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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. Sq. rt(3)
1.7
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.
1.4
s Sq. rt (x^r)

2. Dependent events: When are two events said to be dependent events?
Divide 4999 by 15 => 333 integers
If the outcome of one event affects the outcome of the other event.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
4/3 TT r ^3

3. Properties of 0
Sum of digits is multiple of 3 - last two digits multiple of 4.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The probability of event occurring is...
(total A) / (total B)

4. 5/6 = what %
83.3%
(sum of bases)(height) / 2
22
Balancing

5. How to check for a prime number.

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6. Work problem rule
Gross Profit = Selling Price - Cost
______ |m-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.
2 steps

7. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
The probability of event occurring is...
Find simple interest then look for the answer that is a little bigger
22

8. How to check whether a number is a multiple of 12.
P(E)P(F)
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)
Sum of digits is multiple of 3 - last two digits multiple of 4.
1

9. In general - difficult questions require how many steps to solve?
1
at least 3 steps
3-4-5 - 5-12-13 - 9-12-15
Purchase price

10. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
0.15n + 0.08(5) = 0.1(n+5)
(n-1)!
12^3

11. Odd Factors
Balancing
Odd numbers only have ___________
P(E)P(F)
(amount of change) / (original amount)

12. Combined Events: E and F
A = P(1 + r) ^n
P(E)P(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.
Figure out the probability for each individual event. Multiply the individual probabilities together.

13. 3^3 x 4^3 = ?
Figure out the probability for each individual event. Multiply the individual probabilities together.
P(E)P(F)
12^3
16.6%

14. 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
1st Rule of Probability: Basic Rule is what?
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.
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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

15. Percent increase = ?
Minor arc = 2(inscribed angle)
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)
Number is a multiple of 3 and 2
(amount of change) / (original amount)

16. Always try to factor
always try to factor
Sum of digits is multiple of 9
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.
(x-n(n)y-n)

17. x^r/s = ?
Sum of digits is multiple of 3
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
s Sq. rt (x^r)

18. Inscribed Angle - Minor Arc
Figure out the probability for each individual event. Multiply the individual probabilities together.
n! / (n - r)!
A = P(1 + r) ^n
Minor arc = 2(inscribed angle)

19. What to do with equations that have fractions
sum = (average)(number of terms)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately try factoring/simplifying when possible
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

20. Permutations: Order Matters
n! / (n - r)!
P(E)P(F)
Even
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.

21. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
180(n-2)
(total distance) / (total time)
(n-1)!

22. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
market value
Last two digits are multiple of 4 or the number can be divided by 2 twice.
$11 - 025
Immediately try factoring/simplifying when possible

23. The average of consecutive numbers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
3 - 6 - 9 - 12
(total distance) / (total time)
x - x - x(sq. rt 2)

24. 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
22
If the outcome of one event affects the outcome of the other event.

25. 3rd Rule of Probability: Conditional Probability
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.
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.
A = P(1 + r) ^n
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

26. Price purchased for by wholesaler
12^3
12.5%
Purchase price
Organize into a grid.

27. 1/8 = what %
x(sq. rt 3) - x - 2x
s Sq. rt (x^r)
12.5%
Group 1 + Group 2 + Neither - Both = Total

28. Simple probability
______ |m-n|
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 probability of an event occurring plus the probability of the event not occurring = 1
(# of favorable outcomes) / (# of possible outcomes)

29. What does the Sum of the angles in a Regular Polygon formula look like?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
180(n-2)
(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.

30. 45-45-90 triangle basic lengths of sides
Sum of digits is multiple of 3 - last two digits multiple of 4.
x(sq. rt 3) - x - 2x
y2 - y1 / x2 - x1
x - x - x(sq. rt 2)

31. Average Rate: Average A per B
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(total A) / (total B)
______ |m-n|

32. Formula for Mixed Group problems (involving Both/Neither)
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
Group 1 + Group 2 + Neither - Both = Total
gcd(m,n)*lcm(m,n) = mn
3-4-5 - 5-12-13 - 9-12-15

33. 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)
Find all prime factors
The amount after deductions
Even

34. gcd(m,n)*lcm(m,n)
Group 1 + Group 2 + Neither - Both = Total
gcd(m,n)*lcm(m,n) = mn
The probability of an event occurring plus the probability of the event not occurring = 1
3 - 6 - 9 - 12

35. Gross Profit formula
Exterior angle d is equal to the sum of the two remote interior angles a and b
Gross Profit = Selling Price - Cost
83.3%
n! / (n - r)!

36. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
3-4-5 - 5-12-13 - 9-12-15
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
always try to factor
Number is a multiple of 3 and 2

37. (1/4)^2
3 - 6 - 9 - 12
P(event NOT occurring) = 1 - P(event occurring)
1/16
16.6%

38. 2nd Rule of Probability: P(E) = 1 - P(not E)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
2 steps
The probability of an event occurring plus the probability of the event not occurring = 1
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.

39. To determine multiple-event probability where each individual event must occur in a certain way.
Sum of digits is multiple of 3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Figure out the probability for each individual event. Multiply the individual probabilities together.
Organize into a grid.

40. How to check whether number is multiple of 9
Balancing
Sum of digits is multiple of 9
n! / (n - r)!
22

41. Sum of consecutive numbers
at least 3 steps
sum = (average)(number of terms)
Gross Profit = Selling Price - Cost
The total amount before any deductions

42. Combined Events: E or F
1/16
P(E) + P(F) - P(E and F)
-b +- sq. rt(b^2 - 4ac) / 2a
Divide 4999 by 15 => 333 integers

43. Probability and Geometry.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
4/3 TT r ^3
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

44. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
1.4
347
16.6%
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

45. Sq. rt(2)
12.5%
14 liters
1.4
Immediately try factoring/simplifying when possible

46. Number added or deleted
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.
Find simple interest then look for the answer that is a little bigger
A = P(1 + r) ^n

47. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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
D or E
always try to factor
Divide 4999 by 15 => 333 integers

48. The number of ways independent events can occur together.
A = P(1 + r) ^n
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|
Immediately try factoring/simplifying when possible

49. The number of outcomes that result in A divided by the total number of possible outcomes.
A = P(1 + r) ^n
Purchase price
The probability of event occurring is...
Immediately try factoring/simplifying when possible

50. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
sum = (average)(number of terms)
Find all prime factors
83.3%