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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. 1/8 = what %
12.5%
3-4-5 - 5-12-13 - 9-12-15
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)
3 - 6 - 9 - 12

2. What to do with equations that have fractions
gcd(m,n)*lcm(m,n) = mn
y2 - y1 / x2 - x1
Immediately try factoring/simplifying when possible
Find all prime factors

3. Number added or deleted
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)
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

4. Volume of a sphere
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.
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.
Find all prime factors
4/3 TT r ^3

5. Multiplication principle
1 - P(E)
Group 1 + Group 2 + Neither - Both = Total
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
If the outcome of one event affects the outcome of the other event.

6. Set Problems formula
2 steps
Find simple interest then look for the answer that is a little bigger
(x-n(n)y-n)
y2 - y1 / x2 - x1

7. What does the Sum of the angles in a Regular Polygon formula look like?
Find simple interest then look for the answer that is a little bigger
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
180(n-2)
1/16

8. The average of consecutive numbers
0.15n + 0.08(5) = 0.1(n+5)
Principal (1 + interest/number times compounded)^(t)(n)
2 steps
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

9. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
A = P(1 + r) ^n
22
347
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

10. In general - difficult questions require how many steps to solve?
12^3
Odd
1.4
at least 3 steps

11. 3rd Rule of Probability: Conditional Probability
(# of favorable outcomes) / (# of possible outcomes)
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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Group 1 + Group 2 + Neither - Both = Total

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
p/100 = is/of
16.6%
1 - P(E)
Balancing

13. Price purchased for by wholesaler
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.
12.5%
Purchase price
Odd

14. 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
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.
(x-n(n)y-n)
Group 1 + Group 2 + Neither - Both = Total

15. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
180(n-2)
x(sq. rt 3) - x - 2x
(total A) / (total B)

16. Formula for Mixed Group problems (involving Both/Neither)
-b +- sq. rt(b^2 - 4ac) / 2a
Group 1 + Group 2 + Neither - Both = Total
14 liters
0.15n + 0.08(5) = 0.1(n+5)

17. Indistinguishable events how to find the number of permutations
1.4
Divide 4999 by 15 => 333 integers
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.
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.

18. How to check whether number is multiple of 9
1.4
Sum of digits is multiple of 3 - last two digits multiple of 4.
Sum of digits is multiple of 9
1st Rule of Probability: Basic Rule is what?

19. 45-45-90 triangle basic lengths of sides
Figure out the probability for each individual event. Multiply the individual probabilities together.
x - x - x(sq. rt 2)
(n-1)!
always try to factor

20. gcd(m,n)
______ |m-n|
1
(x-n(n)y-n)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

21. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
sum = (average)(number of terms)
Odd numbers only have ___________
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

22. Net
The amount after deductions
$11 - 025
(total distance) / (total time)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

23. The number of outcomes that result in A divided by the total number of possible outcomes.
Immediately try factoring/simplifying when possible
gcd(m,n)*lcm(m,n) = mn
2 steps
The probability of event occurring is...

24. 30-60-90 triangle basic lengths of sides
(sum of bases)(height) / 2
x(sq. rt 3) - x - 2x
n! / (n - r)!
(total distance) / (total time)

25. How to check whether a number is a multiple of 12.
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.
3 - 6 - 9 - 12
2 steps
Sum of digits is multiple of 3 - last two digits multiple of 4.

26. Formula for area of a Trapezoid
s Sq. rt (x^r)
83.3%
x(sq. rt 3) - x - 2x
(sum of bases)(height) / 2

27. 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?
-b +- sq. rt(b^2 - 4ac) / 2a
180(n-2)
14 liters
Even

28. In general - medium questions require how many steps to solve?
always try to factor
2 steps
Number is a multiple of 3 and 2
Odd numbers only have ___________

29. Average Rate: Average A per B
principle (interest rate - in decimal form) (time - in years)
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.
(total A) / (total B)

30. 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
1/16
P(event NOT occurring) = 1 - P(event occurring)
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 ___________

31. How do you multiply roots together.
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
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)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

32. Trial Problems: look at the probability of NOT OCCURRING
1st Rule of Probability: Basic Rule is what?
P(event NOT occurring) = 1 - P(event occurring)
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.
P(E)P(F)

33. Sq. rt(2)
Balancing
347
1.4
16.6%

34. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
The amount after deductions
always try to factor
x - x - x(sq. rt 2)
A = P(1 + r) ^n

35. 0! = ?
1
Number is a multiple of 3 and 2
sum = (average)(number of terms)
12.5%

36. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Minor arc = 2(inscribed angle)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
principle (interest rate - in decimal form) (time - in years)
Figure out the probability for each individual event. Multiply the individual probabilities together.

37. Inscribed Angle - Minor Arc
(sum of bases)(height) / 2
(x-n(n)y-n)
Minor arc = 2(inscribed angle)
0.15n + 0.08(5) = 0.1(n+5)

38. Odd Factors
P(E)P(F)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Odd numbers only have ___________
4/3 TT r ^3

39. 2nd Rule of Probability: P(E) = 1 - P(not E)
Immediately UNFACTOR or vice versa
Minor arc = 2(inscribed angle)
The probability of an event occurring plus the probability of the event not occurring = 1
Immediately try factoring/simplifying when possible

40. 3^3 x 4^3 = ?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(n-1)!
83.3%
12^3

41. 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)
347
1.7
Find simple interest then look for the answer that is a little bigger

42. 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?
The probability of an event occurring plus the probability of the event not occurring = 1
14 liters
0.15n + 0.08(5) = 0.1(n+5)
Balancing

43. Quadratic formula
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.
-b +- sq. rt(b^2 - 4ac) / 2a
14 liters
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

44. Compound interest rule
(x-n(n)y-n)
Minor arc = 2(inscribed angle)
Find simple interest then look for the answer that is a little bigger
Odd numbers only have ___________

45. How to check whether a number is a multiple of 3.
3 - 6 - 9 - 12
Sum of digits is multiple of 3
Figure out the probability for each individual event. Multiply the individual probabilities together.
1.4

46. Odd and Even rule.
If the outcome of one event affects the outcome of the other event.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.
Any multiplication involving an even number creates an even product.

47. How to check whether a number is a multiple of 4.
Figure out the probability for each individual event. Multiply the individual probabilities together.
y2 - y1 / x2 - x1
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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 find the slope.
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.
y2 - y1 / x2 - x1
D or E
Sum of digits is multiple of 3 - last two digits multiple of 4.

49. Combined Events: E or F
180(n-2)
(n-1)!
3-4-5 - 5-12-13 - 9-12-15
P(E) + P(F) - P(E and F)

50. Triangle abc with d on the outside with a line. What does d = ?
3-4-5 - 5-12-13 - 9-12-15
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.
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
Exterior angle d is equal to the sum of the two remote interior angles a and b

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GMAT Quantitative General

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