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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. Work problem rule
Even
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.

2. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
P(E)P(F)
Sum of digits is multiple of 3
Number is a multiple of 3 and 2
D or E

3. Price purchased for by wholesaler
14 liters
-b +- sq. rt(b^2 - 4ac) / 2a
Purchase price
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

4. Percent increase = ?
14 liters
(# of favorable outcomes) / (# of possible outcomes)
(amount of change) / (original amount)
s Sq. rt (x^r)

5. Gross Profit formula
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 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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Gross Profit = Selling Price - Cost

6. Net
(total distance) / (total time)
x - x - x(sq. rt 2)
The amount after deductions
83.3%

7. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Immediately try factoring/simplifying when possible
A = P(1 + r) ^n
12.5%
(total A) / (total B)

8. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
gcd(m,n)*lcm(m,n) = mn
Immediately UNFACTOR or vice versa
$11 - 025

9. gcd(m,n)
x(sq. rt 3) - x - 2x
1
______ |m-n|
Find simple interest then look for the answer that is a little bigger

10. Percent Formula
| A union B| = |A| + |B| - |A intersect B|
1 - P(E)
(amount of change) / (original amount)
p/100 = is/of

11. Three triangle length patterns
If the outcome of one event affects the outcome of the other event.
3-4-5 - 5-12-13 - 9-12-15
Purchase price
0.15n + 0.08(5) = 0.1(n+5)

12. Sq. rt(2)
347
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1.4
D or E

13. 1/8 = what %
Balancing
3-4-5 - 5-12-13 - 9-12-15
(sum of bases)(height) / 2
12.5%

14. How to check whether a number is a multiple of 12.
(# of favorable outcomes) / (# of possible outcomes)
The amount after deductions
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.

15. 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.
83.3%
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
The probability of event occurring is...

16. Indistinguishable events how to find the number of permutations

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17. Gross
The total amount before any deductions
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
16.6%
Group 1 + Group 2 + Neither - Both = Total

18. 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.
Principal (1 + interest/number times compounded)^(t)(n)
x(sq. rt 3) - x - 2x
4/3 TT r ^3

19. 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 - P(E)
1st Rule of Probability: Basic Rule is what?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
A = P(1 + r) ^n

20. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
1
22
Odd
1.4

21. 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
Immediately UNFACTOR or vice versa
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Balancing
(sum of bases)(height) / 2

22. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
The total amount before any deductions
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
Immediately try factoring/simplifying when possible

23. 4th rule of Probability
0.15n + 0.08(5) = 0.1(n+5)
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)
14 liters
The amount after deductions

24. Dependent events: When are two events said to be dependent events?
Immediately try factoring/simplifying when possible
Last two digits are multiple of 4 or the number can be divided by 2 twice.
If the outcome of one event affects the outcome of the other event.
(# of favorable outcomes) / (# of possible outcomes)

25. Price sold for by retailer (after markup)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
p/100 = is/of
Gross Profit = Selling Price - Cost
market value

26. Formula for area of a Trapezoid
sum = (average)(number of terms)
(sum of bases)(height) / 2
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

27. 0! = ?
3-4-5 - 5-12-13 - 9-12-15
1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
P(E)P(F)

28. To determine the number of integers less than 5000 that are evenly divisible by 15...?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Divide 4999 by 15 => 333 integers
Group 1 + Group 2 + Neither - Both = Total
180(n-2)

29. gcd(m,n)*lcm(m,n)
The probability of event occurring is...
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Any multiplication involving an even number creates an even product.
gcd(m,n)*lcm(m,n) = mn

30. Odd Factors
Odd numbers only have ___________
$11 - 025
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.

31. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
P(E)P(F)
(x-n(n)y-n)
347

32. How to check for a prime number.

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33. 1/6 = what %
16.6%
$11 - 025
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
P(event NOT occurring) = 1 - P(event occurring)

34. How to check whether a number is a multiple of 6
The probability of an event occurring plus the probability of the event not occurring = 1
$11 - 025
Number is a multiple of 3 and 2
3-4-5 - 5-12-13 - 9-12-15

35. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
always try to factor
Group 1 + Group 2 + Neither - Both = Total
16.6%

36. Sq. rt(3)
Sum of digits is multiple of 3
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
1.7
P(E)P(F)

37. Permutations: Order Matters
| A union B| = |A| + |B| - |A intersect B|
n! / (n - r)!
x - x - x(sq. rt 2)
P(E)P(F)

38. 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.
3 - 6 - 9 - 12
market value
Organize into a grid.
Sum of digits is multiple of 3

39. Average Rate: Average speed
Sum of digits is multiple of 9
Any multiplication involving an even number creates an even product.
(total distance) / (total time)
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

40. Average Rate: Average A per B
1/16
Purchase price
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)

41. Combined Events: Not E = P(not E) = ?
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.
s Sq. rt (x^r)
4/3 TT r ^3
1 - P(E)

42. 3^3 x 4^3 = ?
p/100 = is/of
The amount after deductions
12^3
(total A) / (total B)

43. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
1/16
principle (interest rate - in decimal form) (time - in years)
Principal (1 + interest/number times compounded)^(t)(n)
(total A) / (total B)

44. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
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.
Any multiplication involving an even number creates an even product.
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

45. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
(# of favorable outcomes) / (# of possible outcomes)
P(E) + P(F) - P(E and F)
347
$11 - 025

46. In general - medium questions require how many steps to solve?
2 steps
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
s Sq. rt (x^r)
Minor arc = 2(inscribed angle)

47. 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/100 = is/of
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.
always try to factor
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.

48. Odd and Even rule.
A = P(1 + r) ^n
Even
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

49. Always try to factor
Principal (1 + interest/number times compounded)^(t)(n)
always try to factor
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.
83.3%

50. How to check whether number is multiple of 9
at least 3 steps
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 9
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.