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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. Triangle abc with d on the outside with a line. What does d = ?
If the outcome of one event affects the outcome of the other event.
Exterior angle d is equal to the sum of the two remote interior angles a and b
1.4
sum = (average)(number of terms)

2. Combined Events: E and F
1.7
12.5%
P(E)P(F)
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. 30-60-90 triangle basic lengths of sides
1st Rule of Probability: Basic Rule is what?
(n-1)!
Last two digits are multiple of 4 or the number can be divided by 2 twice.
x(sq. rt 3) - x - 2x

4. Multiples of 3
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Find simple interest then look for the answer that is a little bigger
3 - 6 - 9 - 12
(total distance) / (total time)

5. 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
1.7
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 digits is multiple of 9
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.

6. Work problem rule
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%
Sum of digits is multiple of 3 - last two digits multiple of 4.
(# of favorable outcomes) / (# of possible outcomes)

7. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
2 steps
(n-1)!
Find simple interest then look for the answer that is a little bigger
P(event NOT occurring) = 1 - P(event occurring)

8. Intersecting Sets
3 - 6 - 9 - 12
| A union B| = |A| + |B| - |A intersect B|
3-4-5 - 5-12-13 - 9-12-15
16.6%

9. How to check whether number is multiple of 9
180(n-2)
Sum of digits is multiple of 9
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
D or E

10. 2n+1 - 2n+3 - 2n+5
Figure out the probability for each individual event. Multiply the individual probabilities together.
Odd
Minor arc = 2(inscribed angle)
Immediately try factoring/simplifying when possible

11. The average of consecutive numbers
347
______ |m-n|
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

12. What to do with equations that have fractions
Sum of digits is multiple of 9
p/100 = is/of
______ |m-n|
Immediately try factoring/simplifying when possible

13. 2n - 2n+2 - 2n+4
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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Even
1.4

14. 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?
P(E) + P(F) - P(E and F)
Organize into a grid.
1/16
0.15n + 0.08(5) = 0.1(n+5)

15. 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
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Figure out the probability for each individual event. Multiply the individual probabilities together.
1

16. Trial Problems: look at the probability of NOT OCCURRING
x(sq. rt 3) - x - 2x
Figure out the probability for each individual event. Multiply the individual probabilities together.
P(event NOT occurring) = 1 - P(event occurring)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

17. What does the Sum of the angles in a Regular Polygon formula look like?
Immediately UNFACTOR or vice versa
180(n-2)
The probability of an event occurring plus the probability of the event not occurring = 1
n! / (n - r)!

18. 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
Balancing
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.
If the outcome of one event affects the outcome of the other event.

19. Gross Profit formula
Gross Profit = Selling Price - Cost
x - x - x(sq. rt 2)
P(E)P(F)
The probability of an event occurring plus the probability of the event not occurring = 1

20. Average Rate: Average speed
D or E
347
(total distance) / (total time)
Organize into a grid.

21. Quadratic formula
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Principal (1 + interest/number times compounded)^(t)(n)
-b +- sq. rt(b^2 - 4ac) / 2a
0.15n + 0.08(5) = 0.1(n+5)

22. Combined Events: E or F
12.5%
P(E)P(F)
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(E) + P(F) - P(E and F)

23. 3rd Rule of Probability: Conditional Probability
Odd
Any multiplication involving an even number creates an even product.
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.
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.

24. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
14 liters
Any multiplication involving an even number creates an even product.
A = P(1 + r) ^n
16.6%

25. Average Rate: Average A per B
P(E)P(F)
-b +- sq. rt(b^2 - 4ac) / 2a
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(total A) / (total B)

26. gcd(m,n)*lcm(m,n)
principle (interest rate - in decimal form) (time - in years)
Odd
gcd(m,n)*lcm(m,n) = mn
4/3 TT r ^3

27. 3^3 x 4^3 = ?
1 - P(E)
always try to factor
12^3
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

28. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
(n-1)!
______ |m-n|
0.15n + 0.08(5) = 0.1(n+5)
347

29. Price purchased for by wholesaler
(total distance) / (total time)
Purchase price
(x-n(n)y-n)
Gross Profit = Selling Price - Cost

30. How to find the slope.
3-4-5 - 5-12-13 - 9-12-15
y2 - y1 / x2 - x1
(x-n(n)y-n)
at least 3 steps

31. x^r/s = ?
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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
s Sq. rt (x^r)

32. 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.
Figure out the probability for each individual event. Multiply the individual probabilities together.
Immediately UNFACTOR or vice versa
Find simple interest then look for the answer that is a little bigger

33. In general - difficult questions require how many steps to solve?
s Sq. rt (x^r)
16.6%
at least 3 steps
14 liters

34. Prime Factorization to find Greatest Common Factor
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
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
(total A) / (total B)
(x-n(n)y-n)

35. Net
Find simple interest then look for the answer that is a little bigger
Any multiplication involving an even number creates an even product.
Group 1 + Group 2 + Neither - Both = Total
The amount after deductions

36. Odd Factors
Sum of digits is multiple of 9
Exterior angle d is equal to the sum of the two remote interior angles a and b
Odd numbers only have ___________
| A union B| = |A| + |B| - |A intersect B|

37. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
P(E) + P(F) - P(E and F)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1/16

38. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
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(event NOT occurring) = 1 - P(event occurring)
p/100 = is/of

39. Permutations: Order Matters
P(E) + P(F) - P(E and F)
n! / (n - r)!
The amount after deductions
market value

40. Probability and Geometry.
14 liters
s Sq. rt (x^r)
$11 - 025
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

41. Simple probability
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)
Find all prime factors
x(sq. rt 3) - x - 2x

42. 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.
1.7
______ |m-n|
The amount after deductions

43. Percent increase = ?
(amount of change) / (original amount)
Even
The amount after deductions
| A union B| = |A| + |B| - |A intersect B|

44. Always try to factor
Principal (1 + interest/number times compounded)^(t)(n)
| A union B| = |A| + |B| - |A intersect B|
$11 - 025
always try to factor

45. How to check for a prime number.

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46. gcd(m,n)
Minor arc = 2(inscribed angle)
______ |m-n|
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
sum = (average)(number of terms)

47. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Organize into a grid.
Divide 4999 by 15 => 333 integers
Immediately try factoring/simplifying when possible
1/16

48. Odd and Even rule.
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
1/16
Any multiplication involving an even number creates an even product.

49. Gross
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(sum of bases)(height) / 2
The total amount before any deductions
1st Rule of Probability: Basic Rule is what?

50. (1/4)^2
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.
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 3 - last two digits multiple of 4.
1/16