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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. 3rd Rule of Probability: Conditional Probability
(x-n(n)y-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.
Sum of digits is multiple of 3
D or E

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?
(total A) / (total B)
14 liters
always try to factor
1.4

3. 1/6 = what %
347
16.6%
14 liters
Figure out the probability for each individual event. Multiply the individual probabilities together.

4. 4th rule of Probability
4/3 TT r ^3
Sum of digits is multiple of 9
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)
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.

5. Multiplication principle
P(E) + P(F) - P(E and F)
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
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.

6. What to do with equations that have fractions
market value
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.
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 3 - last two digits multiple of 4.

7. Gross
The total amount before any deductions
1.7
x - x - x(sq. rt 2)
Exterior angle d is equal to the sum of the two remote interior angles a and b

8. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
at least 3 steps
(n-1)!
market value
347

9. What does the Sum of the angles in a Regular Polygon formula look like?
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. 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.
180(n-2)
Divide 4999 by 15 => 333 integers

10. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1.4
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

11. Sq. rt(2)
347
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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

12. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Sum of digits is multiple of 3 - last two digits multiple of 4.
$11 - 025
If the outcome of one event affects the outcome of the other event.

13. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(total A) / (total B)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Number is a multiple of 3 and 2

14. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
Odd
always try to factor
3 - 6 - 9 - 12

15. Simple probability
Figure out the probability for each individual event. Multiply the individual probabilities together.
(# of favorable outcomes) / (# of possible outcomes)
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.
$11 - 025

16. Intersecting Sets
Immediately try factoring/simplifying when possible
Group 1 + Group 2 + Neither - Both = Total
| A union B| = |A| + |B| - |A intersect B|
at least 3 steps

17. In general - difficult questions require how many steps to solve?
Find simple interest then look for the answer that is a little bigger
The total amount before any deductions
always try to factor
at least 3 steps

18. In general - medium questions require how many steps to solve?
at least 3 steps
2 steps
3-4-5 - 5-12-13 - 9-12-15
14 liters

19. The number of outcomes that result in A divided by the total number of possible outcomes.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The probability of event occurring is...
347
Immediately try factoring/simplifying when possible

20. How to check whether a number is a multiple of 4.
| A union B| = |A| + |B| - |A intersect B|
Exterior angle d is equal to the sum of the two remote interior angles a and b
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(n-1)!

21. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Exterior angle d is equal to the sum of the two remote interior angles a and b
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
22
Group 1 + Group 2 + Neither - Both = Total

22. 5/6 = what %
1.4
83.3%
(sum of bases)(height) / 2
2 steps

23. Sq. rt(3)
1.7
The amount after deductions
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
gcd(m,n)*lcm(m,n) = mn

24. 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
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.
The total amount before any deductions
Figure out the probability for each individual event. Multiply the individual probabilities together.

25. Permutations: Order Matters
Even
1.4
-b +- sq. rt(b^2 - 4ac) / 2a
n! / (n - r)!

26. 1/8 = what %
(# of favorable outcomes) / (# of possible outcomes)
-b +- sq. rt(b^2 - 4ac) / 2a
12.5%
347

27. Indistinguishable events how to find the number of permutations

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28. Price sold for by retailer (after markup)
market value
Immediately try factoring/simplifying when possible
2 steps
1

29. 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?
12.5%
0.15n + 0.08(5) = 0.1(n+5)
Purchase price
market value

30. Average Rate: Average A per B
(total A) / (total B)
1.4
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(# of favorable outcomes) / (# of possible outcomes)

31. Percent increase = ?
(amount of change) / (original amount)
16.6%
Figure out the probability for each individual event. Multiply the individual probabilities 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.

32. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
at least 3 steps
(total A) / (total B)
12.5%

33. Probability and Geometry.
(# of favorable outcomes) / (# of possible outcomes)
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
Find all prime factors
1.7

34. (1/4)^2
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The total amount before any deductions
x - x - x(sq. rt 2)
1/16

35. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 9
Any multiplication involving an even number creates an even product.
Sum of digits is multiple of 3
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.

36. Combined Events: 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
(n-1)!
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
P(E)P(F)

37. Price purchased for by wholesaler
Odd
Immediately try factoring/simplifying when possible
p/100 = is/of
Purchase price

38. Number added or deleted
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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1
gcd(m,n)*lcm(m,n) = mn

39. 2n - 2n+2 - 2n+4
Even
(# of favorable outcomes) / (# of possible outcomes)
16.6%
(n-1)!

40. 45-45-90 triangle basic lengths of sides
always try to factor
(amount of change) / (original amount)
x - x - x(sq. rt 2)
s Sq. rt (x^r)

41. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
principle (interest rate - in decimal form) (time - in years)
1 - P(E)
A = P(1 + r) ^n
If the outcome of one event affects the outcome of the other event.

42. To determine multiple-event probability where each individual event must occur in a certain way.
p/100 = is/of
Odd
1.7
Figure out the probability for each individual event. Multiply the individual probabilities together.

43. Triangle abc with d on the outside with a line. What does d = ?
14 liters
Group 1 + Group 2 + Neither - Both = Total
x - x - x(sq. rt 2)
Exterior angle d is equal to the sum of the two remote interior angles a and b

44. How to check for a prime number.

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45. Some GMAT word problems involve groups with distinct 'either/or' categories (male/female - blue collar/white collar - etc.) The key is to do what with the information? 1. Find total number of possible outcomes. 2. Find the number of desired outcomes.
$11 - 025
y2 - y1 / x2 - x1
Odd numbers only have ___________
Organize into a grid.

46. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
4/3 TT r ^3
1 - P(E)
Minor arc = 2(inscribed angle)

47. 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
3 - 6 - 9 - 12
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Balancing

48. Odd Factors
1/16
Sum of digits is multiple of 3
Odd numbers only have ___________
P(E) + P(F) - P(E and F)

49. Combined Events: Not E = P(not E) = ?
P(E) + P(F) - P(E and F)
0.15n + 0.08(5) = 0.1(n+5)
sum = (average)(number of terms)
1 - P(E)

50. x^r/s = ?
x - x - x(sq. rt 2)
12.5%
s Sq. rt (x^r)
Exterior angle d is equal to the sum of the two remote interior angles a and b