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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.
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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. Multiples of 3
Sum of digits is multiple of 3
Odd numbers only have ___________
3 - 6 - 9 - 12
(sum of bases)(height) / 2

2. Percent Formula
Organize into a grid.
p/100 = is/of
83.3%
180(n-2)

3. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
x(sq. rt 3) - x - 2x
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.
D or E
16.6%

4. Number added or deleted
12^3
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
14 liters
Odd

5. Trial Problems: look at the probability of NOT OCCURRING
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.
P(event NOT occurring) = 1 - P(event occurring)
Figure out the probability for each individual event. Multiply the individual probabilities together.

6. When you see an equation in factored form in a question?
16.6%
Minor arc = 2(inscribed angle)
14 liters
Immediately UNFACTOR or vice versa

7. 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?
s Sq. rt (x^r)
3-4-5 - 5-12-13 - 9-12-15
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
0.15n + 0.08(5) = 0.1(n+5)

8. 30-60-90 triangle basic lengths of sides
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
x(sq. rt 3) - x - 2x
Minor arc = 2(inscribed angle)
14 liters

9. What to do with equations that have fractions
3-4-5 - 5-12-13 - 9-12-15
Immediately try factoring/simplifying when possible
1.7
4/3 TT r ^3

10. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
(sum of bases)(height) / 2
p/100 = is/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

11. 2n+1 - 2n+3 - 2n+5
Gross Profit = Selling Price - Cost
Odd
Find all prime factors
$11 - 025

12. Gross Profit formula
Gross Profit = Selling Price - Cost
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
12.5%
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.

13. Probability and Geometry.
The total amount before any deductions
D or E
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
Figure out the probability for each individual event. Multiply the individual probabilities together.

14. Formula for Mixed Group problems (involving Both/Neither)
1 - P(E)
Odd
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Group 1 + Group 2 + Neither - Both = Total

15. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
0.15n + 0.08(5) = 0.1(n+5)
Find all prime factors
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

16. Combined Events: E and F
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
P(event NOT occurring) = 1 - P(event occurring)
P(E)P(F)

17. The number of ways independent events can occur together.
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 bases)(height) / 2
Sum of digits is multiple of 3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

18. How to check whether number is multiple of 9
Sum of digits is multiple of 9
2 steps
12^3
(total A) / (total B)

19. Dependent events: When are two events said to be dependent events?
sum = (average)(number of terms)
P(event NOT occurring) = 1 - P(event occurring)
If the outcome of one event affects the outcome of the other event.
n! / (n - r)!

20. 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.
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The total amount before any deductions

21. How to check whether a number is a multiple of 4.
(n-1)!
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Sum of digits is multiple of 3 - last two digits multiple of 4.
(total distance) / (total time)

22. 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
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(total A) / (total B)
Balancing
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

23. Volume of a sphere
p/100 = is/of
0.15n + 0.08(5) = 0.1(n+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
4/3 TT r ^3

24. How to find the slope.
market value
(amount of change) / (original amount)
Odd numbers only have ___________
y2 - y1 / x2 - x1

25. gcd(m,n)
______ |m-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.
Even
Sum of digits is multiple of 3 - last two digits multiple of 4.

26. Formula for area of a Trapezoid
1
1.4
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
(sum of bases)(height) / 2

27. Average Rate: Average speed
(# of favorable outcomes) / (# of possible outcomes)
(total distance) / (total time)
3-4-5 - 5-12-13 - 9-12-15
Group 1 + Group 2 + Neither - Both = Total

28. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
x(sq. rt 3) - x - 2x
x - x - x(sq. rt 2)
(n-1)!
Gross Profit = Selling Price - Cost

29. Percent increase = ?
(amount of change) / (original amount)
Exterior angle d is equal to the sum of the two remote interior angles a and b
(total distance) / (total time)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

30. How do you multiply roots together.
gcd(m,n)*lcm(m,n) = mn
Balancing
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

31. x^r/s = ?
If the outcome of one event affects the outcome of the other event.
s Sq. rt (x^r)
Balancing
(# of favorable outcomes) / (# of possible outcomes)

32. 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?
(x-n(n)y-n)
-b +- sq. rt(b^2 - 4ac) / 2a
If the outcome of one event affects the outcome of the other event.
14 liters

33. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
p/100 = is/of
Sum of digits is multiple of 3
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

34. Always try to factor
always try to factor
D or E
(total distance) / (total time)
The probability of event occurring is...

35. Combined Events: E or F
Find all prime factors
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1 - P(E)
P(E) + P(F) - P(E and F)

36. Prime Factorization to find Greatest Common Factor
The amount after deductions
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
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

37. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
s Sq. rt (x^r)
347
The probability of event occurring is...
| A union B| = |A| + |B| - |A intersect B|

38. Permutations: Order Matters
Odd
n! / (n - r)!
Organize into a grid.
Immediately UNFACTOR or vice versa

39. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Immediately UNFACTOR or vice versa
______ |m-n|
12.5%
Divide 4999 by 15 => 333 integers

40. Price sold for by retailer (after markup)
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)
market value
(x-n(n)y-n)

41. 1/8 = what %
12.5%
______ |m-n|
0.15n + 0.08(5) = 0.1(n+5)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

42. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
3 - 6 - 9 - 12
p/100 = is/of
P(E) + P(F) - P(E and F)

43. How to check for a prime number.

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44. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
s Sq. rt (x^r)
P(event NOT occurring) = 1 - P(event occurring)
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

45. Price purchased for by wholesaler
Immediately try factoring/simplifying when possible
22
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Purchase price

46. In general - medium questions require how many steps to solve?
Immediately UNFACTOR or vice versa
2 steps
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1

47. Average Rate: Average A per B
1 - P(E)
83.3%
(total A) / (total B)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

48. Set Problems formula
2 steps
(x-n(n)y-n)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(amount of change) / (original amount)

49. 2n - 2n+2 - 2n+4
Odd numbers only have ___________
1.7
Even
The amount after deductions

50. Triangle abc with d on the outside with a line. What does d = ?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
0.15n + 0.08(5) = 0.1(n+5)
Exterior angle d is equal to the sum of the two remote interior angles a and b

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GMAT Quantitative General

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