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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. 30-60-90 triangle basic lengths of sides
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.
x(sq. rt 3) - x - 2x
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
(sum of bases)(height) / 2

2. Combined Events: E and F
Figure out the probability for each individual event. Multiply the individual probabilities together.
P(E)P(F)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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)

3. In general - difficult questions require how many steps to solve?
16.6%
at least 3 steps
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Principal (1 + interest/number times compounded)^(t)(n)

4. Compound interest formula
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)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
| A union B| = |A| + |B| - |A intersect B|

5. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
83.3%
(total A) / (total B)

6. (1/4)^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.
always try to factor
principle (interest rate - in decimal form) (time - in years)
1/16

7. The number of ways independent events can occur together.
principle (interest rate - in decimal form) (time - in years)
(x-n(n)y-n)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Find all prime factors

8. Net
Sum of digits is multiple of 9
12.5%
The amount after deductions
x - x - x(sq. rt 2)

9. Probability and Geometry.
(total A) / (total B)
Odd
1.4
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

10. Formula for area of a Trapezoid
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.
$11 - 025
(sum of bases)(height) / 2

11. The number of outcomes that result in A divided by the total number of possible outcomes.
Principal (1 + interest/number times compounded)^(t)(n)
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.
Organize into a grid.

12. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
The probability of an event occurring plus the probability of the event not occurring = 1
at least 3 steps
Gross Profit = Selling Price - Cost
$11 - 025

13. Average Rate: Average A per B
(total A) / (total 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.
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.
always try to factor

14. 3rd Rule of Probability: Conditional Probability
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.
180(n-2)
(amount of change) / (original amount)
Immediately try factoring/simplifying when possible

15. Percent increase = ?
The amount after deductions
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Gross Profit = Selling Price - Cost
(amount of change) / (original amount)

16. Dependent events: When are two events said to be dependent events?
(total distance) / (total time)
P(E) + P(F) - P(E and F)
If the outcome of one event affects the outcome of the other event.
The total amount before any deductions

17. How to check for a prime number.

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18. Formula for Mixed Group problems (involving Both/Neither)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(E)P(F)
1.4
Group 1 + Group 2 + Neither - Both = Total

19. 45-45-90 triangle basic lengths of sides
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
s Sq. rt (x^r)
14 liters
x - x - x(sq. rt 2)

20. How do you multiply roots together.
1.7
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)
x(sq. rt 3) - x - 2x

21. Trial Problems: look at the probability of NOT OCCURRING
-b +- sq. rt(b^2 - 4ac) / 2a
If the outcome of one event affects the outcome of the other event.
Organize into a grid.
P(event NOT occurring) = 1 - P(event occurring)

22. To determine the number of integers less than 5000 that are evenly divisible by 15...?
P(E)P(F)
Divide 4999 by 15 => 333 integers
16.6%
(total A) / (total B)

23. 1/6 = what %
14 liters
principle (interest rate - in decimal form) (time - in years)
16.6%
The total amount before any deductions

24. x^r/s = ?
(sum of bases)(height) / 2
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.
4/3 TT r ^3
s Sq. rt (x^r)

25. 2n+1 - 2n+3 - 2n+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.
(# 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
Odd

26. Sq. rt(2)
1.4
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.
p/100 = is/of

27. Odd Factors
Any multiplication involving an even number creates an even product.
Odd numbers only have ___________
Immediately try factoring/simplifying when possible
12^3

28. Volume of a sphere
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The total amount before any deductions
Exterior angle d is equal to the sum of the two remote interior angles a and b
4/3 TT r ^3

29. Number added or deleted
| A union B| = |A| + |B| - |A intersect B|
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

30. 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.
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.
16.6%
1st Rule of Probability: Basic Rule is what?
1 - P(E)

31. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Principal (1 + interest/number times compounded)^(t)(n)
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. gcd(m,n)
1.4
Minor arc = 2(inscribed angle)
347
______ |m-n|

33. 4th rule of Probability
Exterior angle d is equal to the sum of the two remote interior angles a and b
Group 1 + Group 2 + Neither - Both = Total
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)

34. Lowest Common Multiple 60: 2 x 2 x 3 x 5 - 72: 2 x 2 x 2 x 3 x 3 - LCM: 2 x 2 x 2 x 3 x 3 x 5
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.
4/3 TT r ^3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
If the outcome of one event affects the outcome of the other event.

35. To determine multiple-event probability where each individual event must occur in a certain way.
(total A) / (total B)
Figure out the probability for each individual event. Multiply the individual probabilities together.
1.7
Last two digits are multiple of 4 or the number can be divided by 2 twice.

36. How to find all divisors of a number
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
Find all prime factors
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

37. Work problem rule
gcd(m,n)*lcm(m,n) = mn
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.
Group 1 + Group 2 + Neither - Both = Total
(n-1)!

38. Combined Events: Not E = P(not E) = ?
12^3
at least 3 steps
3-4-5 - 5-12-13 - 9-12-15
1 - P(E)

39. How to check whether a number is a multiple of 4.
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
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.

40. Multiples of 3
(amount of change) / (original amount)
3 - 6 - 9 - 12
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

41. 0! = ?
1
The probability of an event occurring plus the probability of the event not occurring = 1
always try to factor
market value

42. Set Problems formula
sum = (average)(number of terms)
16.6%
Group 1 + Group 2 + Neither - Both = Total
(x-n(n)y-n)

43. gcd(m,n)*lcm(m,n)
(x-n(n)y-n)
gcd(m,n)*lcm(m,n) = mn
Odd numbers only have ___________
22

44. Properties of 0
The probability of an event occurring plus the probability of the event not occurring = 1
Odd
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
gcd(m,n)*lcm(m,n) = mn

45. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
(total distance) / (total time)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1.4

46. Sum of consecutive numbers
The probability of an event occurring plus the probability of the event not occurring = 1
______ |m-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)
sum = (average)(number of terms)

47. In general - medium questions require how many steps to solve?
2 steps
Find simple interest then look for the answer that is a little bigger
Any multiplication involving an even number creates an even product.
Figure out the probability for each individual event. Multiply the individual probabilities together.

48. 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?
always try to factor
0.15n + 0.08(5) = 0.1(n+5)
Sum of digits is multiple of 3
Number is a multiple of 3 and 2

49. Average Rate: Average speed
Group 1 + Group 2 + Neither - Both = Total
(total distance) / (total time)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
y2 - y1 / x2 - x1

50. Odd and Even rule.
(x-n(n)y-n)
Any multiplication involving an even number creates an even product.
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 3