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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. How to check for a prime number.

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2. 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?
y2 - y1 / x2 - x1
$11 - 025
14 liters
(n-1)!

3. Prime Factorization to find Greatest Common Factor
A = P(1 + r) ^n
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.
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
1.4

4. 3^3 x 4^3 = ?
12^3
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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

5. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1.7
A = P(1 + r) ^n

6. Indistinguishable events how to find the number of permutations

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7. Average Rate: Average A per B
3-4-5 - 5-12-13 - 9-12-15
p/100 = is/of
(x-n(n)y-n)
(total A) / (total B)

8. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Find simple interest then look for the answer that is a little bigger
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
-b +- sq. rt(b^2 - 4ac) / 2a
$11 - 025

9. Sq. rt(2)
Sum of digits is multiple of 9
2 steps
1st Rule of Probability: Basic Rule is what?
1.4

10. Odd Factors
Figure out the probability for each individual event. Multiply the individual probabilities together.
Odd numbers only have ___________
1 - P(E)
Purchase price

11. 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
Immediately UNFACTOR or vice versa
s Sq. rt (x^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)
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.

12. 2n - 2n+2 - 2n+4
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.
n! / (n - r)!
Even
-b +- sq. rt(b^2 - 4ac) / 2a

13. How to check whether a number is a multiple of 12.
1
Sum of digits is multiple of 3 - last two digits multiple of 4.
-b +- sq. rt(b^2 - 4ac) / 2a
Any multiplication involving an even number creates an even product.

14. How to find all divisors of a number
Find all prime factors
Sum of digits is multiple of 3
$11 - 025
(total A) / (total B)

15. Trial Problems: look at the probability of NOT OCCURRING
Even
Sum of digits is multiple of 9
2 steps
P(event NOT occurring) = 1 - P(event occurring)

16. Volume of a sphere
4/3 TT r ^3
The probability of an event occurring plus the probability of the event not occurring = 1
(total distance) / (total time)
The amount after deductions

17. gcd(m,n)*lcm(m,n)
(x-n(n)y-n)
gcd(m,n)*lcm(m,n) = mn
83.3%
1 - P(E)

18. 1/6 = what %
A = P(1 + r) ^n
Odd
at least 3 steps
16.6%

19. Triangle abc with d on the outside with a line. What does d = ?
(sum of bases)(height) / 2
Immediately UNFACTOR or vice versa
Exterior angle d is equal to the sum of the two remote interior angles a and b
Odd

20. To determine the number of integers less than 5000 that are evenly divisible by 15...?
-b +- sq. rt(b^2 - 4ac) / 2a
principle (interest rate - in decimal form) (time - in years)
180(n-2)
Divide 4999 by 15 => 333 integers

21. 30-60-90 triangle basic lengths of sides
Odd numbers only have ___________
x(sq. rt 3) - x - 2x
Balancing
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

22. Price sold for by retailer (after markup)
y2 - y1 / x2 - x1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
market value
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

23. Properties of 0
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
Odd
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

24. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
P(E)P(F)
The total amount before any deductions
(n-1)!
Number is a multiple of 3 and 2

25. What does the Sum of the angles in a Regular Polygon formula look like?
83.3%
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
16.6%
180(n-2)

26. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
always try to factor
Divide 4999 by 15 => 333 integers
(sum of bases)(height) / 2

27. Combined Events: E and F
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
(x-n(n)y-n)
s Sq. rt (x^r)
P(E)P(F)

28. Inscribed Angle - Minor Arc
83.3%
Minor arc = 2(inscribed angle)
14 liters
1.4

29. Odd and Even rule.
Immediately UNFACTOR or vice versa
Any multiplication involving an even number creates an even product.
(n-1)!
The amount after deductions

30. The number of ways independent events can occur together.
The probability of an event occurring plus the probability of the event not occurring = 1
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
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

31. 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?
Find simple interest then look for the answer that is a little bigger
0.15n + 0.08(5) = 0.1(n+5)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Any multiplication involving an even number creates an even product.

32. Multiples of 3
3 - 6 - 9 - 12
0.15n + 0.08(5) = 0.1(n+5)
sum = (average)(number of terms)
Any multiplication involving an even number creates an even product.

33. 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
(n-1)!
12.5%
12^3

34. How to check whether number is multiple of 9
Sum of digits is multiple of 9
22
The amount after deductions
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

35. gcd(m,n)
______ |m-n|
1.4
$11 - 025
1 - P(E)

36. Compound interest rule
x - x - x(sq. rt 2)
$11 - 025
Find simple interest then look for the answer that is a little bigger
The probability of event occurring is...

37. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
Sum of digits is multiple of 3 - last two digits multiple of 4.
2 steps
Find all prime factors

38. Gross
D or E
The total amount before any deductions
always try to factor
180(n-2)

39. Sq. rt(3)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1.7
Principal (1 + interest/number times compounded)^(t)(n)
Sum of digits is multiple of 3

40. Work problem rule
4/3 TT r ^3
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.
1st Rule of Probability: Basic Rule is what?
The amount after deductions

41. How to check whether a number is a multiple of 4.
1
Gross Profit = Selling Price - Cost
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(sum of bases)(height) / 2

42. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

43. How to check whether a number is a multiple of 6
s Sq. rt (x^r)
Number is a multiple of 3 and 2
Principal (1 + interest/number times compounded)^(t)(n)
n! / (n - r)!

44. Formula for Mixed Group problems (involving Both/Neither)
1/16
0.15n + 0.08(5) = 0.1(n+5)
Group 1 + Group 2 + Neither - Both = Total
4/3 TT r ^3

45. In general - difficult questions require how many steps to solve?
Minor arc = 2(inscribed angle)
at least 3 steps
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.
Number is a multiple of 3 and 2

46. Percent Formula
p/100 = is/of
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
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(E) + P(F) - P(E and F)

47. Combined Events: E or F
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.
______ |m-n|
P(E) + P(F) - P(E and F)
x(sq. rt 3) - x - 2x

48. In general - medium questions require how many steps to solve?
Sum of digits is multiple of 3 - last two digits multiple of 4.
2 steps
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
12.5%

49. Number added or deleted
The total amount before any deductions
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.
Balancing

50. Compound interest formula
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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
(sum of bases)(height) / 2
Principal (1 + interest/number times compounded)^(t)(n)