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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. In general - medium questions require how many steps to solve?
2 steps
(total distance) / (total time)
83.3%
n! / (n - r)!

2. Average Rate: Average A per B
Even
83.3%
(total A) / (total B)
Organize into a grid.

3. Set Problems formula
(x-n(n)y-n)
y2 - y1 / x2 - x1
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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

4. How to check whether a number is a multiple of 4.
Immediately try factoring/simplifying when possible
Number is a multiple of 3 and 2
3 - 6 - 9 - 12
Last two digits are multiple of 4 or the number can be divided by 2 twice.

5. 1/6 = what %
16.6%
347
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 occurring is...

6. 45-45-90 triangle basic lengths of sides
s Sq. rt (x^r)
at least 3 steps
P(event NOT occurring) = 1 - P(event occurring)
x - x - x(sq. rt 2)

7. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
p/100 = is/of
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Divide 4999 by 15 => 333 integers
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.

8. Odd and Even rule.
Any multiplication involving an even number creates an even product.
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
4/3 TT r ^3
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.

9. Sum of consecutive numbers
sum = (average)(number of terms)
Sum of digits is multiple of 3 - last two digits multiple of 4.
P(E) + P(F) - P(E and F)
22

10. (1/4)^2
1/16
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Organize into a grid.
principle (interest rate - in decimal form) (time - in years)

11. How to check whether a number is a multiple of 12.
The probability of an event occurring plus the probability of the event not occurring = 1
| A union B| = |A| + |B| - |A intersect B|
Sum of digits is multiple of 3 - last two digits multiple of 4.
$11 - 025

12. Three triangle length patterns
Even
P(event NOT occurring) = 1 - P(event occurring)
3-4-5 - 5-12-13 - 9-12-15
Odd

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)
at least 3 steps
D or E
(sum of bases)(height) / 2

14. Probability and Geometry.
-b +- sq. rt(b^2 - 4ac) / 2a
Sum of digits is multiple of 3 - last two digits multiple of 4.
P(E)P(F)
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

15. Percent Formula
p/100 = is/of
The total amount before any deductions
D or E
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.

16. Compound interest formula
1st Rule of Probability: Basic Rule is what?
y2 - y1 / x2 - x1
1.7
Principal (1 + interest/number times compounded)^(t)(n)

17. 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.
347
If the outcome of one event affects the outcome of the other event.
Figure out the probability for each individual event. Multiply the individual probabilities together.

18. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
x(sq. rt 3) - x - 2x
22
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

19. Compound interest rule
1
Find simple interest then look for the answer that is a little bigger
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.
1/16

20. 3^3 x 4^3 = ?
sum = (average)(number of terms)
n! / (n - r)!
12^3
The total amount before any deductions

21. 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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Minor arc = 2(inscribed angle)
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.
Odd

22. 1/8 = what %
s Sq. rt (x^r)
Find all prime factors
12.5%
1/16

23. 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?
Exterior angle d is equal to the sum of the two remote interior angles a and b
Even
x(sq. rt 3) - x - 2x
0.15n + 0.08(5) = 0.1(n+5)

24. Always try to factor
always try to factor
Group 1 + Group 2 + Neither - Both = Total
market value
Figure out the probability for each individual event. Multiply the individual probabilities together.

25. 4th rule of Probability
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 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 an event occurring plus the probability of the event not occurring = 1
1.4

26. Formula for Mixed Group problems (involving Both/Neither)
1/16
Number is a multiple of 3 and 2
Group 1 + Group 2 + Neither - Both = Total
gcd(m,n)*lcm(m,n) = mn

27. x^r/s = ?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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)
s Sq. rt (x^r)
(n-1)!

28. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
x - x - x(sq. rt 2)
Divide 4999 by 15 => 333 integers
Gross Profit = Selling Price - Cost

29. Number added or deleted
3-4-5 - 5-12-13 - 9-12-15
1st Rule of Probability: Basic Rule is what?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1/16

30. Volume of a sphere
1.7
______ |m-n|
4/3 TT r ^3
The probability of event occurring is...

31. Odd Factors
Organize into a grid.
The amount after deductions
Odd numbers only have ___________
Gross Profit = Selling Price - Cost

32. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
gcd(m,n)*lcm(m,n) = mn
2 steps
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

33. How to check for a prime number.

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34. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
1/16
at least 3 steps
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

35. What to do with equations that have fractions
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.
Immediately UNFACTOR or vice versa
Immediately try factoring/simplifying when possible
Last two digits are multiple of 4 or the number can be divided by 2 twice.

36. 2n+1 - 2n+3 - 2n+5
(# of favorable outcomes) / (# of possible outcomes)
Odd
Find simple interest then look for the answer that is a little bigger
14 liters

37. Permutations: Order Matters
Even
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.
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)
n! / (n - r)!

38. How to find the slope.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
y2 - y1 / x2 - x1
Any multiplication involving an even number creates an even product.
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.

39. The number of outcomes that result in A divided by the total number of possible outcomes.
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.
Immediately try factoring/simplifying when possible
The probability of event occurring is...
2 steps

40. To determine multiple-event probability where each individual event must occur in a certain way.
(n-1)!
Figure out the probability for each individual event. Multiply the individual probabilities together.
1.7
y2 - y1 / x2 - x1

41. Multiplication principle
P(E)P(F)
Principal (1 + interest/number times compounded)^(t)(n)
x(sq. rt 3) - x - 2x
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

42. 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?
market value
The total amount before any deductions
14 liters
If the outcome of one event affects the outcome of the other event.

43. Intersecting Sets
Figure out the probability for each individual event. Multiply the individual probabilities together.
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.
1/16
| A union B| = |A| + |B| - |A intersect B|

44. 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
(sum of bases)(height) / 2
Balancing
Sum of digits is multiple of 3
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

45. Work problem rule
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Any multiplication involving an even number creates an even product.
A = P(1 + r) ^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.

46. 2nd Rule of Probability: P(E) = 1 - P(not E)
Divide 4999 by 15 => 333 integers
The probability of an event occurring plus the probability of the event not occurring = 1
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Purchase price

47. 0! = ?
P(E) + P(F) - P(E and F)
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)
1

48. In general - difficult questions require how many steps to solve?
P(event NOT occurring) = 1 - P(event occurring)
Minor arc = 2(inscribed angle)
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.
at least 3 steps

49. What does the Sum of the angles in a Regular Polygon formula look like?
0.15n + 0.08(5) = 0.1(n+5)
(total distance) / (total time)
180(n-2)
(# of favorable outcomes) / (# of possible outcomes)

50. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
The total amount before any deductions
The probability of an event occurring plus the probability of the event not occurring = 1
sum = (average)(number of terms)