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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. Combined Events: Not E = P(not E) = ?
180(n-2)
Find simple interest then look for the answer that is a little bigger
Sum of digits is multiple of 3 - last two digits multiple of 4.
1 - P(E)

2. In general - medium questions require how many steps to solve?
2 steps
1/16
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
Purchase price

3. How do you multiply roots together.
347
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)
16.6%
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

4. Three triangle length patterns
Principal (1 + interest/number times compounded)^(t)(n)
3-4-5 - 5-12-13 - 9-12-15
$11 - 025
Balancing

5. 45-45-90 triangle basic lengths of sides
Find all prime factors
Exterior angle d is equal to the sum of the two remote interior angles a and b
x - x - x(sq. rt 2)
D or E

6. 30-60-90 triangle basic lengths of sides
Find simple interest then look for the answer that is a little bigger
Group 1 + Group 2 + Neither - Both = Total
x(sq. rt 3) - x - 2x
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

7. How to find all divisors of a number
Find all prime factors
1.4
$11 - 025
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

8. Odd Factors
Find simple interest then look for the answer that is a little bigger
Odd numbers only have ___________
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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

9. Inscribed Angle - Minor Arc
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)
Minor arc = 2(inscribed angle)
x - x - x(sq. rt 2)
x(sq. rt 3) - x - 2x

10. Quadratic formula
Odd numbers only have ___________
x - x - x(sq. rt 2)
-b +- sq. rt(b^2 - 4ac) / 2a
p/100 = is/of

11. Sq. rt(2)
1.4
347
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
______ |m-n|

12. Compound interest formula
(total distance) / (total time)
Principal (1 + interest/number times compounded)^(t)(n)
Sum of digits is multiple of 3
n! / (n - r)!

13. Gross
The total amount before any deductions
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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
12.5%

14. The average of consecutive numbers
Find simple interest then look for the answer that is a little bigger
Last two digits are multiple of 4 or the number can be divided by 2 twice.
y2 - y1 / x2 - x1
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

15. 0! = ?
1
Sum of digits is multiple of 9
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.
Figure out the probability for each individual event. Multiply the individual probabilities together.

16. What to do with equations that have fractions
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 probability of an event occurring plus the probability of the event not occurring = 1
y2 - y1 / x2 - x1
Immediately try factoring/simplifying when possible

17. Compound interest rule
(n-1)!
x - x - x(sq. rt 2)
Find simple interest then look for the answer that is a little bigger
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

18. Formula for area of a Trapezoid
(sum of bases)(height) / 2
always try to factor
at least 3 steps
$11 - 025

19. In general - difficult questions require how many steps to solve?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Odd numbers only have ___________
at least 3 steps
(sum of bases)(height) / 2

20. When you see an equation in factored form in a question?
Principal (1 + interest/number times compounded)^(t)(n)
Immediately UNFACTOR or vice versa
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)
1.4

21. 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
Number is a multiple of 3 and 2
P(event NOT occurring) = 1 - P(event occurring)
180(n-2)
Balancing

22. 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?
1/16
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.
$11 - 025
14 liters

23. What does the Sum of the angles in a Regular Polygon formula look like?
s Sq. rt (x^r)
Find all prime factors
| A union B| = |A| + |B| - |A intersect B|
180(n-2)

24. Average Rate: Average speed
1/16
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The probability of an event occurring plus the probability of the event not occurring = 1
(total distance) / (total time)

25. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
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)
(total A) / (total B)
sum = (average)(number of terms)

26. 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.
Odd numbers only have ___________
The probability of an event occurring plus the probability of the event not occurring = 1
180(n-2)

27. How to check for a prime number.

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28. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
always try to factor
(n-1)!
(amount of change) / (original amount)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

29. Prime Factorization to find Greatest Common Factor
n! / (n - r)!
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
Principal (1 + interest/number times compounded)^(t)(n)
(total A) / (total B)

30. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
3-4-5 - 5-12-13 - 9-12-15
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
(# of favorable outcomes) / (# of possible outcomes)
347

31. Percent increase = ?
1.7
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(sum of bases)(height) / 2
(amount of change) / (original amount)

32. Average Rate: Average A per B
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
P(E)P(F)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(total A) / (total B)

33. Price purchased for by wholesaler
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
16.6%
Sum of digits is multiple of 3
Purchase price

34. Combined Events: E or F
12.5%
Minor arc = 2(inscribed angle)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
P(E) + P(F) - P(E and F)

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
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.
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.
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
16.6%

36. How to check whether a number is a multiple of 6
______ |m-n|
Number is a multiple of 3 and 2
3 - 6 - 9 - 12
1 - P(E)

37. Dependent events: When are two events said to be dependent events?
12^3
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.
1.4
If the outcome of one event affects the outcome of the other event.

38. Simple probability
always try to factor
22
______ |m-n|
(# of favorable outcomes) / (# of possible outcomes)

39. 1/8 = what %
12.5%
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(x-n(n)y-n)
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.

40. The number of outcomes that result in A divided by the total number of possible outcomes.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
2 steps
14 liters
The probability of event occurring is...

41. Multiplication principle
P(E)P(F)
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
180(n-2)
Odd

42. Combined Events: E and F
Balancing
12^3
The total amount before any deductions
P(E)P(F)

43. Volume of a sphere
P(E)P(F)
12.5%
1
4/3 TT r ^3

44. 3^3 x 4^3 = ?
1.4
y2 - y1 / x2 - x1
sum = (average)(number of terms)
12^3

45. Formula for Mixed Group problems (involving Both/Neither)
s Sq. rt (x^r)
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
Any multiplication involving an even number creates an even product.
Group 1 + Group 2 + Neither - Both = Total

46. Number added or deleted
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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
$11 - 025

47. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
16.6%
-b +- sq. rt(b^2 - 4ac) / 2a
$11 - 025
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.

48. Percent Formula
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
______ |m-n|
The amount after deductions
p/100 = is/of

49. x^r/s = ?
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.
Any multiplication involving an even number creates an even product.
Minor arc = 2(inscribed angle)
s Sq. rt (x^r)

50. Sq. rt(3)
(total A) / (total B)
1.7
y2 - y1 / x2 - x1
n! / (n - r)!

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GMAT Quantitative General

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