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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. What does the Sum of the angles in a Regular Polygon formula look like?
Sum of digits is multiple of 9
y2 - y1 / x2 - x1
(x-n(n)y-n)
180(n-2)

2. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
always try to factor
(sum of bases)(height) / 2
The amount after deductions

3. 45-45-90 triangle basic lengths of sides
1.4
x - x - x(sq. rt 2)
Sum of digits is multiple of 9
Any multiplication involving an even number creates an even product.

4. In general - difficult questions require how many steps to solve?
______ |m-n|
at least 3 steps
A = P(1 + r) ^n
Balancing

5. Set Problems formula
(x-n(n)y-n)
The amount after deductions
Balancing
12.5%

6. Formula for area of a Trapezoid
1.7
Sum of digits is multiple of 9
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(sum of bases)(height) / 2

7. The average of consecutive numbers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(event NOT occurring) = 1 - P(event occurring)

8. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
The amount after deductions
(amount of change) / (original amount)
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

9. Volume of a sphere
12.5%
4/3 TT r ^3
83.3%
Sum of digits is multiple of 3

10. 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?
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
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
0.15n + 0.08(5) = 0.1(n+5)
sum = (average)(number of terms)

11. Average Rate: Average A per B
(total A) / (total B)
______ |m-n|
4/3 TT r ^3
Sum of digits is multiple of 9

12. 1/6 = what %
16.6%
sum = (average)(number of terms)
Immediately UNFACTOR or vice versa
3-4-5 - 5-12-13 - 9-12-15

13. Gross
1/16
Organize into a grid.
The total amount before any deductions
Find all prime factors

14. Odd and Even rule.
Any multiplication involving an even number creates an even product.
1
Gross Profit = Selling Price - Cost
Number is a multiple of 3 and 2

15. (1/4)^2
Odd numbers only have ___________
1.7
1/16
y2 - y1 / x2 - x1

16. Number added or deleted
83.3%
Group 1 + Group 2 + Neither - Both = Total
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.

17. Sq. rt(2)
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.
Odd
1.4
12.5%

18. Combined Events: E or F
P(E) + P(F) - P(E and F)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Organize into a grid.
Find all prime factors

19. How to find the slope.
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 3 - last two digits multiple of 4.
y2 - y1 / x2 - x1
180(n-2)

20. Average Rate: Average speed
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.
(x-n(n)y-n)
(total distance) / (total time)
principle (interest rate - in decimal form) (time - in years)

21. 30-60-90 triangle basic lengths of sides
The total amount before any deductions
Number is a multiple of 3 and 2
x(sq. rt 3) - x - 2x
347

22. When you see an equation in factored form in a question?
Immediately try factoring/simplifying when possible
| A union B| = |A| + |B| - |A intersect B|
Gross Profit = Selling Price - Cost
Immediately UNFACTOR or vice versa

23. Properties of 0
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
1st Rule of Probability: Basic Rule is what?
1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

24. 2n+1 - 2n+3 - 2n+5
always try to factor
(x-n(n)y-n)
Odd
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

25. Indistinguishable events how to find the number of permutations

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26. 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
2 steps
The probability of an event occurring plus the probability of the event not occurring = 1
12^3

27. Compound interest formula
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.
Number is a multiple of 3 and 2
Principal (1 + interest/number times compounded)^(t)(n)

28. Net
The probability of event occurring is...
Number is a multiple of 3 and 2
The amount after deductions
The total amount before any deductions

29. Work problem rule
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Sum of digits is multiple of 3
| A union B| = |A| + |B| - |A intersect B|
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.

30. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
at least 3 steps
3 - 6 - 9 - 12
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. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
22
-b +- sq. rt(b^2 - 4ac) / 2a
If the outcome of one event affects the outcome of the other event.

32. 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?
(amount of change) / (original amount)
(x-n(n)y-n)
14 liters
p/100 = is/of

33. How to check whether a number is a multiple of 6
at least 3 steps
gcd(m,n)*lcm(m,n) = mn
Number is a multiple of 3 and 2
(total distance) / (total time)

34. Odd Factors
14 liters
1/16
Odd numbers only have ___________
at least 3 steps

35. x^r/s = ?
Purchase price
Sum of digits is multiple of 3 - last two digits multiple of 4.
s Sq. rt (x^r)
3 - 6 - 9 - 12

36. Dependent events: When are two events said to be dependent events?
Find simple interest then look for the answer that is a little bigger
Balancing
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
If the outcome of one event affects the outcome of the other event.

37. How do you multiply roots together.
The probability of an event occurring plus the probability of the event not occurring = 1
1
Find all prime factors
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

38. How to check whether number is multiple of 9
Sum of digits is multiple of 9
The probability of event occurring is...
(x-n(n)y-n)
1st Rule of Probability: Basic Rule is what?

39. Prime Factorization to find Greatest Common Factor
Number is a multiple of 3 and 2
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
14 liters
12^3

40. 4th rule of Probability
12^3
Principal (1 + interest/number times compounded)^(t)(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)
Immediately UNFACTOR or vice versa

41. Combined Events: Not E = P(not E) = ?
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.
1
Exterior angle d is equal to the sum of the two remote interior angles a and b

42. The number of outcomes that result in A divided by the total number of possible outcomes.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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
______ |m-n|
The probability of event occurring is...

43. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
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.
22
12.5%
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

44. Triangle abc with d on the outside with a line. What does d = ?
1/16
market value
1st Rule of Probability: Basic Rule is what?
Exterior angle d is equal to the sum of the two remote interior angles a and b

45. Multiples of 3
at least 3 steps
______ |m-n|
(sum of bases)(height) / 2
3 - 6 - 9 - 12

46. Sum of consecutive 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
The probability of event occurring is...
sum = (average)(number of terms)
Purchase price

47. To determine multiple-event probability where each individual event must occur in a certain way.
1/16
Figure out the probability for each individual event. Multiply the individual probabilities together.
(total A) / (total B)
Group 1 + Group 2 + Neither - Both = Total

48. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(n-1)!
If the outcome of one event affects the outcome of the other event.
p/100 = is/of

49. The number of ways independent events can occur together.
Immediately UNFACTOR or vice versa
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.
347

50. Inscribed Angle - Minor Arc
$11 - 025
principle (interest rate - in decimal form) (time - in years)
Minor arc = 2(inscribed angle)
-b +- sq. rt(b^2 - 4ac) / 2a