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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. 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
The total amount before any deductions
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.
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)

2. In general - medium questions require how many steps to solve?
Find simple interest then look for the answer that is a little bigger
180(n-2)
Even
2 steps

3. The number of ways independent events can occur together.
s Sq. rt (x^r)
(sum of bases)(height) / 2
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.

4. 45-45-90 triangle basic lengths of sides
A = P(1 + r) ^n
x - x - x(sq. rt 2)
1st Rule of Probability: Basic Rule is what?
Immediately UNFACTOR or vice versa

5. 2n+1 - 2n+3 - 2n+5
Odd
Exterior angle d is equal to the sum of the two remote interior angles a and b
Immediately UNFACTOR or vice versa
Last two digits are multiple of 4 or the number can be divided by 2 twice.

6. Average Rate: Average A per B
Balancing
Even
D or E
(total A) / (total B)

7. Percent increase = ?
$11 - 025
P(E) + P(F) - P(E and F)
(amount of change) / (original amount)
Group 1 + Group 2 + Neither - Both = Total

8. 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.
D or E
Purchase price
Group 1 + Group 2 + Neither - Both = Total
1st Rule of Probability: Basic Rule is what?

9. Combined Events: E or F
P(E) + P(F) - P(E and F)
(sum of bases)(height) / 2
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Divide 4999 by 15 => 333 integers

10. Sq. rt(2)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(total A) / (total B)
Divide 4999 by 15 => 333 integers
1.4

11. 1/8 = what %
$11 - 025
12.5%
3-4-5 - 5-12-13 - 9-12-15
A = P(1 + r) ^n

12. gcd(m,n)*lcm(m,n)
22
If the outcome of one event affects the outcome of the other event.
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.
gcd(m,n)*lcm(m,n) = mn

13. 3rd Rule of Probability: Conditional Probability
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.
The probability of event occurring is...
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
A = P(1 + r) ^n

14. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
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.
p/100 = is/of
Sum of digits is multiple of 3

15. How do you multiply roots together.
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.
at least 3 steps
Figure out the probability for each individual event. Multiply the individual probabilities together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

16. Odd and Even rule.
Any multiplication involving an even number creates an even product.
Balancing
3 - 6 - 9 - 12
12.5%

17. Odd Factors
Odd numbers only have ___________
Gross Profit = Selling Price - Cost
n! / (n - r)!
principle (interest rate - in decimal form) (time - in years)

18. 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
The amount after deductions
A = P(1 + r) ^n
Balancing
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

19. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
| A union B| = |A| + |B| - |A intersect B|
principle (interest rate - in decimal form) (time - in years)
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.

20. Volume of a sphere
Group 1 + Group 2 + Neither - Both = Total
A = P(1 + r) ^n
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.

21. Work problem rule
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Immediately UNFACTOR or vice versa
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.
Find simple interest then look for the answer that is a little bigger

22. Net
Even
Sum of digits is multiple of 3 - last two digits multiple of 4.
The amount after deductions
Find all prime factors

23. How to check whether a number is a multiple of 3.
The total amount before any deductions
Sum of digits is multiple of 3
Find all prime factors
The amount after deductions

24. 30-60-90 triangle basic lengths of sides
Balancing
(# of favorable outcomes) / (# of possible outcomes)
A = P(1 + r) ^n
x(sq. rt 3) - x - 2x

25. Sum of consecutive numbers
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(sum of bases)(height) / 2
sum = (average)(number of terms)
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

26. 0! = ?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1 - P(E)
1
always try to factor

27. x^r/s = ?
14 liters
s Sq. rt (x^r)
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 9

28. 1/6 = what %
sum = (average)(number of terms)
gcd(m,n)*lcm(m,n) = mn
16.6%
Odd numbers only have ___________

29. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
Minor arc = 2(inscribed angle)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1.4

30. (1/4)^2
The amount after deductions
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.
Divide 4999 by 15 => 333 integers

31. Probability and Geometry.
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
$11 - 025
(# of favorable outcomes) / (# of possible outcomes)
(amount of change) / (original amount)

32. Three triangle length patterns
n! / (n - r)!
14 liters
Immediately UNFACTOR or vice versa
3-4-5 - 5-12-13 - 9-12-15

33. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Divide 4999 by 15 => 333 integers
22
1
A = P(1 + r) ^n

34. 2nd Rule of Probability: P(E) = 1 - P(not E)
at least 3 steps
12.5%
The probability of an event occurring plus the probability of the event not occurring = 1
347

35. 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
Group 1 + Group 2 + Neither - Both = Total
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1.7

36. How to find all divisors of a number
14 liters
(# of favorable outcomes) / (# of possible outcomes)
2 steps
Find all prime factors

37. Permutations: Order Matters
Principal (1 + interest/number times compounded)^(t)(n)
Minor arc = 2(inscribed angle)
Any multiplication involving an even number creates an even product.
n! / (n - r)!

38. Average Rate: Average speed
16.6%
-b +- sq. rt(b^2 - 4ac) / 2a
D or E
(total distance) / (total time)

39. 5/6 = what %
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.
83.3%
347
The probability of event occurring is...

40. Indistinguishable events how to find the number of permutations

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41. Trial Problems: look at the probability of NOT OCCURRING
Odd
14 liters
P(event NOT occurring) = 1 - P(event occurring)
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.

42. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
Any multiplication involving an even number creates an even product.
-b +- sq. rt(b^2 - 4ac) / 2a
market value

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

44. Inscribed Angle - Minor Arc
P(event NOT occurring) = 1 - P(event occurring)
Minor arc = 2(inscribed angle)
Organize into a grid.
Group 1 + Group 2 + Neither - Both = Total

45. 3^3 x 4^3 = ?
14 liters
12^3
$11 - 025
sum = (average)(number of terms)

46. Formula for Mixed Group problems (involving Both/Neither)
Gross Profit = Selling Price - Cost
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)
Odd
Group 1 + Group 2 + Neither - Both = Total

47. Combined Events: Not E = P(not E) = ?
The probability of an event occurring plus the probability of the event not occurring = 1
A = P(1 + r) ^n
1 - P(E)
The probability of event occurring is...

48. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
always try to 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
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.

49. Multiples of 3
Number is a multiple of 3 and 2
3 - 6 - 9 - 12
12.5%
Figure out the probability for each individual event. Multiply the individual probabilities together.

50. 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 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.
0.15n + 0.08(5) = 0.1(n+5)
14 liters
180(n-2)