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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. Gross
market value
Number is a multiple of 3 and 2
Purchase price
The total amount before any deductions

2. Volume of a sphere
Find simple interest then look for the answer that is a little bigger
4/3 TT r ^3
s Sq. rt (x^r)
Odd

3. 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?
Minor arc = 2(inscribed angle)
14 liters
x(sq. rt 3) - x - 2x
sum = (average)(number of terms)

4. Gross Profit formula
12^3
Gross Profit = Selling Price - Cost
Organize into a grid.
14 liters

5. How to check whether a number is a multiple of 6
16.6%
Number is a multiple of 3 and 2
(sum of bases)(height) / 2
Divide 4999 by 15 => 333 integers

6. To determine multiple-event probability where each individual event must occur in a certain way.
market value
Sum of digits is multiple of 3
Figure out the probability for each individual event. Multiply the individual probabilities together.
$11 - 025

7. x^r/s = ?
12^3
s Sq. rt (x^r)
-b +- sq. rt(b^2 - 4ac) / 2a
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

8. Percent increase = ?
Purchase price
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.
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
(amount of change) / (original amount)

9. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
Gross Profit = Selling Price - Cost
Principal (1 + interest/number times compounded)^(t)(n)
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

10. Indistinguishable events how to find the number of permutations

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11. Prime Factorization to find Greatest Common Factor
Gross Profit = Selling Price - Cost
12.5%
p/100 = is/of
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

12. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
Exterior angle d is equal to the sum of the two remote interior angles a and b
______ |m-n|
Sum of digits is multiple of 3 - last two digits multiple of 4.

13. How to check for a prime number.

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14. Compound interest formula
The probability of event occurring is...
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Principal (1 + interest/number times compounded)^(t)(n)
Balancing

15. Sum of consecutive numbers
16.6%
(n-1)!
sum = (average)(number of terms)
Sum of digits is multiple of 3 - last two digits multiple of 4.

16. Properties of 0
The amount after deductions
P(E) + P(F) - P(E and F)
Group 1 + Group 2 + Neither - Both = Total
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

17. Multiplication principle
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.
Immediately UNFACTOR or vice versa
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
Odd

18. 3^3 x 4^3 = ?
12^3
14 liters
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.
Figure out the probability for each individual event. Multiply the individual probabilities together.

19. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
Number is a multiple of 3 and 2
The probability of event occurring is...
(sum of bases)(height) / 2

20. How to find the slope.
Sum of digits is multiple of 3
(amount of change) / (original amount)
y2 - y1 / x2 - x1
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.

21. Average Rate: Average A per B
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
3-4-5 - 5-12-13 - 9-12-15
A = P(1 + r) ^n
(total A) / (total B)

22. 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)
If the outcome of one event affects the outcome of the other event.
Principal (1 + interest/number times compounded)^(t)(n)
p/100 = is/of

23. 3rd Rule of Probability: Conditional Probability
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.
Immediately UNFACTOR or vice versa
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)

24. 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?
Number is a multiple of 3 and 2
4/3 TT r ^3
0.15n + 0.08(5) = 0.1(n+5)
principle (interest rate - in decimal form) (time - in years)

25. How to find all divisors of a number
Find all prime factors
4/3 TT r ^3
3-4-5 - 5-12-13 - 9-12-15
market value

26. 2nd Rule of Probability: P(E) = 1 - P(not E)
(total A) / (total 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.
D or E
The probability of an event occurring plus the probability of the event not occurring = 1

27. Intersecting Sets
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1 - P(E)
Odd
| A union B| = |A| + |B| - |A intersect B|

28. Combined Events: E or F
s Sq. rt (x^r)
Minor arc = 2(inscribed angle)
(sum of bases)(height) / 2
P(E) + P(F) - P(E and F)

29. 2n+1 - 2n+3 - 2n+5
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Odd
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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

30. 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
180(n-2)
Gross Profit = Selling Price - Cost
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Balancing

31. gcd(m,n)*lcm(m,n)
p/100 = is/of
(total A) / (total B)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
gcd(m,n)*lcm(m,n) = mn

32. 1/6 = what %
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
Immediately try factoring/simplifying when possible
16.6%
Even

33. The average of consecutive numbers
Find all prime factors
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Odd numbers only have ___________

34. 1/8 = what %
(total A) / (total B)
Number is a multiple of 3 and 2
12.5%
(amount of change) / (original amount)

35. 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
Figure out the probability for each individual event. Multiply the individual probabilities together.
(# of favorable outcomes) / (# of possible outcomes)
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.
(total distance) / (total time)

36. Price purchased for by wholesaler
Any multiplication involving an even number creates an even product.
Purchase price
$11 - 025
1 - P(E)

37. Always try to factor
Find all prime factors
x - x - x(sq. rt 2)
1
always try to factor

38. 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)
Sum of digits is multiple of 9
The probability of event occurring is...
Odd numbers only have ___________

39. Triangle abc with d on the outside with a line. What does d = ?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Exterior angle d is equal to the sum of the two remote interior angles a and b
83.3%
Find simple interest then look for the answer that is a little bigger

40. Number added or deleted
1/16
12^3
180(n-2)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

41. Permutations: Order Matters
Find simple interest then look for the answer that is a little bigger
3-4-5 - 5-12-13 - 9-12-15
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.

42. Price sold for by retailer (after markup)
x(sq. rt 3) - x - 2x
n! / (n - r)!
market value
The amount after deductions

43. Three triangle length patterns
Gross Profit = Selling Price - Cost
3-4-5 - 5-12-13 - 9-12-15
sum = (average)(number of terms)
The probability of event occurring is...

44. Odd Factors
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Figure out the probability for each individual event. Multiply the individual probabilities together.
Odd numbers only have ___________
s Sq. rt (x^r)

45. 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.
Organize into a grid.
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
Immediately UNFACTOR or vice versa

46. Set Problems formula
P(E)P(F)
s Sq. rt (x^r)
(x-n(n)y-n)
always try to factor

47. Quadratic formula
Purchase price
-b +- sq. rt(b^2 - 4ac) / 2a
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
| A union B| = |A| + |B| - |A intersect B|

48. (1/4)^2
1/16
0.15n + 0.08(5) = 0.1(n+5)
The total amount before any deductions
Even

49. 0! = ?
p/100 = is/of
Principal (1 + interest/number times compounded)^(t)(n)
1
(total A) / (total B)

50. Formula for Mixed Group problems (involving Both/Neither)
p/100 = is/of
Odd
Group 1 + Group 2 + Neither - Both = Total
Immediately try factoring/simplifying when possible

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GMAT Quantitative General

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