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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. 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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(n-1)!

2. Multiples of 3
1 - P(E)
180(n-2)
3 - 6 - 9 - 12
P(event NOT occurring) = 1 - P(event occurring)

3. Gross Profit formula
x(sq. rt 3) - x - 2x
Gross Profit = Selling Price - Cost
market value
P(E) + P(F) - P(E and F)

4. 1/8 = what %
12.5%
347
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
1st Rule of Probability: Basic Rule is what?

5. What to do with equations that have fractions
Sum of digits is multiple of 3
p/100 = is/of
Immediately try factoring/simplifying when possible
principle (interest rate - in decimal form) (time - in years)

6. Average Rate: Average speed
(total distance) / (total time)
2 steps
83.3%
The total amount before any deductions

7. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Organize into a grid.
$11 - 025
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 total amount before any deductions

8. Compound interest rule
Find simple interest then look for the answer that is a little bigger
Sum of digits is multiple of 9
Immediately try factoring/simplifying when possible
______ |m-n|

9. Permutations: Order Matters
Sum of digits is multiple of 3 - last two digits multiple of 4.
16.6%
n! / (n - r)!
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.

10. Triangle abc with d on the outside with a line. What does d = ?
P(E) + P(F) - P(E and F)
p/100 = is/of
Exterior angle d is equal to the sum of the two remote interior angles a and b
12^3

11. Price purchased for by wholesaler
Sum of digits is multiple of 3
1.7
Purchase price
1

12. 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?
14 liters
83.3%
Sum of digits is multiple of 3 - last two digits multiple of 4.
Principal (1 + interest/number times compounded)^(t)(n)

13. Multiplication principle
principle (interest rate - in decimal form) (time - in years)
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
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
Divide 4999 by 15 => 333 integers

14. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Sum of digits is multiple of 9
Figure out the probability for each individual event. Multiply the individual probabilities together.
347
always try to factor

15. The average of consecutive numbers
Sum of digits is multiple of 3 - last two digits multiple of 4.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Odd
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

16. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
s Sq. rt (x^r)
4/3 TT r ^3
Group 1 + Group 2 + Neither - Both = Total
A = P(1 + r) ^n

17. 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.
Balancing
sum = (average)(number of terms)
1st Rule of Probability: Basic Rule is what?
12^3

18. Trial Problems: look at the probability of NOT OCCURRING
P(E) + P(F) - P(E and F)
Principal (1 + interest/number times compounded)^(t)(n)
-b +- sq. rt(b^2 - 4ac) / 2a
P(event NOT occurring) = 1 - P(event occurring)

19. 45-45-90 triangle basic lengths of sides
s Sq. rt (x^r)
x - x - x(sq. rt 2)
If the outcome of one event affects the outcome of the other event.
always try to factor

20. Combined Events: E and F
P(E)P(F)
2 steps
Sum of digits is multiple of 3 - last two digits multiple of 4.
The amount after deductions

21. How to check whether number is multiple of 9
Gross Profit = Selling Price - Cost
(# of favorable outcomes) / (# of possible outcomes)
A = P(1 + r) ^n
Sum of digits is multiple of 9

22. To determine multiple-event probability where each individual event must occur in a certain way.
x - x - x(sq. rt 2)
Figure out the probability for each individual event. Multiply the individual probabilities together.
Immediately try factoring/simplifying when possible
market value

23. 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?
Figure out the probability for each individual event. Multiply the individual probabilities together.
0.15n + 0.08(5) = 0.1(n+5)
(total A) / (total B)
2 steps

24. Quadratic formula
Sum of digits is multiple of 9
The probability of event occurring is...
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
-b +- sq. rt(b^2 - 4ac) / 2a

25. Combined Events: Not E = P(not E) = ?
1
83.3%
1 - P(E)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

26. Percent Formula
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.
Odd
D or E
p/100 = is/of

27. 2nd Rule of Probability: P(E) = 1 - P(not 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
1st Rule of Probability: Basic Rule is what?
The probability of an event occurring plus the probability of the event not occurring = 1
A = P(1 + r) ^n

28. How to find the slope.
(total distance) / (total time)
y2 - y1 / x2 - x1
2 steps
| A union B| = |A| + |B| - |A intersect B|

29. Probability and Geometry.
s Sq. rt (x^r)
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.
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

30. Set Problems formula
(sum of bases)(height) / 2
(x-n(n)y-n)
A = P(1 + r) ^n
Organize into a grid.

31. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
16.6%
12^3
Number is a multiple of 3 and 2

32. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
12.5%
Sum of digits is multiple of 9
22
The probability of event occurring is...

33. Work problem rule
(amount of change) / (original amount)
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.
Odd
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.

34. Formula for area of a Trapezoid
Sum of digits is multiple of 9
(sum of bases)(height) / 2
Sum of digits is multiple of 3 - last two digits multiple of 4.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

35. 4th rule of Probability
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
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)
(total distance) / (total time)
(# of favorable outcomes) / (# of possible outcomes)

36. Gross
14 liters
(n-1)!
The total amount before any deductions
1.7

37. How to check whether a number is a multiple of 6
Sum of digits is multiple of 3
1 - P(E)
Number is a multiple of 3 and 2
1.4

38. 3rd Rule of Probability: Conditional Probability
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(sum of bases)(height) / 2
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.
347

39. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
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.
principle (interest rate - in decimal form) (time - in years)
always try to factor
-b +- sq. rt(b^2 - 4ac) / 2a

40. In general - difficult questions require how many steps to solve?
Figure out the probability for each individual event. Multiply the individual probabilities together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
at least 3 steps
Immediately try factoring/simplifying when possible

41. Average Rate: Average A per B
(total A) / (total B)
sum = (average)(number of terms)
180(n-2)
P(E) + P(F) - P(E and F)

42. Combined Events: E or F
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
Immediately UNFACTOR or vice versa
P(E) + P(F) - P(E and F)

43. 5/6 = what %
22
83.3%
Immediately try factoring/simplifying when possible
1

44. 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
Minor arc = 2(inscribed angle)
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. 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.
(amount of change) / (original amount)

45. Number added or deleted
market value
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.
always try to factor

46. 0! = ?
14 liters
1
D or E
P(event NOT occurring) = 1 - P(event occurring)

47. 3^3 x 4^3 = ?
12^3
3 - 6 - 9 - 12
$11 - 025
Find all prime factors

48. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
12.5%
D or E
Odd
Figure out the probability for each individual event. Multiply the individual probabilities together.

49. Compound interest formula
Purchase price
P(E)P(F)
Principal (1 + interest/number times compounded)^(t)(n)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

50. gcd(m,n)
(# of favorable outcomes) / (# of possible outcomes)
______ |m-n|
Group 1 + Group 2 + Neither - Both = Total
Organize into a grid.