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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. Formula for area of a Trapezoid
14 liters
(sum of bases)(height) / 2
347
Odd numbers only have ___________

2. 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.
Group 1 + Group 2 + Neither - Both = Total
market value
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

3. How do you multiply roots together.
12^3
at least 3 steps
Sum of digits is multiple of 3 - last two digits multiple of 4.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

4. Dependent events: When are two events said to be dependent events?
16.6%
If the outcome of one event affects the outcome of the other event.
Gross Profit = Selling Price - Cost
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

5. Price sold for by retailer (after markup)
market value
The probability of an event occurring plus the probability of the event not occurring = 1
Find simple interest then look for the answer that is a little bigger
gcd(m,n)*lcm(m,n) = mn

6. 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
3-4-5 - 5-12-13 - 9-12-15
1.7
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.
Find simple interest then look for the answer that is a little bigger

7. Average Rate: Average speed
(total distance) / (total time)
Even
Purchase price
12^3

8. 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.
Organize into a grid.
(n-1)!
0.15n + 0.08(5) = 0.1(n+5)
Balancing

9. 2n+1 - 2n+3 - 2n+5
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
s Sq. rt (x^r)
y2 - y1 / x2 - x1
Odd

10. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
market value
Sum of digits is multiple of 3 - last two digits multiple of 4.
If the outcome of one event affects the outcome of the other event.

11. Percent Formula
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/100 = is/of
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)

12. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
Balancing
The amount after deductions
P(E) + P(F) - P(E and F)

13. Multiples of 3
Find simple interest then look for the answer that is a little bigger
(sum of bases)(height) / 2
D or E
3 - 6 - 9 - 12

14. In general - medium questions require how many steps to solve?
$11 - 025
0.15n + 0.08(5) = 0.1(n+5)
2 steps
3 - 6 - 9 - 12

15. 3^3 x 4^3 = ?
12^3
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/100 = is/of
2 steps

16. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
2 steps
(total A) / (total B)
Any multiplication involving an even number creates an even product.

17. (1/4)^2
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.
3-4-5 - 5-12-13 - 9-12-15
1/16
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

18. Volume of a sphere
4/3 TT r ^3
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)
Any multiplication involving an even number creates an even product.

19. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
12^3
Principal (1 + interest/number times compounded)^(t)(n)
x(sq. rt 3) - x - 2x
22

20. Combined Events: E or F
-b +- sq. rt(b^2 - 4ac) / 2a
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
______ |m-n|
P(E) + P(F) - P(E and F)

21. Permutations: Order Matters
4/3 TT r ^3
n! / (n - r)!
Exterior angle d is equal to the sum of the two remote interior angles a and b
at least 3 steps

22. Probability and Geometry.
Number is a multiple of 3 and 2
Sum of digits is multiple of 3 - last two digits multiple of 4.
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
Principal (1 + interest/number times compounded)^(t)(n)

23. Sum of consecutive numbers
Sum of digits is multiple of 3 - last two digits multiple of 4.
sum = (average)(number of terms)
(amount of change) / (original amount)
(x-n(n)y-n)

24. 1/8 = what %
y2 - y1 / x2 - x1
22
12.5%
Figure out the probability for each individual event. Multiply the individual probabilities together.

25. Always try to factor
always try to factor
Immediately try factoring/simplifying when possible
principle (interest rate - in decimal form) (time - in years)
at least 3 steps

26. Triangle abc with d on the outside with a line. What does d = ?
______ |m-n|
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The probability of an event occurring plus the probability of the event not occurring = 1
Exterior angle d is equal to the sum of the two remote interior angles a and b

27. 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)
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.
(x-n(n)y-n)
x(sq. rt 3) - x - 2x

28. How to check whether a number is a multiple of 6
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
Number is a multiple of 3 and 2
Gross Profit = Selling Price - Cost
P(event NOT occurring) = 1 - P(event occurring)

29. How to check whether number is multiple of 9
Immediately UNFACTOR or vice versa
(x-n(n)y-n)
Sum of digits is multiple of 9
$11 - 025

30. Compound interest formula
(# of favorable outcomes) / (# of possible outcomes)
| A union B| = |A| + |B| - |A intersect B|
Principal (1 + interest/number times compounded)^(t)(n)
If the outcome of one event affects the outcome of the other event.

31. Percent increase = ?
x - x - x(sq. rt 2)
x(sq. rt 3) - x - 2x
(amount of change) / (original amount)
A = P(1 + r) ^n

32. Trial Problems: look at the probability of NOT OCCURRING
(n-1)!
P(event NOT occurring) = 1 - P(event occurring)
Group 1 + Group 2 + Neither - Both = Total
Even

33. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
market value
at least 3 steps
Find simple interest then look for the answer that is a little bigger

34. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
$11 - 025

35. Number added or deleted
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.
Purchase price
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
x(sq. rt 3) - x - 2x

36. Average Rate: Average A per B
Figure out the probability for each individual event. Multiply the individual probabilities together.
(total A) / (total B)
The amount after deductions
Immediately try factoring/simplifying when possible

37. Odd and Even rule.
principle (interest rate - in decimal form) (time - in years)
1 - P(E)
Any multiplication involving an even number creates an even product.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

38. 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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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
at least 3 steps

39. Properties of 0
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.
347
(total distance) / (total time)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

40. 5/6 = what %
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)
83.3%
(total A) / (total B)

41. Net
y2 - y1 / x2 - x1
The amount after deductions
(sum of bases)(height) / 2
(x-n(n)y-n)

42. Formula for Mixed Group problems (involving Both/Neither)
The total amount before any deductions
Group 1 + Group 2 + Neither - Both = Total
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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

43. 2n - 2n+2 - 2n+4
Even
Immediately UNFACTOR or vice versa
12^3
180(n-2)

44. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
at least 3 steps
$11 - 025
x(sq. rt 3) - x - 2x
Even

45. 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.
1.7
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.
1st Rule of Probability: Basic Rule is what?
0.15n + 0.08(5) = 0.1(n+5)

46. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
P(E) + P(F) - P(E and F)
347
Balancing
12^3

47. Work problem rule
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.
$11 - 025
12.5%
1 - P(E)

48. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
Immediately try factoring/simplifying when possible
Divide 4999 by 15 => 333 integers
1/16

49. How to check whether a number is a multiple of 12.
2 steps
22
Sum of digits is multiple of 3 - last two digits multiple of 4.
Odd

50. The number of outcomes that result in A divided by the total number of possible outcomes.
sum = (average)(number of terms)
347
The probability of event occurring is...
D or E