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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. 0! = ?
1
x - x - x(sq. rt 2)
If the outcome of one event affects the outcome of the other event.
A = P(1 + r) ^n

2. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
gcd(m,n)*lcm(m,n) = mn
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Number is a multiple of 3 and 2

3. Formula for Mixed Group problems (involving Both/Neither)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Group 1 + Group 2 + Neither - Both = Total
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(total A) / (total B)

4. In general - medium questions require how many steps to solve?
3-4-5 - 5-12-13 - 9-12-15
1 - P(E)
2 steps
n! / (n - r)!

5. Gross Profit formula
Gross Profit = Selling Price - Cost
P(event NOT occurring) = 1 - P(event occurring)
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
Sum of digits is multiple of 9

6. Always try to factor
Gross Profit = Selling Price - Cost
always try to factor
Immediately UNFACTOR or vice versa
(n-1)!

7. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(x-n(n)y-n)
-b +- sq. rt(b^2 - 4ac) / 2a

8. x^r/s = ?
Minor arc = 2(inscribed angle)
If the outcome of one event affects the outcome of the other event.
s Sq. rt (x^r)
P(E) + P(F) - P(E and F)

9. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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
Immediately try factoring/simplifying when possible
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
D or E

10. How to check whether a number is a multiple of 3.
The probability of an event occurring plus the probability of the event not occurring = 1
-b +- sq. rt(b^2 - 4ac) / 2a
Sum of digits is multiple of 3
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

11. Quadratic formula
x(sq. rt 3) - x - 2x
-b +- sq. rt(b^2 - 4ac) / 2a
y2 - y1 / x2 - x1
market value

12. Combined Events: E or F
Exterior angle d is equal to the sum of the two remote interior angles a and b
P(E) + P(F) - P(E and F)
n! / (n - 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

13. The average of consecutive numbers
1.7
P(E)P(F)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(total distance) / (total time)

14. Intersecting Sets
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The total amount before any deductions
| A union B| = |A| + |B| - |A intersect B|
-b +- sq. rt(b^2 - 4ac) / 2a

15. 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?
1 - P(E)
14 liters
2 steps
x - x - x(sq. rt 2)

16. How to find all divisors of a number
| A union B| = |A| + |B| - |A intersect B|
sum = (average)(number of terms)
Find all prime factors
Even

17. 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
s Sq. rt (x^r)
16.6%
12.5%

18. Sq. rt(2)
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
Sum of digits is multiple of 9
1
1.4

19. Compound interest rule
Find simple interest then look for the answer that is a little bigger
| A union B| = |A| + |B| - |A intersect B|
(n-1)!
If the outcome of one event affects the outcome of the other event.

20. How to find the slope.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
market value
y2 - y1 / x2 - x1
Sum of digits is multiple of 3

21. 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
p/100 = is/of
Balancing
Any multiplication involving an even number creates an even product.
Last two digits are multiple of 4 or the number can be divided by 2 twice.

22. Simple probability
Gross Profit = Selling Price - Cost
(# of favorable outcomes) / (# of possible outcomes)
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
Purchase price

23. The number of outcomes that result in A divided by the total number of possible outcomes.
(sum of bases)(height) / 2
Sum of digits is multiple of 3
Principal (1 + interest/number times compounded)^(t)(n)
The probability of event occurring is...

24. Combined Events: Not E = P(not E) = ?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1 - P(E)
1
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

25. Three triangle length patterns
If the outcome of one event affects the outcome of the other event.
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
3-4-5 - 5-12-13 - 9-12-15
sum = (average)(number of terms)

26. How to check whether number is multiple of 9
Organize into a grid.
x(sq. rt 3) - x - 2x
12.5%
Sum of digits is multiple of 9

27. Price purchased for by wholesaler
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Purchase price
22
D or E

28. (1/4)^2
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
4/3 TT r ^3
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

29. Gross
14 liters
A = P(1 + r) ^n
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
The total amount before any deductions

30. Odd and Even rule.
3-4-5 - 5-12-13 - 9-12-15
1st Rule of Probability: Basic Rule is what?
Any multiplication involving an even number creates an even product.
D or E

31. 1/8 = what %
12.5%
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
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

32. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
14 liters
sum = (average)(number of terms)
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 3 - last two digits multiple of 4.

33. How to check whether a number is a multiple of 4.
Immediately try factoring/simplifying when possible
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.

34. 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.
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.
1.4
0.15n + 0.08(5) = 0.1(n+5)

35. Inscribed Angle - Minor Arc
| A union B| = |A| + |B| - |A intersect B|
4/3 TT r ^3
Minor arc = 2(inscribed angle)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

36. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
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.
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
0.15n + 0.08(5) = 0.1(n+5)

37. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
The amount after deductions
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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

38. Multiples of 3
Immediately try factoring/simplifying when possible
3 - 6 - 9 - 12
P(event NOT occurring) = 1 - P(event occurring)
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. 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
$11 - 025
3-4-5 - 5-12-13 - 9-12-15
(amount of change) / (original amount)

40. 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.
0.15n + 0.08(5) = 0.1(n+5)
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
1st Rule of Probability: Basic Rule is what?

41. Volume of a sphere
sum = (average)(number of terms)
The probability of an event occurring plus the probability of the event not occurring = 1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
4/3 TT r ^3

42. 2nd Rule of Probability: P(E) = 1 - P(not E)
Immediately try factoring/simplifying when possible
(total distance) / (total time)
The probability of an event occurring plus the probability of the event not occurring = 1
p/100 = is/of

43. Indistinguishable events how to find the number of permutations

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44. Sum of consecutive numbers
The probability of event occurring is...
sum = (average)(number of terms)
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)
Sum of digits is multiple of 9

45. 1/6 = what %
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
P(E) + P(F) - P(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
16.6%

46. Triangle abc with d on the outside with a line. What does d = ?
12^3
x(sq. rt 3) - x - 2x
Exterior angle d is equal to the sum of the two remote interior angles a and b
Group 1 + Group 2 + Neither - Both = Total

47. When you see an equation in factored form in a question?
1/16
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately UNFACTOR or vice versa
Minor arc = 2(inscribed angle)

48. Properties of 0
347
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(amount of change) / (original amount)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

49. Probability and Geometry.
sum = (average)(number of terms)
12^3
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
Last two digits are multiple of 4 or the number can be divided by 2 twice.

50. gcd(m,n)*lcm(m,n)
n! / (n - r)!
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)
(amount of change) / (original amount)
gcd(m,n)*lcm(m,n) = mn