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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. gcd(m,n)*lcm(m,n)
83.3%
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
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 9

2. How to check for a prime number.

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3. Volume of a sphere
The total amount before any deductions
1st Rule of Probability: Basic Rule is what?
4/3 TT r ^3
D or E

4. Compound interest formula
Minor arc = 2(inscribed angle)
If the outcome of one event affects the outcome of the other event.
P(E)P(F)
Principal (1 + interest/number times compounded)^(t)(n)

5. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
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
(sum of bases)(height) / 2
| A union B| = |A| + |B| - |A intersect B|

6. Formula for Mixed Group problems (involving Both/Neither)
1.4
Group 1 + Group 2 + Neither - Both = Total
Any multiplication involving an even number creates an even product.
sum = (average)(number of terms)

7. Multiples of 3
1.7
Sum of digits is multiple of 9
3 - 6 - 9 - 12
D or E

8. 1/8 = what %
12.5%
The amount after deductions
P(event NOT occurring) = 1 - P(event occurring)
always try to factor

9. Prime Factorization to find Greatest Common 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
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)
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)

10. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
Sum of digits is multiple of 3 - last two digits multiple of 4.
3 - 6 - 9 - 12
180(n-2)

11. 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?
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)
14 liters
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

12. 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
Sum of digits is multiple of 3 - last two digits multiple of 4.
(sum of bases)(height) / 2
(total A) / (total B)
Balancing

13. Sum of consecutive numbers
Organize into a grid.
sum = (average)(number of terms)
(x-n(n)y-n)
Immediately try factoring/simplifying when possible

14. 3^3 x 4^3 = ?
Sum of digits is multiple of 3 - last two digits multiple of 4.
12^3
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Balancing

15. 1/6 = what %
y2 - y1 / x2 - x1
x - x - x(sq. rt 2)
16.6%
1

16. 2n+1 - 2n+3 - 2n+5
D or E
Divide 4999 by 15 => 333 integers
Odd
P(event NOT occurring) = 1 - P(event occurring)

17. Net
Group 1 + Group 2 + Neither - Both = Total
Immediately try factoring/simplifying when possible
The amount after deductions
The total amount before any deductions

18. 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.
| A union B| = |A| + |B| - |A intersect B|
22
Figure out the probability for each individual event. Multiply the individual probabilities together.

19. Percent increase = ?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(amount of change) / (original amount)
180(n-2)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

20. What does the Sum of the angles in a Regular Polygon formula look like?
If the outcome of one event affects the outcome of the other event.
(x-n(n)y-n)
180(n-2)
(n-1)!

21. Dependent events: When are two events said to be dependent events?
Odd
If the outcome of one event affects the outcome of the other event.
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
______ |m-n|

22. Average Rate: Average A per B
Purchase price
(total A) / (total B)
3-4-5 - 5-12-13 - 9-12-15
Figure out the probability for each individual event. Multiply the individual probabilities together.

23. The number of ways independent events can occur together.
P(event NOT occurring) = 1 - P(event occurring)
The total amount before any deductions
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)!

24. 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.
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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

25. Trial Problems: look at the probability of NOT OCCURRING
(x-n(n)y-n)
P(event NOT occurring) = 1 - P(event occurring)
Any multiplication involving an even number creates an even product.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

26. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
$11 - 025
always try to factor
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

27. (1/4)^2
y2 - y1 / x2 - x1
3 - 6 - 9 - 12
1/16
Find all prime factors

28. How to find all divisors of a number
Find all prime factors
Find simple interest then look for the answer that is a little bigger
22
Sum of digits is multiple of 3 - last two digits multiple of 4.

29. 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
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
Group 1 + Group 2 + Neither - Both = Total
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)

30. Sq. rt(3)
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
(total A) / (total B)
$11 - 025

31. How to check whether a number is a multiple of 3.
(x-n(n)y-n)
Immediately UNFACTOR or vice versa
Sum of digits is multiple of 3
market value

32. Average Rate: Average speed
P(event NOT occurring) = 1 - P(event occurring)
Find simple interest then look for the answer that is a little bigger
(total distance) / (total time)
3 - 6 - 9 - 12

33. 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
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.
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.
______ |m-n|
y2 - y1 / x2 - x1

34. Sq. rt(2)
(total A) / (total B)
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
P(E)P(F)
1.4

35. Set Problems formula
(x-n(n)y-n)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Principal (1 + interest/number times compounded)^(t)(n)
P(E)P(F)

36. Inscribed Angle - Minor Arc
Balancing
83.3%
market value
Minor arc = 2(inscribed angle)

37. How do you multiply roots together.
P(E) + P(F) - P(E and F)
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.
D or E
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

38. 5/6 = what %
$11 - 025
83.3%
A = P(1 + r) ^n
Divide 4999 by 15 => 333 integers

39. x^r/s = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
1 - P(E)
s Sq. rt (x^r)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

40. Price sold for by retailer (after markup)
$11 - 025
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
market value
Find simple interest then look for the answer that is a little bigger

41. Gross Profit formula
The amount after deductions
Gross Profit = Selling Price - Cost
gcd(m,n)*lcm(m,n) = mn
Figure out the probability for each individual event. Multiply the individual probabilities together.

42. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
3-4-5 - 5-12-13 - 9-12-15
(n-1)!
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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

43. Combined Events: Not E = P(not E) = ?
1 - P(E)
(sum of bases)(height) / 2
P(E)P(F)
If the outcome of one event affects the outcome of the other event.

44. Compound interest rule
Principal (1 + interest/number times compounded)^(t)(n)
Find simple interest then look for the answer that is a little bigger
22
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

45. 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
Immediately try factoring/simplifying when possible
(amount of change) / (original amount)
n! / (n - r)!

46. In general - difficult questions require how many steps to solve?
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
Balancing
sum = (average)(number of terms)

47. When you see an equation in factored form in a question?
The total amount before any deductions
Immediately UNFACTOR or vice versa
1.4
______ |m-n|

48. How to check whether a number is a multiple of 4.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
principle (interest rate - in decimal form) (time - in years)
2 steps
Gross Profit = Selling Price - Cost

49. Odd Factors
Odd numbers only have ___________
1.7
1 - P(E)
D or E

50. Combined Events: E and F
P(E)P(F)
$11 - 025
Sum of digits is multiple of 3 - last two digits multiple of 4.
sum = (average)(number of terms)

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GMAT Quantitative General

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