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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. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
83.3%
22
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.

2. How to check whether a number is a multiple of 4.
x(sq. rt 3) - x - 2x
A = P(1 + r) ^n
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.

3. Formula for area of a Trapezoid
(sum of bases)(height) / 2
(amount of change) / (original amount)
s Sq. rt (x^r)
n! / (n - r)!

4. Price purchased for by wholesaler
83.3%
market value
Purchase price
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.

5. gcd(m,n)
______ |m-n|
-b +- sq. rt(b^2 - 4ac) / 2a
(total A) / (total 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.

6. Probability and Geometry.
Group 1 + Group 2 + Neither - Both = Total
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
If the outcome of one event affects the outcome of the other event.
(n-1)!

7. Set Problems formula
Immediately try factoring/simplifying when possible
(x-n(n)y-n)
(amount of change) / (original amount)
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

8. How to check for a prime number.

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9. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
Group 1 + Group 2 + Neither - Both = Total
1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

10. Combined Events: E and F
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
P(E)P(F)
(sum of bases)(height) / 2

11. Average Rate: Average A per B
(total A) / (total B)
Any multiplication involving an even number creates an even product.
3 - 6 - 9 - 12
Principal (1 + interest/number times compounded)^(t)(n)

12. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
1
Immediately UNFACTOR or vice versa
Group 1 + Group 2 + Neither - Both = Total
principle (interest rate - in decimal form) (time - in years)

13. 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?
Number is a multiple of 3 and 2
14 liters
| A union B| = |A| + |B| - |A intersect B|
(total A) / (total B)

14. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
3 - 6 - 9 - 12
347
s Sq. rt (x^r)
y2 - y1 / x2 - x1

15. Odd and Even rule.
1
Any multiplication involving an even number creates an even product.
Divide 4999 by 15 => 333 integers
14 liters

16. 1/8 = what %
A = P(1 + r) ^n
gcd(m,n)*lcm(m,n) = mn
(total distance) / (total time)
12.5%

17. Sum of consecutive numbers
y2 - y1 / x2 - x1
s Sq. rt (x^r)
sum = (average)(number of terms)
at least 3 steps

18. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
Organize into a grid.
| A union B| = |A| + |B| - |A intersect B|
(x-n(n)y-n)

19. How to find the slope.
y2 - y1 / x2 - x1
(total distance) / (total time)
market value
(amount of change) / (original amount)

20. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
1.7
Sum of digits is multiple of 3 - last two digits multiple of 4.
Odd numbers only have ___________

21. How to check whether a number is a multiple of 6
| A union B| = |A| + |B| - |A intersect B|
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Number is a multiple of 3 and 2
$11 - 025

22. 45-45-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
x - x - x(sq. rt 2)
D or E
Group 1 + Group 2 + Neither - Both = Total

23. What does the Sum of the angles in a Regular Polygon formula look like?
12^3
The total amount before any deductions
Principal (1 + interest/number times compounded)^(t)(n)
180(n-2)

24. 30-60-90 triangle basic lengths of sides
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(sq. rt 3) - x - 2x
Figure out the probability for each individual event. Multiply the individual probabilities together.
83.3%

25. Number added or deleted
(sum of bases)(height) / 2
180(n-2)
at least 3 steps
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

26. How to find all divisors of a number
Odd numbers only have ___________
principle (interest rate - in decimal form) (time - in years)
Find all prime factors
Number is a multiple of 3 and 2

27. Trial Problems: look at the probability of NOT OCCURRING
(x-n(n)y-n)
P(event NOT occurring) = 1 - P(event occurring)
Odd
1.4

28. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Balancing
Divide 4999 by 15 => 333 integers
y2 - y1 / x2 - x1
The probability of event occurring is...

29. Volume of a sphere
12.5%
4/3 TT r ^3
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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.

30. Indistinguishable events how to find the number of permutations

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31. How do you multiply roots together.
D or E
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
83.3%
The total amount before any deductions

32. Multiples of 3
3 - 6 - 9 - 12
Divide 4999 by 15 => 333 integers
1.7
16.6%

33. 3rd Rule of Probability: Conditional Probability
The probability of an event occurring plus the probability of the event not occurring = 1
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.
P(E)P(F)
180(n-2)

34. Permutations: Order Matters
Exterior angle d is equal to the sum of the two remote interior angles a and b
n! / (n - r)!
The probability of an event occurring plus the probability of the event not occurring = 1
gcd(m,n)*lcm(m,n) = mn

35. 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
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.
Organize into a grid.
1.4
(total A) / (total B)

36. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
If the outcome of one event affects the outcome of the other event.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The probability of an event occurring plus the probability of the event not occurring = 1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

37. Net
D or E
The amount after deductions
1.4
180(n-2)

38. Combined Events: Not E = P(not E) = ?
1 - P(E)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
gcd(m,n)*lcm(m,n) = mn
1/16

39. Average Rate: Average speed
Principal (1 + interest/number times compounded)^(t)(n)
(total distance) / (total time)
-b +- sq. rt(b^2 - 4ac) / 2a
y2 - y1 / x2 - x1

40. Combined Events: E or F
p/100 = is/of
(amount of change) / (original amount)
P(E) + P(F) - P(E and F)
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

41. 2n - 2n+2 - 2n+4
p/100 = is/of
______ |m-n|
Even
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

42. 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?
0.15n + 0.08(5) = 0.1(n+5)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The probability of event occurring is...
The probability of an event occurring plus the probability of the event not occurring = 1

43. In general - difficult questions require how many steps to solve?
(# of favorable outcomes) / (# of possible outcomes)
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.
P(E) + P(F) - P(E and F)
at least 3 steps

44. 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.
Number is a multiple of 3 and 2
(x-n(n)y-n)
Even
1st Rule of Probability: Basic Rule is what?

45. 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
Find all prime factors
$11 - 025
P(E) + P(F) - P(E and F)

46. Intersecting Sets
at least 3 steps
Sum of digits is multiple of 9
| A union B| = |A| + |B| - |A intersect B|
12^3

47. Sq. rt(3)
The probability of event occurring is...
1.7
0.15n + 0.08(5) = 0.1(n+5)
x - x - x(sq. rt 2)

48. To determine multiple-event probability where each individual event must occur in a certain way.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Figure out the probability for each individual event. Multiply the individual probabilities together.
16.6%
Organize into a grid.

49. 2n+1 - 2n+3 - 2n+5
Purchase price
Odd
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 A) / (total B)

50. Formula for Mixed Group problems (involving Both/Neither)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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
s Sq. rt (x^r)
Group 1 + Group 2 + Neither - Both = Total