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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. Gross
A = P(1 + r) ^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
(total distance) / (total time)
The total amount before any deductions

2. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Immediately UNFACTOR or vice versa
Sum of digits is multiple of 3
Organize into a grid.

3. To determine multiple-event probability where each individual event must occur in a certain way.
sum = (average)(number of terms)
3-4-5 - 5-12-13 - 9-12-15
Any multiplication involving an even number creates an even product.
Figure out the probability for each individual event. Multiply the individual probabilities together.

4. Volume of a sphere
Figure out the probability for each individual event. Multiply the individual probabilities together.
4/3 TT r ^3
Find all prime factors
at least 3 steps

5. gcd(m,n)*lcm(m,n)
sum = (average)(number of terms)
gcd(m,n)*lcm(m,n) = mn
P(E) + P(F) - P(E and F)
The probability of an event occurring plus the probability of the event not occurring = 1

6. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
0.15n + 0.08(5) = 0.1(n+5)
Sum of digits is multiple of 3 - last two digits multiple of 4.
(sum of bases)(height) / 2

7. How to check whether a number is a multiple of 4.
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.
market value
(sum of bases)(height) / 2
Last two digits are multiple of 4 or the number can be divided by 2 twice.

8. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
principle (interest rate - in decimal form) (time - in years)
(# of favorable outcomes) / (# of possible outcomes)
Minor arc = 2(inscribed angle)

9. The average of consecutive numbers
The probability of event occurring is...
Divide 4999 by 15 => 333 integers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
0.15n + 0.08(5) = 0.1(n+5)

10. Average Rate: Average A per B
-b +- sq. rt(b^2 - 4ac) / 2a
(sum of bases)(height) / 2
Immediately try factoring/simplifying when possible
(total A) / (total B)

11. How to check whether a number is a multiple of 3.
0.15n + 0.08(5) = 0.1(n+5)
P(E)P(F)
(total distance) / (total time)
Sum of digits is multiple of 3

12. 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
16.6%
Purchase price
Find all prime factors

13. Average Rate: Average speed
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.
principle (interest rate - in decimal form) (time - in years)
(total distance) / (total time)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

14. Always try to factor
(sum of bases)(height) / 2
P(E)P(F)
always try to factor
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

15. Intersecting Sets
Number is a multiple of 3 and 2
market value
| A union B| = |A| + |B| - |A intersect B|
gcd(m,n)*lcm(m,n) = mn

16. 3^3 x 4^3 = ?
12^3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
s Sq. rt (x^r)
at least 3 steps

17. 2nd Rule of Probability: P(E) = 1 - P(not E)
If the outcome of one event affects the outcome of the other event.
The probability of an event occurring plus the probability of the event not occurring = 1
market value
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.

18. 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.
Find all prime factors
(amount of change) / (original amount)
1.4
Organize into a grid.

19. Combined Events: Not E = P(not E) = ?
D or E
n! / (n - r)!
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1 - P(E)

20. In general - medium questions require how many steps to solve?
2 steps
16.6%
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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.

21. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
12^3
If the outcome of one event affects the outcome of the other event.
______ |m-n|

22. Prime Factorization to find Greatest Common Factor
Number is a multiple of 3 and 2
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
(n-1)!

23. 1/6 = what %
Purchase price
Divide 4999 by 15 => 333 integers
D or E
16.6%

24. Sum of consecutive numbers
(total distance) / (total time)
Even
sum = (average)(number of terms)
Gross Profit = Selling Price - Cost

25. Work problem rule
Group 1 + Group 2 + Neither - Both = Total
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.
1
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

26. How to check whether number is multiple of 9
Sum of digits is multiple of 9
14 liters
The probability of event occurring is...
Number is a multiple of 3 and 2

27. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
P(E) + P(F) - P(E and F)
180(n-2)
2 steps
A = P(1 + r) ^n

28. Inscribed Angle - Minor Arc
14 liters
(n-1)!
Sum of digits is multiple of 9
Minor arc = 2(inscribed angle)

29. How to check for a prime number.

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30. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
P(E)P(F)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
180(n-2)

31. Quadratic formula
1 - P(E)
P(E) + P(F) - P(E and F)
| A union B| = |A| + |B| - |A intersect B|
-b +- sq. rt(b^2 - 4ac) / 2a

32. Combined Events: E and F
P(event NOT occurring) = 1 - P(event occurring)
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.
P(E)P(F)
22

33. 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
principle (interest rate - in decimal form) (time - in years)
x - x - x(sq. rt 2)
3-4-5 - 5-12-13 - 9-12-15
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.

34. 3rd Rule of Probability: Conditional Probability
1st Rule of Probability: Basic Rule is what?
(x-n(n)y-n)
n! / (n - r)!
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.

35. In general - difficult questions require how many steps to solve?
at least 3 steps
P(E)P(F)
Organize into a grid.
Immediately try factoring/simplifying when possible

36. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
12^3
Immediately try factoring/simplifying when possible
(# of favorable outcomes) / (# of possible outcomes)
D or E

37. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
4/3 TT r ^3
347
If the outcome of one event affects the outcome of the other event.
12^3

38. How to check whether a number is a multiple of 6
Sum of digits is multiple of 3 - last two digits multiple of 4.
gcd(m,n)*lcm(m,n) = mn
Figure out the probability for each individual event. Multiply the individual probabilities together.
Number is a multiple of 3 and 2

39. Multiplication principle
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)
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
A = P(1 + r) ^n

40. Three triangle length patterns
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Find simple interest then look for the answer that is a little bigger
(n-1)!
3-4-5 - 5-12-13 - 9-12-15

41. Trial Problems: look at the probability of NOT OCCURRING
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
P(event NOT occurring) = 1 - P(event occurring)
If the outcome of one event affects the outcome of the other event.
347

42. Formula for Mixed Group problems (involving Both/Neither)
The probability of event occurring is...
Number is a multiple of 3 and 2
The total amount before any deductions
Group 1 + Group 2 + Neither - Both = Total

43. Compound interest formula
(sum of bases)(height) / 2
Principal (1 + interest/number times compounded)^(t)(n)
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
3 - 6 - 9 - 12

44. Net
Group 1 + Group 2 + Neither - Both = Total
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
The amount after deductions

45. 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?
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.
s Sq. rt (x^r)
0.15n + 0.08(5) = 0.1(n+5)
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

46. (1/4)^2
1/16
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.
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.

47. x^r/s = ?
s Sq. rt (x^r)
(total distance) / (total time)
Divide 4999 by 15 => 333 integers
Odd numbers only have ___________

48. 0! = ?
1
Exterior angle d is equal to the sum of the two remote interior angles a and b
2 steps
Any multiplication involving an even number creates an even product.

49. Percent Formula
(x-n(n)y-n)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Number is a multiple of 3 and 2
p/100 = is/of

50. gcd(m,n)
Exterior angle d is equal to the sum of the two remote interior angles a and b
______ |m-n|
s Sq. rt (x^r)
principle (interest rate - in decimal form) (time - in years)