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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. Formula for Mixed Group problems (involving Both/Neither)
Principal (1 + interest/number times compounded)^(t)(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
Group 1 + Group 2 + Neither - Both = Total
Minor arc = 2(inscribed angle)

2. 3^3 x 4^3 = ?
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.
Group 1 + Group 2 + Neither - Both = Total
83.3%
12^3

3. Sum of consecutive numbers
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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
sum = (average)(number of terms)
1.4

4. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
The total amount before any deductions
sum = (average)(number of terms)
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

5. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
(sum of bases)(height) / 2
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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.

6. Work problem rule
12^3
Balancing
16.6%
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.

7. Average Rate: Average A per B
Even
(total A) / (total B)
Figure out the probability for each individual event. Multiply the individual probabilities together.
p/100 = is/of

8. How to find all divisors of a number
P(event NOT occurring) = 1 - P(event occurring)
Find all prime factors
sum = (average)(number of terms)
Figure out the probability for each individual event. Multiply the individual probabilities together.

9. In general - medium questions require how many steps to solve?
12^3
2 steps
(x-n(n)y-n)
(total distance) / (total time)

10. Combined Events: Not E = P(not E) = ?
Find simple interest then look for the answer that is a little bigger
3 - 6 - 9 - 12
Odd
1 - P(E)

11. Sq. rt(2)
Immediately try factoring/simplifying when possible
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
(total A) / (total B)
1.4

12. Sq. rt(3)
______ |m-n|
1.7
(x-n(n)y-n)
Group 1 + Group 2 + Neither - Both = Total

13. gcd(m,n)
$11 - 025
Sum of digits is multiple of 9
______ |m-n|
The probability of an event occurring plus the probability of the event not occurring = 1

14. 1/8 = what %
12.5%
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.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

15. Multiplication principle
Immediately try factoring/simplifying when possible
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
2 steps
16.6%

16. Formula for area of a Trapezoid
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1/16
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.
(sum of bases)(height) / 2

17. The number of outcomes that result in A divided by the total number of possible outcomes.
P(E) + P(F) - P(E and F)
347
The probability of event occurring is...
______ |m-n|

18. 2nd Rule of Probability: P(E) = 1 - P(not E)
The amount after deductions
The probability of an event occurring plus the probability of the event not occurring = 1
Find simple interest then look for the answer that is a little bigger
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

19. Always try to factor
Find all prime factors
P(E) + P(F) - P(E and F)
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
always try to factor

20. How to check for a prime number.

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21. Permutations: Order Matters
22
y2 - y1 / x2 - x1
n! / (n - r)!
Immediately try factoring/simplifying when possible

22. What to do with equations that have fractions
(x-n(n)y-n)
Immediately try factoring/simplifying when possible
x(sq. rt 3) - x - 2x
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.

23. How to check whether a number is a multiple of 6
(amount of change) / (original amount)
4/3 TT r ^3
Number is a multiple of 3 and 2
347

24. 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.
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.
Odd
(sum of bases)(height) / 2

25. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1st Rule of Probability: Basic Rule is what?
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.

26. 2n - 2n+2 - 2n+4
Immediately UNFACTOR or vice versa
| A union B| = |A| + |B| - |A intersect B|
0.15n + 0.08(5) = 0.1(n+5)
Even

27. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
principle (interest rate - in decimal form) (time - in years)
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.
1
sum = (average)(number of terms)

28. Compound interest rule
1st Rule of Probability: Basic Rule is what?
Find simple interest then look for the answer that is a little bigger
P(event NOT occurring) = 1 - P(event occurring)
p/100 = is/of

29. Set Problems formula
83.3%
0.15n + 0.08(5) = 0.1(n+5)
x(sq. rt 3) - x - 2x
(x-n(n)y-n)

30. Inscribed Angle - Minor Arc
at least 3 steps
Minor arc = 2(inscribed angle)
principle (interest rate - in decimal form) (time - in years)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

31. How do you multiply roots together.
x(sq. rt 3) - x - 2x
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
3-4-5 - 5-12-13 - 9-12-15
P(event NOT occurring) = 1 - P(event occurring)

32. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-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
(sum of bases)(height) / 2
The probability of event occurring is...

33. (1/4)^2
1/16
principle (interest rate - in decimal form) (time - in years)
Number is a multiple of 3 and 2
0.15n + 0.08(5) = 0.1(n+5)

34. Trial Problems: look at the probability of NOT OCCURRING
Organize into a grid.
The amount after deductions
P(event NOT occurring) = 1 - P(event occurring)
Minor arc = 2(inscribed angle)

35. 30-60-90 triangle basic lengths of sides
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.
x(sq. rt 3) - x - 2x
1 - P(E)
2 steps

36. Probability and Geometry.
Any multiplication involving an even number creates an even product.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
P(E) + P(F) - P(E and 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

37. Number added or deleted
1.7
Group 1 + Group 2 + Neither - Both = Total
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.

38. 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.
Odd numbers only have ___________
Odd
(x-n(n)y-n)

39. Properties of 0
The probability of an event occurring plus the probability of the event not occurring = 1
x - x - x(sq. rt 2)
Any multiplication involving an even number creates an even product.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

40. 4th rule of Probability
1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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)
(n-1)!

41. 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
P(E) + P(F) - P(E and F)
12^3
gcd(m,n)*lcm(m,n) = mn

42. 5/6 = what %
2 steps
83.3%
s Sq. rt (x^r)
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

43. Compound interest formula
P(E) + P(F) - P(E and F)
Principal (1 + interest/number times compounded)^(t)(n)
P(event NOT occurring) = 1 - P(event occurring)
83.3%

44. When you see an equation in factored form in a question?
83.3%
Immediately UNFACTOR or vice versa
Principal (1 + interest/number times compounded)^(t)(n)
gcd(m,n)*lcm(m,n) = mn

45. Price purchased for by wholesaler
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.
Purchase price
Organize into a grid.
The probability of event occurring is...

46. Multiples of 3
Divide 4999 by 15 => 333 integers
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.
n! / (n - r)!
3 - 6 - 9 - 12

47. 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.
The total amount before any deductions
1
______ |m-n|

48. Odd and Even rule.
1.4
Any multiplication involving an even number creates an even product.
4/3 TT r ^3
Odd

49. Average Rate: Average speed
If the outcome of one event affects the outcome of the other event.
(total distance) / (total time)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
D or E

50. Gross
P(E) + P(F) - P(E and F)
1/16
The total amount before any deductions
n! / (n - r)!

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GMAT Quantitative General

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