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GMAT Quantitative General

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. Triangle abc with d on the outside with a line. What does d = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
347
n! / (n - r)!
1.7

2. Sq. rt(2)
-b +- sq. rt(b^2 - 4ac) / 2a
1.4
1st Rule of Probability: Basic Rule is what?
y2 - y1 / x2 - x1

3. Quadratic formula
180(n-2)
-b +- sq. rt(b^2 - 4ac) / 2a
The total amount before any deductions
Group 1 + Group 2 + Neither - Both = Total

4. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Sum of digits is multiple of 3 - last two digits multiple of 4.
1
gcd(m,n)*lcm(m,n) = mn
Divide 4999 by 15 => 333 integers

5. Always try to factor
always try to factor
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
1.4

6. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
Odd numbers only have ___________
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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

7. 3rd Rule of Probability: Conditional Probability
(total A) / (total B)
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.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Number is a multiple of 3 and 2

8. 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?
14 liters
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.
Figure out the probability for each individual event. Multiply the individual probabilities together.
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.

9. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
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 the outcome of one event affects the outcome of the other event.
1

10. gcd(m,n)*lcm(m,n)
-b +- sq. rt(b^2 - 4ac) / 2a
The probability of an event occurring plus the probability of the event not occurring = 1
16.6%
gcd(m,n)*lcm(m,n) = mn

11. 2n+1 - 2n+3 - 2n+5
16.6%
Odd
Any multiplication involving an even number creates an even product.
Group 1 + Group 2 + Neither - Both = Total

12. Trial Problems: look at the probability of NOT OCCURRING
Sum of digits is multiple of 3
(# of favorable outcomes) / (# of possible outcomes)
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)

13. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Sum of digits is multiple of 3 - last two digits multiple of 4.
(n-1)!
Divide 4999 by 15 => 333 integers
sum = (average)(number of terms)

14. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Balancing
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(amount of change) / (original amount)

15. Simple probability
n! / (n - r)!
sum = (average)(number of terms)
(# of favorable outcomes) / (# of possible outcomes)
14 liters

16. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Sum of digits is multiple of 9
347
P(event NOT occurring) = 1 - P(event occurring)
-b +- sq. rt(b^2 - 4ac) / 2a

17. Combined Events: E or F
P(E) + P(F) - P(E and F)
n! / (n - r)!
Find simple interest then look for the answer that is a little bigger
14 liters

18. The number of outcomes that result in A divided by the total number of possible outcomes.
| A union B| = |A| + |B| - |A intersect B|
Find all prime factors
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The probability of event occurring is...

19. How to find all divisors of a number
Group 1 + Group 2 + Neither - Both = Total
market value
Sum of digits is multiple of 3 - last two digits multiple of 4.
Find all prime factors

20. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
P(E) + P(F) - P(E and F)
D or E
| A union B| = |A| + |B| - |A intersect B|

21. How to check whether a number is a multiple of 3.
(amount of change) / (original amount)
Sum of digits is multiple of 3
Sum of digits is multiple of 9
| A union B| = |A| + |B| - |A intersect B|

22. Price purchased for by wholesaler
Sum of digits is multiple of 3 - last two digits multiple of 4.
Even
Purchase price
x(sq. rt 3) - x - 2x

23. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Divide 4999 by 15 => 333 integers
3-4-5 - 5-12-13 - 9-12-15
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

24. What does the Sum of the angles in a Regular Polygon formula look like?
s Sq. rt (x^r)
180(n-2)
Balancing
347

25. Number added or deleted
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The probability of an event occurring plus the probability of the event not occurring = 1
P(event NOT occurring) = 1 - P(event occurring)

26. How to check whether number is multiple of 9
A = P(1 + r) ^n
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Sum of digits is multiple of 9
83.3%

27. Formula for Mixed Group problems (involving Both/Neither)
y2 - y1 / x2 - x1
Group 1 + Group 2 + Neither - Both = Total
1st Rule of Probability: Basic Rule is what?
2 steps

28. How to check whether a number is a multiple of 12.
A = P(1 + r) ^n
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.
Sum of digits is multiple of 3 - last two digits multiple of 4.
1st Rule of Probability: Basic Rule is what?

29. Price sold for by retailer (after markup)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The amount after deductions
x(sq. rt 3) - x - 2x
market value

30. Sq. rt(3)
1 - P(E)
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.
1.7

31. (1/4)^2
1/16
Find simple interest then look for the answer that is a little bigger
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

32. 1. A and B < A or B 2. A or B > Individual probabilities of A - B 3. P(A and B) = P(A) x P(B) <-- 'fewer options' 4. P(A or B) = P(A) + P(B) <-- 'more options' - Probability of multiple events rules.
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.
P(event NOT occurring) = 1 - P(event occurring)
1st Rule of Probability: Basic Rule is what?
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.

33. Probability and Geometry.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
-b +- sq. rt(b^2 - 4ac) / 2a
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

34. Odd and Even rule.
______ |m-n|
P(E) + P(F) - P(E and F)
Any multiplication involving an even number creates an even product.
If the outcome of one event affects the outcome of the other event.

35. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Number is a multiple of 3 and 2
12.5%
22
P(E) + P(F) - P(E and F)

36. Intersecting Sets
Divide 4999 by 15 => 333 integers
The total amount before any deductions
1
| A union B| = |A| + |B| - |A intersect B|

37. Percent Formula
p/100 = is/of
gcd(m,n)*lcm(m,n) = mn
y2 - y1 / x2 - x1
The amount after deductions

38. Compound interest formula
$11 - 025
1.7
Principal (1 + interest/number times compounded)^(t)(n)
P(event NOT occurring) = 1 - P(event occurring)

39. Odd Factors
Odd numbers only have ___________
Figure out the probability for each individual event. Multiply the individual probabilities together.
The total amount before any deductions
D or E

40. Net
Any multiplication involving an even number creates an even product.
The amount after deductions
1 - P(E)
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.

41. How do you multiply roots together.
(total A) / (total B)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
n! / (n - r)!
Divide 4999 by 15 => 333 integers

42. Volume of a sphere
D or E
4/3 TT r ^3
sum = (average)(number of terms)
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

43. Sum of consecutive numbers
Minor arc = 2(inscribed angle)
Figure out the probability for each individual event. Multiply the individual probabilities together.
Sum of digits is multiple of 9
sum = (average)(number of terms)

44. When you see an equation in factored form in a question?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
always try to factor
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Immediately UNFACTOR or vice versa

45. Set Problems formula
16.6%
P(E)P(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
(x-n(n)y-n)

46. 1/6 = what %
Immediately try factoring/simplifying when possible
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1.7
16.6%

47. Gross Profit formula
Gross Profit = Selling Price - Cost
(sum of bases)(height) / 2
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.

48. 2n - 2n+2 - 2n+4
Even
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
s Sq. rt (x^r)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

49. Work problem rule
at least 3 steps
The probability of event occurring is...
P(event NOT occurring) = 1 - P(event occurring)
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.

50. 45-45-90 triangle basic lengths of sides
n! / (n - r)!
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
x - x - x(sq. rt 2)
22