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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. In general - medium questions require how many steps to solve?
2 steps
sum = (average)(number of terms)
4/3 TT r ^3
x - x - x(sq. rt 2)

2. Compound interest formula
x - x - x(sq. rt 2)
Principal (1 + interest/number times compounded)^(t)(n)
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.

3. 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
Minor arc = 2(inscribed angle)
Immediately try factoring/simplifying when possible
Balancing
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

4. Indistinguishable events how to find the number of permutations

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5. 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?
Sum of digits is multiple of 9
Odd numbers only have ___________
0.15n + 0.08(5) = 0.1(n+5)
Purchase price

6. Percent increase = ?
2 steps
(total A) / (total B)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(amount of change) / (original amount)

7. Net
$11 - 025
12.5%
The amount after deductions
P(E)P(F)

8. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
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.
The probability of an event occurring plus the probability of the event not occurring = 1
p/100 = is/of

9. Inscribed Angle - Minor Arc
Find simple interest then look for the answer that is a little bigger
2 steps
always try to factor
Minor arc = 2(inscribed angle)

10. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
83.3%
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Odd numbers only have ___________

11. Sum of consecutive numbers
sum = (average)(number of terms)
Find simple interest then look for the answer that is a little bigger
s Sq. rt (x^r)
1 - P(E)

12. Work problem rule
______ |m-n|
(x-n(n)y-n)
at least 3 steps
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.

13. To determine multiple-event probability where each individual event must occur in a certain way.
The amount after deductions
P(E)P(F)
Figure out the probability for each individual event. Multiply the individual probabilities together.
Balancing

14. Formula for area of a Trapezoid
Immediately try factoring/simplifying when possible
(sum of bases)(height) / 2
Odd
(total A) / (total B)

15. Formula for Mixed Group problems (involving Both/Neither)
(amount of change) / (original amount)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Group 1 + Group 2 + Neither - Both = Total
14 liters

16. Gross Profit formula
Sum of digits is multiple of 3 - last two digits multiple of 4.
Gross Profit = Selling Price - Cost
Find simple interest then look for the answer that is a little bigger
(sum of bases)(height) / 2

17. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Organize into a grid.
The amount after deductions
$11 - 025
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

18. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1st Rule of Probability: Basic Rule is what?
always try to factor
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

19. Prime Factorization to find Greatest Common Factor
0.15n + 0.08(5) = 0.1(n+5)
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 occurring is...
2 steps

20. Combined Events: E or F
Immediately try factoring/simplifying when possible
P(E) + P(F) - P(E and F)
16.6%
(n-1)!

21. gcd(m,n)*lcm(m,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
gcd(m,n)*lcm(m,n) = mn
Balancing
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

22. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
P(E) + P(F) - P(E and F)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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)

23. 1/6 = what %
0.15n + 0.08(5) = 0.1(n+5)
Sum of digits is multiple of 9
16.6%
Immediately UNFACTOR or vice versa

24. 1/8 = what %
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
12.5%
0.15n + 0.08(5) = 0.1(n+5)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

25. Simple probability
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.
gcd(m,n)*lcm(m,n) = mn
180(n-2)
(# of favorable outcomes) / (# of possible outcomes)

26. Sq. rt(2)
Organize into a grid.
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
1.4

27. 4th rule of Probability
n! / (n - r)!
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)
1/16
Group 1 + Group 2 + Neither - Both = Total

28. Always try to factor
always try to factor
Any multiplication involving an even number creates an even product.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Immediately UNFACTOR or vice versa

29. Permutations: Order Matters
12^3
Sum of digits is multiple of 3 - last two digits multiple of 4.
2 steps
n! / (n - r)!

30. 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
(sum of bases)(height) / 2
Figure out the probability for each individual event. Multiply the individual probabilities together.
Sum of digits is multiple of 3

31. What to do with equations that have fractions
4/3 TT r ^3
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Immediately try factoring/simplifying when possible
y2 - y1 / x2 - x1

32. Multiples of 3
3 - 6 - 9 - 12
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
always try to factor
(amount of change) / (original amount)

33. 3^3 x 4^3 = ?
(n-1)!
at least 3 steps
12^3
Last two digits are multiple of 4 or the number can be divided by 2 twice.

34. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
0.15n + 0.08(5) = 0.1(n+5)
market value

35. Trial Problems: look at the probability of NOT OCCURRING
Find simple interest then look for the answer that is a little bigger
P(event NOT occurring) = 1 - P(event occurring)
1.4
______ |m-n|

36. Triangle abc with d on the outside with a line. What does d = ?
Odd numbers only have ___________
Gross Profit = Selling Price - Cost
Exterior angle d is equal to the sum of the two remote interior angles a and b
Sum of digits is multiple of 3

37. 45-45-90 triangle basic lengths of sides
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 9
x - x - x(sq. rt 2)
12.5%

38. (1/4)^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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
-b +- sq. rt(b^2 - 4ac) / 2a
1/16

39. How to check for a prime number.

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40. 2nd Rule of Probability: P(E) = 1 - P(not E)
n! / (n - r)!
The probability of an event occurring plus the probability of the event not occurring = 1
The amount after deductions
Principal (1 + interest/number times compounded)^(t)(n)

41. The average of consecutive numbers
12.5%
(total distance) / (total time)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
3 - 6 - 9 - 12

42. Set Problems formula
Odd
(x-n(n)y-n)
p/100 = is/of
Divide 4999 by 15 => 333 integers

43. How to check whether number is multiple of 9
Sum of digits is multiple of 9
14 liters
A = P(1 + r) ^n
Minor arc = 2(inscribed angle)

44. Combined Events: E and F
D or E
P(event NOT occurring) = 1 - P(event occurring)
P(E)P(F)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

45. Price sold for by retailer (after markup)
market value
Gross Profit = Selling Price - Cost
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
3 - 6 - 9 - 12

46. 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?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Any multiplication involving an even number creates an even product.
180(n-2)
14 liters

47. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
Sum of digits is multiple of 9
Even
P(event NOT occurring) = 1 - P(event occurring)

48. 5/6 = what %
(total distance) / (total time)
Organize into a grid.
Purchase price
83.3%

49. gcd(m,n)
Find simple interest then look for the answer that is a little bigger
principle (interest rate - in decimal form) (time - in years)
Figure out the probability for each individual event. Multiply the individual probabilities together.
______ |m-n|

50. Sq. rt(3)
The total amount before any deductions
3 - 6 - 9 - 12
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
1.7

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GMAT Quantitative General

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