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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. Sum of consecutive numbers
1
n! / (n - r)!
Principal (1 + interest/number times compounded)^(t)(n)
sum = (average)(number of terms)

2. gcd(m,n)*lcm(m,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.
gcd(m,n)*lcm(m,n) = mn
$11 - 025
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

3. 30-60-90 triangle basic lengths of sides
p/100 = is/of
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
(x-n(n)y-n)
x(sq. rt 3) - x - 2x

4. 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.
(total distance) / (total time)
(sum of bases)(height) / 2
1

5. How to find the slope.
sum = (average)(number of terms)
y2 - y1 / x2 - x1
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

6. Compound interest formula
The amount after deductions
Principal (1 + interest/number times compounded)^(t)(n)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Sum of digits is multiple of 3

7. To determine multiple-event probability where each individual event must occur in a certain way.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
180(n-2)
Number is a multiple of 3 and 2
Figure out the probability for each individual event. Multiply the individual probabilities together.

8. 0! = ?
always try to factor
Sum of digits is multiple of 3
1
sum = (average)(number of terms)

9. 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?
Immediately try factoring/simplifying when possible
4/3 TT r ^3
0.15n + 0.08(5) = 0.1(n+5)
3 - 6 - 9 - 12

10. Probability and Geometry.
14 liters
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
Sum of digits is multiple of 3 - last two digits multiple of 4.
1.7

11. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
347
n! / (n - r)!
Immediately UNFACTOR or vice versa
D or E

12. 1/6 = what %
1.7
16.6%
The amount after deductions
(x-n(n)y-n)

13. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
83.3%
gcd(m,n)*lcm(m,n) = mn
Find simple interest then look for the answer that is a little bigger

14. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
x(sq. rt 3) - x - 2x
(total distance) / (total time)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

15. How to check whether number is multiple of 9
Find simple interest then look for the answer that is a little bigger
1st Rule of Probability: Basic Rule is what?
3 - 6 - 9 - 12
Sum of digits is multiple of 9

16. Volume of a sphere
______ |m-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.
4/3 TT r ^3
P(event NOT occurring) = 1 - P(event occurring)

17. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
1.7
principle (interest rate - in decimal form) (time - in years)
sum = (average)(number of terms)
at least 3 steps

18. How do you multiply roots together.
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
1/16
2 steps

19. Average Rate: Average A per B
1.7
Find all prime factors
(total A) / (total B)
Principal (1 + interest/number times compounded)^(t)(n)

20. In general - difficult questions require how many steps to solve?
gcd(m,n)*lcm(m,n) = mn
22
at least 3 steps
Group 1 + Group 2 + Neither - Both = Total

21. Triangle abc with d on the outside with a line. What does d = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
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
Sum of digits is multiple of 3
180(n-2)

22. Multiples of 3
Sum of digits is multiple of 3
3 - 6 - 9 - 12
P(E) + P(F) - P(E and F)
22

23. 3rd Rule of Probability: Conditional Probability
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.
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.
s Sq. rt (x^r)
1.4

24. Odd Factors
Odd numbers only have ___________
| A union B| = |A| + |B| - |A intersect B|
Any multiplication involving an even number creates an even product.
The probability of an event occurring plus the probability of the event not occurring = 1

25. How to check whether a number is a multiple of 3.
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.
Sum of digits is multiple of 3
x(sq. rt 3) - x - 2x
| A union B| = |A| + |B| - |A intersect B|

26. Gross Profit formula
Exterior angle d is equal to the sum of the two remote interior angles a and b
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Gross Profit = Selling Price - Cost
1 - P(E)

27. (1/4)^2
14 liters
Sum of digits is multiple of 3 - last two digits multiple of 4.
1/16
180(n-2)

28. In general - medium questions require how many steps to solve?
sum = (average)(number of terms)
1/16
14 liters
2 steps

29. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
1 - P(E)
Any multiplication involving an even number creates an even product.
22

30. 2nd Rule of Probability: P(E) = 1 - P(not E)
s Sq. rt (x^r)
y2 - y1 / x2 - x1
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.
The probability of an event occurring plus the probability of the event not occurring = 1

31. 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.
1/16
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Organize into a grid.
The total amount before any deductions

32. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
The amount after deductions
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(total distance) / (total time)
180(n-2)

33. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
14 liters
The probability of an event occurring plus the probability of the event not occurring = 1
1.4
A = P(1 + r) ^n

34. 4th rule of Probability
gcd(m,n)*lcm(m,n) = mn
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)
(n-1)!
Purchase price

35. Odd and Even rule.
Find all prime factors
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.
14 liters
Any multiplication involving an even number creates an even product.

36. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
Any multiplication involving an even number creates an even product.
Odd
Odd numbers only have ___________

37. 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
Balancing
1.4
4/3 TT r ^3
D or E

38. Indistinguishable events how to find the number of permutations

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39. 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.
Group 1 + Group 2 + Neither - Both = Total
1st Rule of Probability: Basic Rule is what?
P(E) + P(F) - P(E and F)
x - x - x(sq. rt 2)

40. How to check for a prime number.

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41. 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
4/3 TT r ^3
(total distance) / (total time)
3 - 6 - 9 - 12

42. Combined Events: Not E = P(not E) = ?
347
1 - P(E)
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.
180(n-2)

43. Combined Events: E and F
P(E)P(F)
(total A) / (total B)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(n-1)!

44. Net
1st Rule of Probability: Basic Rule is what?
Sum of digits is multiple of 3
p/100 = is/of
The amount after deductions

45. gcd(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.
______ |m-n|
Group 1 + Group 2 + Neither - Both = Total
If the outcome of one event affects the outcome of the other event.

46. Price sold for by retailer (after markup)
2 steps
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)
market value
16.6%

47. How to check whether a number is a multiple of 4.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Immediately try factoring/simplifying when possible
Balancing
The probability of an event occurring plus the probability of the event not occurring = 1

48. Permutations: Order Matters
n! / (n - r)!
1/16
(total A) / (total B)
sum = (average)(number of terms)

49. Trial Problems: look at the probability of NOT OCCURRING
The probability of event occurring is...
3 - 6 - 9 - 12
P(event NOT occurring) = 1 - P(event occurring)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

50. 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
P(E) + P(F) - P(E and F)
Odd
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.