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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. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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
Balancing
Find all prime factors

2. 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
Immediately UNFACTOR or vice versa
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

3. 2n - 2n+2 - 2n+4
Even
The probability of an event occurring plus the probability of the event not occurring = 1
P(event NOT occurring) = 1 - P(event occurring)
(sum of bases)(height) / 2

4. gcd(m,n)
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
y2 - y1 / x2 - x1
______ |m-n|
-b +- sq. rt(b^2 - 4ac) / 2a

5. Trial Problems: look at the probability of NOT OCCURRING
Number is a multiple of 3 and 2
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(x-n(n)y-n)
P(event NOT occurring) = 1 - P(event occurring)

6. Properties of 0
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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 3
Purchase price

7. The average of consecutive numbers
Find all prime factors
Minor arc = 2(inscribed angle)
1 - P(E)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

8. The number of outcomes that result in A divided by the total number of possible outcomes.
n! / (n - r)!
x(sq. rt 3) - x - 2x
The probability of event occurring is...
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

9. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
(n-1)!
always try to factor
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)

10. Percent increase = ?
(amount of change) / (original amount)
347
4/3 TT r ^3
(# of favorable outcomes) / (# of possible outcomes)

11. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Immediately try factoring/simplifying when possible
Odd numbers only have ___________
(n-1)!
gcd(m,n)*lcm(m,n) = mn

12. Average Rate: Average speed
Balancing
P(E)P(F)
(total distance) / (total time)
-b +- sq. rt(b^2 - 4ac) / 2a

13. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
principle (interest rate - in decimal form) (time - in years)
(sum of bases)(height) / 2
1 - P(E)
Minor arc = 2(inscribed angle)

14. How to check whether number is multiple of 9
Gross Profit = Selling Price - Cost
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.
Sum of digits is multiple of 9
1.7

15. Sum of consecutive numbers
1.7
22
4/3 TT r ^3
sum = (average)(number of terms)

16. Gross
The total amount before any deductions
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 9
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.

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
1.4
Gross Profit = Selling Price - Cost
The amount after deductions

18. Net
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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
The amount after deductions
3-4-5 - 5-12-13 - 9-12-15

19. x^r/s = ?
s Sq. rt (x^r)
Find simple interest then look for the answer that is a little bigger
The amount after deductions
4/3 TT r ^3

20. 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.
12.5%
The probability of event occurring is...
1st Rule of Probability: Basic Rule is what?
Find all prime factors

21. 0! = ?
1
1st Rule of Probability: Basic Rule is what?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

22. The number of ways independent events can occur together.
x - x - x(sq. rt 2)
12^3
P(event NOT occurring) = 1 - P(event occurring)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

23. Triangle abc with d on the outside with a line. What does d = ?
83.3%
sum = (average)(number of terms)
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)

24. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Immediately UNFACTOR or vice versa
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

25. Price sold for by retailer (after markup)
Sum of digits is multiple of 3 - last two digits multiple of 4.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
market value
(total distance) / (total time)

26. Intersecting Sets
The probability of event occurring is...
12^3
| A union B| = |A| + |B| - |A intersect B|
P(E) + P(F) - P(E and F)

27. When you see an equation in factored form in a question?
The probability of an event occurring plus the probability of the event not occurring = 1
y2 - y1 / x2 - x1
Figure out the probability for each individual event. Multiply the individual probabilities together.
Immediately UNFACTOR or vice versa

28. How to check whether a number is a multiple of 4.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Number is a multiple of 3 and 2
Organize into a grid.

29. Quadratic formula
Principal (1 + interest/number times compounded)^(t)(n)
D or E
3 - 6 - 9 - 12
-b +- sq. rt(b^2 - 4ac) / 2a

30. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 9
4/3 TT r ^3
Divide 4999 by 15 => 333 integers

31. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
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
Group 1 + Group 2 + Neither - Both = Total
Organize into a grid.
22

32. Simple probability
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
16.6%
at least 3 steps
(# of favorable outcomes) / (# of possible outcomes)

33. How to find all divisors of a number
Find all prime factors
(x-n(n)y-n)
1/16
1.4

34. 1/6 = what %
x(sq. rt 3) - x - 2x
Find all prime factors
16.6%
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.

35. 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?
14 liters
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

36. Volume of a sphere
P(E)P(F)
4/3 TT r ^3
Find simple interest then look for the answer that is a little bigger
Figure out the probability for each individual event. Multiply the individual probabilities together.

37. Always try to factor
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
always try to factor
1.4
Purchase price

38. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
0.15n + 0.08(5) = 0.1(n+5)
Figure out the probability for each individual event. Multiply the individual probabilities together.
$11 - 025
1 - P(E)

39. Work problem rule
22
x(sq. rt 3) - x - 2x
(n-1)!
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.

40. 3^3 x 4^3 = ?
3-4-5 - 5-12-13 - 9-12-15
A = P(1 + r) ^n
12^3
Sum of digits is multiple of 3

41. Formula for area of a Trapezoid
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)
at least 3 steps
(sum of bases)(height) / 2
1 - P(E)

42. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
principle (interest rate - in decimal form) (time - in years)
1 - P(E)
Find all prime factors

43. Odd Factors
A = P(1 + r) ^n
Odd numbers only have ___________
x - x - x(sq. rt 2)
P(E) + P(F) - P(E and F)

44. What does the Sum of the angles in a Regular Polygon formula look like?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
180(n-2)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(# of favorable outcomes) / (# of possible outcomes)

45. Indistinguishable events how to find the number of permutations

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46. 4th rule of Probability
1
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)
3-4-5 - 5-12-13 - 9-12-15

47. Compound interest rule
14 liters
347
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.

48. 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
Organize into a grid.
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.
4/3 TT r ^3
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.

49. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Group 1 + Group 2 + Neither - Both = Total
A = P(1 + r) ^n
principle (interest rate - in decimal form) (time - in years)
22

50. 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?
(# of favorable outcomes) / (# of possible outcomes)
0.15n + 0.08(5) = 0.1(n+5)
Even
Purchase price