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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. (1/4)^2
Gross Profit = Selling Price - Cost
Odd numbers only have ___________
1/16
at least 3 steps

2. How to find all divisors of a number
Group 1 + Group 2 + Neither - Both = Total
Find all prime factors
P(E)P(F)
Minor arc = 2(inscribed angle)

3. Probability and Geometry.
P(event NOT occurring) = 1 - P(event occurring)
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
market value
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.

4. 5/6 = what %
1
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.
83.3%
s Sq. rt (x^r)

5. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Odd
Gross Profit = Selling Price - Cost
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
principle (interest rate - in decimal form) (time - in years)

6. 2n+1 - 2n+3 - 2n+5
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.
Purchase price
Odd
Principal (1 + interest/number times compounded)^(t)(n)

7. The number of ways independent events can occur together.
22
1/16
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1.7

8. Compound interest rule
Find simple interest then look for the answer that is a little bigger
22
always try to factor
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

9. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
12.5%
A = P(1 + r) ^n
(x-n(n)y-n)
P(event NOT occurring) = 1 - P(event occurring)

10. 4th rule of Probability
Organize into a grid.
Purchase price
(n-1)!
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)

11. 1/6 = what %
Balancing
16.6%
3-4-5 - 5-12-13 - 9-12-15
83.3%

12. 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?
Organize into a grid.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
12.5%

13. 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.
market value
12^3
Organize into a grid.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

14. Multiples of 3
83.3%
D or E
Figure out the probability for each individual event. Multiply the individual probabilities together.
3 - 6 - 9 - 12

15. 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?
Minor arc = 2(inscribed angle)
(sum of bases)(height) / 2
The probability of event occurring is...
14 liters

16. To determine multiple-event probability where each individual event must occur in a certain way.
Gross Profit = Selling Price - Cost
Figure out the probability for each individual event. Multiply the individual probabilities together.
4/3 TT r ^3
12^3

17. Permutations: Order Matters
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
The probability of an event occurring plus the probability of the event not occurring = 1
The amount after deductions
n! / (n - r)!

18. 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
16.6%
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Sum of digits is multiple of 3

19. In general - difficult questions require how many steps to solve?
at least 3 steps
Odd
(x-n(n)y-n)
Even

20. Prime Factorization to find Greatest Common Factor
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.
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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

21. How to check whether number is multiple of 9
Sum of digits is multiple of 3 - last two digits multiple of 4.
1st Rule of Probability: Basic Rule is what?
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 9

22. Price purchased for by wholesaler
s Sq. rt (x^r)
Purchase price
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
If the outcome of one event affects the outcome of the other event.

23. 3^3 x 4^3 = ?
The total amount before any deductions
12^3
Minor arc = 2(inscribed angle)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

24. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
______ |m-n|
n! / (n - r)!
Sum of digits is multiple of 3 - last two digits multiple of 4.

25. Multiplication principle
1/16
Find all prime factors
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

26. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
Gross Profit = Selling Price - Cost
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
1 - P(E)

27. 2n - 2n+2 - 2n+4
n! / (n - r)!
347
1 - P(E)
Even

28. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
P(E) + P(F) - P(E and F)
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
Number is a multiple of 3 and 2

29. Net
The probability of event occurring is...
22
y2 - y1 / x2 - x1
The amount after deductions

30. 3rd Rule of Probability: Conditional Probability
Figure out the probability for each individual event. Multiply the individual probabilities together.
1.7
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.
(n-1)!

31. x^r/s = ?
Find simple interest then look for the answer that is a little bigger
s Sq. rt (x^r)
Balancing
(total A) / (total B)

32. Dependent events: When are two events said to be dependent events?
Find simple interest then look for the answer that is a little bigger
If the outcome of one event affects the outcome of the other event.
| A union B| = |A| + |B| - |A intersect B|
Balancing

33. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
1.7
A = P(1 + r) ^n
______ |m-n|

34. 0! = ?
Immediately try factoring/simplifying when possible
1.4
1
Number is a multiple of 3 and 2

35. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
always try to factor
$11 - 025
gcd(m,n)*lcm(m,n) = mn
22

36. gcd(m,n)
Sum of digits is multiple of 3
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 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
______ |m-n|

37. How to find the slope.
22
y2 - y1 / x2 - x1
The total amount before any deductions
1.4

38. Gross
The total amount before any deductions
x - x - x(sq. rt 2)
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.
(sum of bases)(height) / 2

39. What to do with equations that have fractions
x - x - x(sq. rt 2)
3-4-5 - 5-12-13 - 9-12-15
Immediately try factoring/simplifying when possible
n! / (n - r)!

40. Odd Factors
The probability of an event occurring plus the probability of the event not occurring = 1
The amount after deductions
Odd numbers only have ___________
market value

41. 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?
The amount after deductions
P(E) + P(F) - P(E and F)
Find simple interest then look for the answer that is a little bigger
0.15n + 0.08(5) = 0.1(n+5)

42. 1/8 = what %
12.5%
(total A) / (total B)
3-4-5 - 5-12-13 - 9-12-15
The amount after deductions

43. The average of consecutive numbers
0.15n + 0.08(5) = 0.1(n+5)
Balancing
83.3%
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

44. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
Immediately try factoring/simplifying when possible
Exterior angle d is equal to the sum of the two remote interior angles a and b
Immediately UNFACTOR or vice versa

45. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Immediately try factoring/simplifying when possible
$11 - 025
The total amount before any deductions
Organize into a grid.

46. Average Rate: Average speed
1.4
always try to factor
(total distance) / (total time)
y2 - y1 / x2 - x1

47. Work problem rule
180(n-2)
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.
Balancing
The total amount before any deductions

48. Percent increase = ?
(amount of change) / (original amount)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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
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.

49. Combined Events: E and F
Gross Profit = Selling Price - Cost
principle (interest rate - in decimal form) (time - in years)
1.7
P(E)P(F)

50. How to check for a prime number.