross Profit formula
22
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Gross Profit = Selling Price - Cost

40. Multiplication principle
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
1.4
12.5%
83.3%

41. 2n - 2n+2 - 2n+4
Even
(n-1)!
______ |m-n|
The probability of event occurring is...

42. 0! = ?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1
Balancing
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

43. Combined Events: Not E = P(not E) = ?
The total amount before any deductions
12.5%
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 - P(E)

44. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
Immediately UNFACTOR or vice versa
(n-1)!
-b +- sq. rt(b^2 - 4ac) / 2a

45. How to check for a prime number.

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46. 45-45-90 triangle basic lengths of sides
1.7
Sum of digits is multiple of 9
347
x - x - x(sq. rt 2)

47. Sum of consecutive numbers
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
sum = (average)(number of terms)
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
at least 3 steps

48. Odd Factors
Divide 4999 by 15 => 333 integers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Odd numbers only have ___________
3-4-5 - 5-12-13 - 9-12-15

49. Combined Events: E or F
(amount of change) / (original amount)
P(E) + P(F) - P(E and F)
x(sq. rt 3) - x - 2x
Figure out the probability for each individual event. Multiply the individual probabilities together.

50. 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?
Immediately try factoring/simplifying when possible
The amount after deductions
22