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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. How to check for a prime number.

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2. The average of consecutive numbers
Organize into a grid.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(# of favorable outcomes) / (# of possible outcomes)
sum = (average)(number of terms)

3. Properties of 0
12^3
sum = (average)(number of terms)
(# of favorable outcomes) / (# of possible outcomes)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

4. Indistinguishable events how to find the number of permutations

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5. Odd and Even rule.
Any multiplication involving an even number creates an even product.
Gross Profit = Selling Price - Cost
y2 - y1 / x2 - x1
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

6. Three triangle length patterns
The amount after deductions
3-4-5 - 5-12-13 - 9-12-15
Organize into a grid.
Gross Profit = Selling Price - Cost

7. Prime Factorization to find Greatest Common Factor
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 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
1/16
12^3

8. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Any multiplication involving an even number creates an even product.
D or E
4/3 TT r ^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)

9. How to check whether a number is a multiple of 3.
1.7
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 3
3-4-5 - 5-12-13 - 9-12-15

10. Price purchased for by wholesaler
Balancing
Purchase price
3-4-5 - 5-12-13 - 9-12-15
(total A) / (total B)

11. x^r/s = ?
s Sq. rt (x^r)
sum = (average)(number of terms)
P(event NOT occurring) = 1 - P(event occurring)
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. Set Problems formula
x(sq. rt 3) - x - 2x
(x-n(n)y-n)
______ |m-n|
Any multiplication involving an even number creates an even product.

13. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
The probability of event occurring is...
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 = P(1 + r) ^n
(x-n(n)y-n)

14. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Find simple interest then look for the answer that is a little bigger
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)

15. How to check whether a number is a multiple of 6
Sum of digits is multiple of 3
2 steps
Principal (1 + interest/number times compounded)^(t)(n)
Number is a multiple of 3 and 2

16. Simple probability
Gross Profit = Selling Price - Cost
3-4-5 - 5-12-13 - 9-12-15
(# 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

17. Permutations: Order Matters
1.4
n! / (n - r)!
p/100 = is/of
-b +- sq. rt(b^2 - 4ac) / 2a

18. Combined Events: E and F
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
P(E)P(F)
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.
16.6%

19. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
4/3 TT r ^3
______ |m-n|
x(sq. rt 3) - x - 2x

20. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
x - x - x(sq. rt 2)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Sum of digits is multiple of 3 - last two digits multiple of 4.

21. Odd Factors
market value
Odd numbers only have ___________
12.5%
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.

22. Probability and Geometry.
0.15n + 0.08(5) = 0.1(n+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
P(event NOT occurring) = 1 - P(event occurring)
180(n-2)

23. 1/6 = what %
The probability of an event occurring plus the probability of the event not occurring = 1
x - x - x(sq. rt 2)
(sum of bases)(height) / 2
16.6%

24. 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?
Immediately UNFACTOR or vice versa
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
14 liters
(amount of change) / (original amount)

25. 0! = ?
1
4/3 TT r ^3
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The probability of an event occurring plus the probability of the event not occurring = 1

26. 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?
Group 1 + Group 2 + Neither - Both = Total
______ |m-n|
0.15n + 0.08(5) = 0.1(n+5)
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.

27. 45-45-90 triangle basic lengths of sides
If the outcome of one event affects the outcome of the other event.
Any multiplication involving an even number creates an even product.
(amount of change) / (original amount)
x - x - x(sq. rt 2)

28. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
The probability of event occurring is...
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.
347
$11 - 025

29. How to check whether a number is a multiple of 12.
Divide 4999 by 15 => 333 integers
Sum of digits is multiple of 3 - last two digits multiple of 4.
(amount of change) / (original amount)
0.15n + 0.08(5) = 0.1(n+5)

30. Triangle abc with d on the outside with a line. What does d = ?
Principal (1 + interest/number times compounded)^(t)(n)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Exterior angle d is equal to the sum of the two remote interior angles a and b
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.

31. Sq. rt(3)
1.7
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Sum of digits is multiple of 3
Purchase price

32. 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.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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
Minor arc = 2(inscribed angle)
Organize into a grid.

33. 30-60-90 triangle basic lengths of sides
347
principle (interest rate - in decimal form) (time - in years)
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.

34. Compound interest formula
1/16
Principal (1 + interest/number times compounded)^(t)(n)
| A union B| = |A| + |B| - |A intersect B|
Purchase price

35. Net
y2 - y1 / x2 - x1
The amount after deductions
1.7
(amount of change) / (original amount)

36. When you see an equation in factored form in a question?
Purchase price
Sum of digits is multiple of 3
Immediately UNFACTOR or vice versa
83.3%

37. Combined Events: Not E = P(not E) = ?
1 - P(E)
Divide 4999 by 15 => 333 integers
Immediately try factoring/simplifying when possible
Organize into a grid.

38. Trial Problems: look at the probability of NOT OCCURRING
(# of favorable outcomes) / (# of possible outcomes)
Minor arc = 2(inscribed angle)
P(event NOT occurring) = 1 - P(event occurring)
3 - 6 - 9 - 12

39. Gross Profit formula
Gross Profit = Selling Price - Cost
Find simple interest then look for the answer that is a little bigger
Sum of digits is multiple of 3 - last two digits multiple of 4.
Any multiplication involving an even number creates an even product.

40. How to check whether number is multiple of 9
Sum of digits is multiple of 9
______ |m-n|
P(event NOT occurring) = 1 - P(event occurring)
Number is a multiple of 3 and 2

41. Quadratic formula
(total A) / (total B)
P(E) + P(F) - P(E and F)
-b +- sq. rt(b^2 - 4ac) / 2a
The probability of event occurring is...

42. How do you multiply roots together.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Divide 4999 by 15 => 333 integers
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
-b +- sq. rt(b^2 - 4ac) / 2a

43. To determine multiple-event probability where each individual event must occur in a certain way.
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)
Figure out the probability for each individual event. Multiply the individual probabilities together.
Balancing
12^3

44. 5/6 = what %
______ |m-n|
83.3%
Even
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.

45. Price sold for by retailer (after markup)
16.6%
The amount after deductions
0.15n + 0.08(5) = 0.1(n+5)
market value

46. How to find the slope.
Odd
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.
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.
y2 - y1 / x2 - x1

47. The number of outcomes that result in A divided by the total number of possible outcomes.
at least 3 steps
0.15n + 0.08(5) = 0.1(n+5)
The probability of event occurring is...
1.7

48. (1/4)^2
1/16
Purchase price
D or E
x - x - x(sq. rt 2)

49. 2nd Rule of Probability: P(E) = 1 - P(not E)
Odd
1.4
(amount of change) / (original amount)
The probability of an event occurring plus the probability of the event not occurring = 1

50. 2n+1 - 2n+3 - 2n+5
at least 3 steps
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.
Odd