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GMAT Quantitative General

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
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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. 45-45-90 triangle basic lengths of sides
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
x - x - x(sq. rt 2)
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 numbers only have ___________

2. How to find all divisors of a number
(n-1)!
D or E
1st Rule of Probability: Basic Rule is what?
Find all prime factors

3. How to check whether a number is a multiple of 3.
The amount after deductions
A = P(1 + r) ^n
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.
Sum of digits is multiple of 3

4. The average of consecutive numbers
(total distance) / (total time)
14 liters
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

5. 2nd Rule of Probability: P(E) = 1 - P(not E)
$11 - 025
The probability of an event occurring plus the probability of the event not occurring = 1
If the outcome of one event affects the outcome of the other event.
Even

6. Multiples of 3
The probability of event occurring is...
Organize into a grid.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
3 - 6 - 9 - 12

7. Compound interest rule
Sum of digits is multiple of 3
$11 - 025
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.
Find simple interest then look for the answer that is a little bigger

8. When you see an equation in factored form in a question?
22
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 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
Immediately UNFACTOR or vice versa

9. Odd Factors
| A union B| = |A| + |B| - |A intersect 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)
principle (interest rate - in decimal form) (time - in years)
Odd numbers only have ___________

10. Probability and Geometry.
3 - 6 - 9 - 12
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.
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

11. x^r/s = ?
s Sq. rt (x^r)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
4/3 TT r ^3
(n-1)!

12. Combined Events: Not E = P(not E) = ?
1 - P(E)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Even
gcd(m,n)*lcm(m,n) = mn

13. Combined Events: E and F
22
P(E)P(F)
Immediately try factoring/simplifying when possible
$11 - 025

14. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
83.3%
If the outcome of one event affects the outcome of the other event.
1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

15. 0! = ?
principle (interest rate - in decimal form) (time - in years)
1
sum = (average)(number of terms)
Even

16. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
1.4
(n-1)!
0.15n + 0.08(5) = 0.1(n+5)
2 steps

17. Percent increase = ?
(total distance) / (total time)
(x-n(n)y-n)
P(E)P(F)
(amount of change) / (original amount)

18. Permutations: Order Matters
Find all prime factors
1st Rule of Probability: Basic Rule is what?
$11 - 025
n! / (n - r)!

19. How to check whether a number is a multiple of 6
| A union B| = |A| + |B| - |A intersect B|
If the outcome of one event affects the outcome of the other event.
The total amount before any deductions
Number is a multiple of 3 and 2

20. In general - difficult questions require how many steps to solve?
at least 3 steps
(amount of change) / (original amount)
Sum of digits is multiple of 3 - last two digits multiple of 4.
The amount after deductions

21. Odd and Even rule.
The amount after deductions
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
| A union B| = |A| + |B| - |A intersect B|
Any multiplication involving an even number creates an even product.

22. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
(x-n(n)y-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
Gross Profit = Selling Price - Cost
347

23. Average Rate: Average A per B
(x-n(n)y-n)
(total A) / (total B)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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.

24. Properties of 0
P(E)P(F)
Even
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
D or E

25. Combined Events: E or F
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.
P(E) + P(F) - P(E and F)
Odd numbers only have ___________
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

26. How do you multiply roots together.
P(E) + P(F) - P(E and F)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
0.15n + 0.08(5) = 0.1(n+5)

27. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
The amount after deductions
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.

28. 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)
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.
2 steps
(sum of bases)(height) / 2

29. How to check whether a number is a multiple of 4.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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)
Find simple interest then look for the answer that is a little bigger
Last two digits are multiple of 4 or the number can be divided by 2 twice.

30. How to check whether number is multiple of 9
The amount after deductions
12^3
Sum of digits is multiple of 9
always try to factor

31. What to do with equations that have fractions
The total amount before any deductions
Immediately try factoring/simplifying when possible
12^3
1.7

32. Gross
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
2 steps
The total amount before any deductions

33. In general - medium questions require how many steps to solve?
2 steps
3-4-5 - 5-12-13 - 9-12-15
83.3%
-b +- sq. rt(b^2 - 4ac) / 2a

34. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
y2 - y1 / x2 - x1
Balancing
12^3
D or E

35. Net
Minor arc = 2(inscribed angle)
The amount after deductions
(sum of bases)(height) / 2
Figure out the probability for each individual event. Multiply the individual probabilities together.

36. 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.
1st Rule of Probability: Basic Rule is what?
Find simple interest then look for the answer that is a little bigger
0.15n + 0.08(5) = 0.1(n+5)
| A union B| = |A| + |B| - |A intersect B|

37. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Organize into a grid.
s Sq. rt (x^r)
1 - P(E)

38. Volume of a sphere
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.
4/3 TT r ^3
| A union B| = |A| + |B| - |A intersect B|
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

39. Simple probability
The probability of an event occurring plus the probability of the event not occurring = 1
Find all prime factors
(# of favorable outcomes) / (# of possible outcomes)
Organize into a grid.

40. (1/4)^2
y2 - y1 / x2 - x1
P(event NOT occurring) = 1 - P(event occurring)
Odd numbers only have ___________
1/16

41. How to check whether a number is a multiple of 12.
principle (interest rate - in decimal form) (time - in years)
Number is a multiple of 3 and 2
Sum of digits is multiple of 3 - last two digits multiple of 4.
Find simple interest then look for the answer that is a little bigger

42. 1/6 = what %
16.6%
-b +- sq. rt(b^2 - 4ac) / 2a
1
(# of favorable outcomes) / (# of possible outcomes)

43. Price sold for by retailer (after markup)
market value
3 - 6 - 9 - 12
______ |m-n|
If the outcome of one event affects the outcome of the other event.

44. Intersecting Sets
14 liters
P(E)P(F)
p/100 = is/of
| A union B| = |A| + |B| - |A intersect B|

45. Set Problems formula
(x-n(n)y-n)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(sum of bases)(height) / 2
4/3 TT r ^3

46. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
$11 - 025
x(sq. rt 3) - x - 2x
The amount after deductions

47. 3rd Rule of Probability: Conditional Probability
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 3
(amount of change) / (original amount)
Organize into a grid.

48. 1/8 = what %
12.5%
Find simple interest then look for the answer that is a little bigger
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
A = P(1 + r) ^n

49. Gross Profit formula
Gross Profit = Selling Price - Cost
Immediately UNFACTOR or vice versa
sum = (average)(number of terms)
1/16

50. To determine the number of integers less than 5000 that are evenly divisible by 15...?
| A union B| = |A| + |B| - |A intersect B|
0.15n + 0.08(5) = 0.1(n+5)
Divide 4999 by 15 => 333 integers
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

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GMAT Quantitative General

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