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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 whether a number is a multiple of 6
P(E) + P(F) - P(E and F)
0.15n + 0.08(5) = 0.1(n+5)
Number is a multiple of 3 and 2
(sum of bases)(height) / 2

2. Triangle abc with d on the outside with a line. What does d = ?
12^3
-b +- sq. rt(b^2 - 4ac) / 2a
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.
Exterior angle d is equal to the sum of the two remote interior angles a and b

3. Gross
p/100 = is/of
Gross Profit = Selling Price - Cost
The total amount before any deductions
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.

4. Always try to factor
1/16
3 - 6 - 9 - 12
always try to factor
P(E) + P(F) - P(E and F)

5. 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
y2 - y1 / x2 - x1
Balancing
12.5%
Sum of digits is multiple of 3

6. How to check whether a number is a multiple of 3.
s Sq. rt (x^r)
Sum of digits is multiple of 3
D or E
(sum of bases)(height) / 2

7. Prime Factorization to find Greatest Common 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
y2 - y1 / x2 - x1
Find simple interest then look for the answer that is a little bigger
(sum of bases)(height) / 2

8. 1/6 = what %
P(E)P(F)
16.6%
D or E
(sum of bases)(height) / 2

9. How to find the slope.
1st Rule of Probability: Basic Rule is what?
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
Odd

10. How to find all divisors of a number
1/16
Find all prime factors
1.7
Immediately UNFACTOR or vice versa

11. 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.
y2 - y1 / x2 - x1
(# of favorable outcomes) / (# of possible outcomes)
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.

12. Formula for area of a Trapezoid
D or E
y2 - y1 / x2 - x1
Balancing
(sum of bases)(height) / 2

13. Price purchased for by wholesaler
Purchase price
(x-n(n)y-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
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.

14. Average Rate: Average A per B
(x-n(n)y-n)
Even
P(E) + P(F) - P(E and F)
(total A) / (total B)

15. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
P(event NOT occurring) = 1 - P(event occurring)
16.6%
Exterior angle d is equal to the sum of the two remote interior angles a and b

16. Compound interest formula
(# of favorable outcomes) / (# of possible outcomes)
Principal (1 + interest/number times compounded)^(t)(n)
P(E) + P(F) - P(E and F)
Even

17. 2n+1 - 2n+3 - 2n+5
Any multiplication involving an even number creates an even product.
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.
1 - P(E)
Odd

18. Combined Events: E or F
Divide 4999 by 15 => 333 integers
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)
P(E) + P(F) - P(E and F)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

19. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
gcd(m,n)*lcm(m,n) = mn
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(event NOT occurring) = 1 - P(event occurring)

20. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
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.
A = P(1 + r) ^n
(n-1)!

21. How to check for a prime number.

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22. How to check whether a number is a multiple of 4.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(event NOT occurring) = 1 - P(event occurring)
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.
14 liters

23. Volume of a sphere
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
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
4/3 TT r ^3
1/16

24. What does the Sum of the angles in a Regular Polygon formula look like?
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.
180(n-2)
Principal (1 + interest/number times compounded)^(t)(n)
(total distance) / (total time)

25. 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?
(sum of bases)(height) / 2
0.15n + 0.08(5) = 0.1(n+5)
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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

26. Average Rate: Average speed
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.
(total distance) / (total time)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

27. Trial Problems: look at the probability of NOT OCCURRING
1.4
A = P(1 + r) ^n
3-4-5 - 5-12-13 - 9-12-15
P(event NOT occurring) = 1 - P(event occurring)

28. How do you multiply roots together.
market value
Gross Profit = Selling Price - Cost
p/100 = is/of
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

29. gcd(m,n)
12.5%
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
D or E
______ |m-n|

30. Odd and Even rule.
(amount of change) / (original amount)
Purchase price
P(E) + P(F) - P(E and F)
Any multiplication involving an even number creates an even product.

31. What to do with equations that have fractions
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Immediately try factoring/simplifying when possible
Group 1 + Group 2 + Neither - Both = Total
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

32. How to check whether a number is a multiple of 12.
180(n-2)
Any multiplication involving an even number creates an even product.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Sum of digits is multiple of 3 - last two digits multiple of 4.

33. Work problem rule
s Sq. rt (x^r)
P(E) + P(F) - P(E and F)
______ |m-n|
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.

34. In general - difficult questions require how many steps to solve?
Sum of digits is multiple of 3
Principal (1 + interest/number times compounded)^(t)(n)
at least 3 steps
Gross Profit = Selling Price - Cost

35. The average of consecutive numbers
$11 - 025
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(n-1)!

36. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
Sum of digits is multiple of 9
Odd numbers only have ___________
(n-1)!

37. To determine multiple-event probability where each individual event must occur in a certain way.
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
Sum of digits is multiple of 3 - last two digits multiple of 4.
D or E
Figure out the probability for each individual event. Multiply the individual probabilities together.

38. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
p/100 = is/of

39. Combined Events: Not E = P(not E) = ?
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
Exterior angle d is equal to the sum of the two remote interior angles a and b
16.6%
1 - P(E)

40. Price sold for by retailer (after markup)
at least 3 steps
market value
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.
-b +- sq. rt(b^2 - 4ac) / 2a

41. Multiplication principle
x - x - x(sq. rt 2)
Number is a multiple of 3 and 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
P(E)P(F)

42. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
0.15n + 0.08(5) = 0.1(n+5)
-b +- sq. rt(b^2 - 4ac) / 2a
Sum of digits is multiple of 9

43. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
Odd numbers only have ___________
at least 3 steps
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

44. Intersecting Sets
Sum of digits is multiple of 3 - last two digits multiple of 4.
12^3
| A union B| = |A| + |B| - |A intersect B|
Odd

45. Sq. rt(3)
Purchase price
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.
1.7

46. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
x - x - x(sq. rt 2)
principle (interest rate - in decimal form) (time - in years)
14 liters
gcd(m,n)*lcm(m,n) = mn

47. 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.
(# of favorable outcomes) / (# of possible outcomes)
Organize into a grid.
market value
Last two digits are multiple of 4 or the number can be divided by 2 twice.

48. Quadratic formula
n! / (n - r)!
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.
| A union B| = |A| + |B| - |A intersect B|
-b +- sq. rt(b^2 - 4ac) / 2a

49. Percent increase = ?
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.
If the outcome of one event affects the outcome of the other event.
(total A) / (total B)
(amount of change) / (original amount)

50. Multiples of 3
3 - 6 - 9 - 12
12^3
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
1/16