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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. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Gross Profit = Selling Price - Cost
D or E
0.15n + 0.08(5) = 0.1(n+5)

2. Odd and Even rule.
principle (interest rate - in decimal form) (time - in years)
Balancing
Any multiplication involving an even number creates an even product.
0.15n + 0.08(5) = 0.1(n+5)

3. 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?
principle (interest rate - in decimal form) (time - in years)
x(sq. rt 3) - x - 2x
3-4-5 - 5-12-13 - 9-12-15
0.15n + 0.08(5) = 0.1(n+5)

4. How to find all divisors of a number
principle (interest rate - in decimal form) (time - in years)
Find all prime factors
(total A) / (total B)
(x-n(n)y-n)

5. Multiplication principle
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 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.
Minor arc = 2(inscribed angle)
Number is a multiple of 3 and 2

6. 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
P(event NOT occurring) = 1 - P(event occurring)
Exterior angle d is equal to the sum of the two remote interior angles a and b

7. Sq. rt(3)
at least 3 steps
1.7
The probability of an event occurring plus the probability of the event not occurring = 1
-b +- sq. rt(b^2 - 4ac) / 2a

8. Average Rate: Average A per B
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)
y2 - y1 / x2 - x1
22

9. 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.
(total distance) / (total time)
x(sq. rt 3) - x - 2x
3 - 6 - 9 - 12

10. Percent Formula
Minor arc = 2(inscribed angle)
(# of favorable outcomes) / (# of possible outcomes)
p/100 = is/of
Find simple interest then look for the answer that is a little bigger

11. gcd(m,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.
347
______ |m-n|
n! / (n - r)!

12. How to check whether a number is a multiple of 6
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(n-1)!
Number is a multiple of 3 and 2
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

13. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
Organize into a grid.
Find simple interest then look for the answer that is a little bigger
14 liters

14. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Gross Profit = Selling Price - Cost
x(sq. rt 3) - x - 2x
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
22

15. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Group 1 + Group 2 + Neither - Both = Total
1
Figure out the probability for each individual event. Multiply the individual probabilities together.

16. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Immediately UNFACTOR or vice versa
P(E) + P(F) - P(E and F)

17. Combined Events: E or F
Group 1 + Group 2 + Neither - Both = Total
Even
Number is a multiple of 3 and 2
P(E) + P(F) - P(E and F)

18. 30-60-90 triangle basic lengths of sides
$11 - 025
The probability of event occurring is...
x(sq. rt 3) - x - 2x
83.3%

19. 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
0.15n + 0.08(5) = 0.1(n+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.
at least 3 steps
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.

20. Net
Balancing
The amount after deductions
(total A) / (total B)
1.4

21. Prime Factorization to find Greatest Common Factor
Minor arc = 2(inscribed angle)
The amount after deductions
always try to factor
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

22. Formula for Mixed Group problems (involving Both/Neither)
market value
Group 1 + Group 2 + Neither - Both = Total
1.7
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

23. Volume of a sphere
2 steps
4/3 TT r ^3
1 - P(E)
1

24. 2n - 2n+2 - 2n+4
$11 - 025
P(event NOT occurring) = 1 - P(event occurring)
-b +- sq. rt(b^2 - 4ac) / 2a
Even

25. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Even
A = P(1 + r) ^n
347
Figure out the probability for each individual event. Multiply the individual probabilities together.

26. Permutations: Order Matters
Immediately try factoring/simplifying when possible
A = P(1 + r) ^n
n! / (n - r)!
0.15n + 0.08(5) = 0.1(n+5)

27. Indistinguishable events how to find the number of permutations

28. Work problem rule
s Sq. rt (x^r)
0.15n + 0.08(5) = 0.1(n+5)
P(event NOT occurring) = 1 - P(event occurring)
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.

29. 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
1st Rule of Probability: Basic Rule is what?
Figure out the probability for each individual event. Multiply the individual probabilities together.
y2 - y1 / x2 - x1
Balancing

30. 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.
Organize into a grid.
sum = (average)(number of terms)
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)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

31. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(x-n(n)y-n)
n! / (n - r)!
P(E)P(F)

32. Always try to factor
s Sq. rt (x^r)
$11 - 025
always try to factor
n! / (n - r)!

33. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
sum = (average)(number of terms)
1.4
Sum of digits is multiple of 9

34. 5/6 = what %
Purchase price
83.3%
Group 1 + Group 2 + Neither - Both = Total
180(n-2)

35. Simple probability
n! / (n - r)!
0.15n + 0.08(5) = 0.1(n+5)
(x-n(n)y-n)
(# of favorable outcomes) / (# of possible outcomes)

36. How to check for a prime number.

37. Triangle abc with d on the outside with a line. What does d = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
Number is a multiple of 3 and 2
market value
Immediately UNFACTOR or vice versa

38. Price purchased for by wholesaler
347
p/100 = is/of
Sum of digits is multiple of 9
Purchase price

39. Sum of consecutive numbers
180(n-2)
Divide 4999 by 15 => 333 integers
22
sum = (average)(number of terms)

40. To determine multiple-event probability where each individual event must occur in a certain way.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Figure out the probability for each individual event. Multiply the individual probabilities together.
Divide 4999 by 15 => 333 integers
14 liters

41. What to do with equations that have fractions
n! / (n - r)!
Immediately try factoring/simplifying when possible
Figure out the probability for each individual event. Multiply the individual probabilities together.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

42. In general - medium questions require how many steps to solve?
2 steps
Immediately UNFACTOR or vice versa
gcd(m,n)*lcm(m,n) = mn
-b +- sq. rt(b^2 - 4ac) / 2a

43. In general - difficult questions require how many steps to solve?
A = P(1 + r) ^n
The total amount before any deductions
D or E
at least 3 steps

44. 45-45-90 triangle basic lengths of sides
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(x-n(n)y-n)
x - x - x(sq. rt 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

45. Percent increase = ?
180(n-2)
(amount of change) / (original amount)
Figure out the probability for each individual event. Multiply the individual probabilities together.
market value

46. Properties of 0
Number is a multiple of 3 and 2
n! / (n - r)!
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(sum of bases)(height) / 2

47. 3^3 x 4^3 = ?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
always try to factor
347
12^3

48. 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.
(total distance) / (total time)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(total A) / (total B)

49. 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?
Purchase price
14 liters
3 - 6 - 9 - 12
Even

50. How to check whether a number is a multiple of 4.
Organize into a grid.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Any multiplication involving an even number creates an even product.
Gross Profit = Selling Price - Cost