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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. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Balancing
14 liters
D or E
Odd

2. How to check whether a number is a multiple of 6
-b +- sq. rt(b^2 - 4ac) / 2a
(amount of change) / (original amount)
Number is a multiple of 3 and 2
______ |m-n|

3. 0! = ?
The total amount before any deductions
0.15n + 0.08(5) = 0.1(n+5)
1
n! / (n - r)!

4. In general - medium questions require how many steps to solve?
3 - 6 - 9 - 12
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.
(x-n(n)y-n)
2 steps

5. Odd and Even rule.
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1.4

6. To determine multiple-event probability where each individual event must occur in a certain way.
(n-1)!
(total A) / (total B)
Figure out the probability for each individual event. Multiply the individual probabilities together.
Last two digits are multiple of 4 or the number can be divided by 2 twice.

7. gcd(m,n)*lcm(m,n)
16.6%
1.4
gcd(m,n)*lcm(m,n) = mn
Odd

8. 1/8 = what %
If the outcome of one event affects the outcome of the other event.
12.5%
gcd(m,n)*lcm(m,n) = mn
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.

9. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
Sum of digits is multiple of 9
s Sq. rt (x^r)
12.5%

10. Triangle abc with d on the outside with a line. What does d = ?
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%
(x-n(n)y-n)
Exterior angle d is equal to the sum of the two remote interior angles a and b

11. How to find the slope.
Number is a multiple of 3 and 2
347
y2 - y1 / x2 - x1
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

12. Net
Principal (1 + interest/number times compounded)^(t)(n)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The amount after deductions
market value

13. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
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
Sum of digits is multiple of 9
22
P(event NOT occurring) = 1 - P(event occurring)

14. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
sum = (average)(number of terms)
Group 1 + Group 2 + Neither - Both = Total
$11 - 025
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.

15. Gross
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 total amount before any deductions
1st Rule of Probability: Basic Rule is what?
Number is a multiple of 3 and 2

16. How to find all divisors of a number
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Find all prime factors
Last two digits are multiple of 4 or the number can be divided by 2 twice.
347

17. Volume of a sphere
4/3 TT r ^3
Purchase price
x(sq. rt 3) - x - 2x
p/100 = is/of

18. Always try to factor
P(E) + P(F) - P(E and F)
always try to factor
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)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

19. 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
2 steps
Organize into a grid.
(sum of bases)(height) / 2

20. 1/6 = what %
16.6%
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
22

21. Gross Profit formula
Principal (1 + interest/number times compounded)^(t)(n)
Gross Profit = Selling Price - Cost
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1 - P(E)

22. Set Problems formula
(amount of change) / (original amount)
(x-n(n)y-n)
1.7
market value

23. Formula for area of a Trapezoid
______ |m-n|
14 liters
(sum of bases)(height) / 2
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

24. 3^3 x 4^3 = ?
(n-1)!
Organize into a grid.
12^3
14 liters

25. The average of consecutive numbers
(total distance) / (total time)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
gcd(m,n)*lcm(m,n) = mn
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

26. 2n - 2n+2 - 2n+4
Even
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.
2 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.

27. How to check for a prime number.

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28. Number added or deleted
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Divide 4999 by 15 => 333 integers
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The total amount before any deductions

29. Sum of consecutive numbers
sum = (average)(number of terms)
12.5%
p/100 = is/of
The total amount before any deductions

30. When you see an equation in factored form in a question?
Sum of digits is multiple of 3 - last two digits multiple of 4.
D or E
1st Rule of Probability: Basic Rule is what?
Immediately UNFACTOR or vice versa

31. Trial Problems: look at the probability of NOT OCCURRING
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 3
P(E) + P(F) - P(E and F)

32. Average Rate: Average A per B
1st Rule of Probability: Basic Rule is what?
P(event NOT occurring) = 1 - P(event occurring)
(total A) / (total B)
Minor arc = 2(inscribed angle)

33. 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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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)
0.15n + 0.08(5) = 0.1(n+5)

34. 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
at least 3 steps
2 steps
4/3 TT r ^3

35. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 3
2 steps
3-4-5 - 5-12-13 - 9-12-15

36. How to check whether a number is a multiple of 12.
y2 - y1 / x2 - x1
Sum of digits is multiple of 3 - last two digits multiple of 4.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
83.3%

37. Combined Events: Not E = P(not E) = ?
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.
Even
market value
1 - P(E)

38. (1/4)^2
(# of favorable outcomes) / (# of possible outcomes)
12^3
Odd
1/16

39. Probability and Geometry.
D or E
2 steps
P(E) + P(F) - P(E and 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

40. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Immediately UNFACTOR or vice versa
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
P(event NOT occurring) = 1 - P(event occurring)
sum = (average)(number of terms)

41. Inscribed Angle - Minor Arc
P(E) + P(F) - P(E and F)
Odd numbers only have ___________
Minor arc = 2(inscribed angle)
(total distance) / (total time)

42. In general - difficult questions require how many steps to solve?
Even
at least 3 steps
(sum of bases)(height) / 2
n! / (n - r)!

43. The number of ways independent events can occur together.
(# of favorable outcomes) / (# of possible outcomes)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
4/3 TT r ^3
Any multiplication involving an even number creates an even product.

44. Combined Events: E and F
22
Group 1 + Group 2 + Neither - Both = Total
P(E)P(F)
(total distance) / (total time)

45. Permutations: Order Matters
Divide 4999 by 15 => 333 integers
y2 - y1 / x2 - x1
Immediately UNFACTOR or vice versa
n! / (n - r)!

46. Percent Formula
always try to factor
1.7
p/100 = is/of
1

47. Compound interest rule
gcd(m,n)*lcm(m,n) = mn
Number is a multiple of 3 and 2
0.15n + 0.08(5) = 0.1(n+5)
Find simple interest then look for the answer that is a little bigger

48. gcd(m,n)
______ |m-n|
Figure out the probability for each individual event. Multiply the individual probabilities together.
(n-1)!
s Sq. rt (x^r)

49. What does the Sum of the angles in a Regular Polygon formula look like?
principle (interest rate - in decimal form) (time - in years)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(event NOT occurring) = 1 - P(event occurring)
180(n-2)

50. Sq. rt(2)
If the outcome of one event affects the outcome of the other event.
1.4
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
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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