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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. x^r/s = ?
14 liters
Figure out the probability for each individual event. Multiply the individual probabilities together.
(sum of bases)(height) / 2
s Sq. rt (x^r)

2. 4th rule of Probability
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)
-b +- sq. rt(b^2 - 4ac) / 2a
1/16
Figure out the probability for each individual event. Multiply the individual probabilities together.

3. Average Rate: Average A per B
(total A) / (total B)
Number is a multiple of 3 and 2
Exterior angle d is equal to the sum of the two remote interior angles a and b
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.

4. 1/8 = what %
12.5%
-b +- sq. rt(b^2 - 4ac) / 2a
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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.

5. Indistinguishable events how to find the number of permutations

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6. 2nd Rule of Probability: P(E) = 1 - P(not E)
3-4-5 - 5-12-13 - 9-12-15
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The probability of an event occurring plus the probability of the event not occurring = 1
3 - 6 - 9 - 12

7. 45-45-90 triangle basic lengths of sides
347
x - x - x(sq. rt 2)
$11 - 025
Find simple interest then look for the answer that is a little bigger

8. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Odd
Group 1 + Group 2 + Neither - Both = Total
Purchase price

9. In general - medium questions require how many steps to solve?
y2 - y1 / x2 - x1
2 steps
1.4
The probability of event occurring is...

10. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Sum of digits is multiple of 3
Even
A = P(1 + r) ^n
p/100 = is/of

11. How to find all divisors of a number
Sum of digits is multiple of 9
347
Find all prime factors
Group 1 + Group 2 + Neither - Both = Total

12. Percent Formula
p/100 = is/of
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Number is a multiple of 3 and 2
2 steps

13. Gross
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 total amount before any deductions
-b +- sq. rt(b^2 - 4ac) / 2a
Number is a multiple of 3 and 2

14. Set Problems formula
-b +- sq. rt(b^2 - 4ac) / 2a
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)
P(E)P(F)
(x-n(n)y-n)

15. Odd Factors
Odd numbers only have ___________
Figure out the probability for each individual event. Multiply the individual probabilities together.
Number is a multiple of 3 and 2
Sum of digits is multiple of 9

16. Triangle abc with d on the outside with a line. What does d = ?
Find all prime factors
Exterior angle d is equal to the sum of the two remote interior angles a and b
| A union B| = |A| + |B| - |A intersect B|
-b +- sq. rt(b^2 - 4ac) / 2a

17. Number added or deleted
2 steps
market value
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original 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)

18. Quadratic formula
p/100 = is/of
-b +- sq. rt(b^2 - 4ac) / 2a
(amount of change) / (original amount)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

19. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
The probability of event occurring is...
1.4
Balancing
347

20. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
x - x - x(sq. rt 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
Exterior angle d is equal to the sum of the two remote interior angles a and b

21. Prime Factorization to find Greatest Common Factor
y2 - y1 / x2 - x1
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
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
The total amount before any deductions

22. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
14 liters
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.
22

23. How to check whether a number is a multiple of 6
Even
Number is a multiple of 3 and 2
Find simple interest then look for the answer that is a little bigger
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.

24. Compound interest rule
Find simple interest then look for the answer that is a little bigger
Exterior angle d is equal to the sum of the two remote interior angles a and b
Immediately UNFACTOR or vice versa
1 - P(E)

25. Multiples of 3
Immediately try factoring/simplifying when possible
(sum of bases)(height) / 2
at least 3 steps
3 - 6 - 9 - 12

26. Price sold for by retailer (after markup)
Odd
market value
The amount after deductions
at least 3 steps

27. 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?
at least 3 steps
22
(n-1)!
0.15n + 0.08(5) = 0.1(n+5)

28. Combined Events: E or F
Figure out the probability for each individual event. Multiply the individual probabilities together.
Principal (1 + interest/number times compounded)^(t)(n)
P(E) + P(F) - P(E and F)
Odd numbers only have ___________

29. In general - difficult questions require how many steps to solve?
1
A = P(1 + r) ^n
P(E) + P(F) - P(E and F)
at least 3 steps

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
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.
Sum of digits is multiple of 3
4/3 TT r ^3

31. Sq. rt(3)
Any multiplication involving an even number creates an even product.
sum = (average)(number of terms)
1.7
4/3 TT r ^3

32. Permutations: Order Matters
Odd numbers only have ___________
n! / (n - r)!
Divide 4999 by 15 => 333 integers
(x-n(n)y-n)

33. Price purchased for by wholesaler
Purchase price
0.15n + 0.08(5) = 0.1(n+5)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
2 steps

34. gcd(m,n)*lcm(m,n)
12^3
83.3%
gcd(m,n)*lcm(m,n) = mn
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.

35. Volume of a sphere
P(E)P(F)
4/3 TT r ^3
Purchase price
| A union B| = |A| + |B| - |A intersect B|

36. When you see an equation in factored form in a question?
Odd numbers only have ___________
Even
Find all prime factors
Immediately UNFACTOR or vice versa

37. Combined Events: Not E = P(not E) = ?
always try to factor
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 - P(E)
Principal (1 + interest/number times compounded)^(t)(n)

38. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(x-n(n)y-n)
0.15n + 0.08(5) = 0.1(n+5)
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)

39. 5/6 = what %
12.5%
Figure out the probability for each individual event. Multiply the individual probabilities together.
83.3%
1 - P(E)

40. The number of outcomes that result in A divided by the total number of possible outcomes.
Sum of digits is multiple of 3
The probability of event occurring is...
Figure out the probability for each individual event. Multiply the individual probabilities together.
(n-1)!

41. 2n+1 - 2n+3 - 2n+5
(total distance) / (total time)
Odd
Sum of digits is multiple of 9
Organize into a grid.

42. Average Rate: Average speed
(total distance) / (total time)
14 liters
D or E
16.6%

43. Simple probability
Number is a multiple of 3 and 2
gcd(m,n)*lcm(m,n) = mn
p/100 = is/of
(# of favorable outcomes) / (# of possible outcomes)

44. 3^3 x 4^3 = ?
12^3
Exterior angle d is equal to the sum of the two remote interior angles a and b
Even
Odd

45. Combined Events: E and F
-b +- sq. rt(b^2 - 4ac) / 2a
(sum of bases)(height) / 2
n! / (n - r)!
P(E)P(F)

46. How do you multiply roots together.
1.7
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
y2 - y1 / x2 - x1

47. The average of consecutive numbers
If the outcome of one event affects the outcome of the other event.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
The amount after deductions
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

48. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
Minor arc = 2(inscribed angle)
Odd numbers only have ___________
(total A) / (total B)

49. 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
(n-1)!
3-4-5 - 5-12-13 - 9-12-15
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

50. Percent increase = ?
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
(amount of change) / (original amount)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Sum of digits is multiple of 3 - last two digits multiple of 4.

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GMAT Quantitative General

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