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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. 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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
y2 - y1 / x2 - x1
Organize into a grid.
p/100 = is/of

2. 2nd Rule of Probability: P(E) = 1 - P(not E)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
principle (interest rate - in decimal form) (time - in years)
The probability of an event occurring plus the probability of the event not occurring = 1
1 - P(E)

3. How to find the slope.
3 - 6 - 9 - 12
A = P(1 + r) ^n
y2 - y1 / x2 - x1
Figure out the probability for each individual event. Multiply the individual probabilities together.

4. Net
Find simple interest then look for the answer that is a little bigger
Principal (1 + interest/number times compounded)^(t)(n)
The amount after deductions
(# of favorable outcomes) / (# of possible outcomes)

5. Gross Profit formula
Immediately try factoring/simplifying when possible
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Gross Profit = Selling Price - Cost
Figure out the probability for each individual event. Multiply the individual probabilities together.

6. (1/4)^2
A = P(1 + r) ^n
n! / (n - r)!
1/16
______ |m-n|

7. 1/6 = what %
83.3%
y2 - y1 / x2 - x1
16.6%
Immediately UNFACTOR or vice versa

8. gcd(m,n)
Principal (1 + interest/number times compounded)^(t)(n)
16.6%
Sum of digits is multiple of 3 - last two digits multiple of 4.
______ |m-n|

9. 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
Purchase price
22
Group 1 + Group 2 + Neither - Both = Total

10. 3^3 x 4^3 = ?
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.
Sum of digits is multiple of 3
12^3
A = P(1 + r) ^n

11. How to check for a prime number.

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12. Quadratic formula
P(E)P(F)
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.
If the outcome of one event affects the outcome of the other event.
-b +- sq. rt(b^2 - 4ac) / 2a

13. Odd and Even rule.
Immediately try factoring/simplifying when possible
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 3
Any multiplication involving an even number creates an even product.

14. Indistinguishable events how to find the number of permutations

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15. 45-45-90 triangle basic lengths of sides
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.
22
x - x - x(sq. rt 2)
Odd numbers only have ___________

16. Sq. rt(2)
Minor arc = 2(inscribed angle)
Organize into a grid.
1.4
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.

17. Gross
The total amount before any deductions
83.3%
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 3

18. To determine the number of integers less than 5000 that are evenly divisible by 15...?
1 - P(E)
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 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
Divide 4999 by 15 => 333 integers

19. 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?
14 liters
12^3
The total amount before any deductions
Even

20. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
(amount of change) / (original amount)
-b +- sq. rt(b^2 - 4ac) / 2a
347
s Sq. rt (x^r)

21. 3rd Rule of Probability: Conditional Probability
Odd numbers only have ___________
D or 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.
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

22. Percent Formula
Odd
p/100 = is/of
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The probability of an event occurring plus the probability of the event not occurring = 1

23. When you see an equation in factored form in a question?
Gross Profit = Selling Price - Cost
Immediately UNFACTOR or vice versa
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)
Exterior angle d is equal to the sum of the two remote interior angles a and b

24. 5/6 = what %
x - x - x(sq. rt 2)
83.3%
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1 - P(E)

25. Multiplication principle
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Odd numbers only have ___________
(amount of change) / (original amount)
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

26. 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.
(total distance) / (total time)
y2 - y1 / x2 - x1
gcd(m,n)*lcm(m,n) = mn

27. Compound interest formula
Balancing
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
2 steps
Principal (1 + interest/number times compounded)^(t)(n)

28. How to check whether a number is a multiple of 6
$11 - 025
P(event NOT occurring) = 1 - P(event occurring)
gcd(m,n)*lcm(m,n) = mn
Number is a multiple of 3 and 2

29. Compound interest rule
Find simple interest then look for the answer that is a little bigger
| A union B| = |A| + |B| - |A intersect B|
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
A = P(1 + r) ^n

30. gcd(m,n)*lcm(m,n)
Sum of digits is multiple of 3 - last two digits multiple of 4.
gcd(m,n)*lcm(m,n) = mn
4/3 TT r ^3
P(E)P(F)

31. Combined Events: E and F
12^3
P(E)P(F)
1/16
180(n-2)

32. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
P(event NOT occurring) = 1 - P(event occurring)
1 - P(E)
(sum of bases)(height) / 2

33. Inscribed Angle - Minor Arc
1.7
Figure out the probability for each individual event. Multiply the individual probabilities together.
12^3
Minor arc = 2(inscribed angle)

34. 1/8 = what %
Principal (1 + interest/number times compounded)^(t)(n)
12.5%
(total A) / (total B)
always try to factor

35. Sq. rt(3)
P(E) + P(F) - P(E and F)
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 = (average)(number of terms)
1.7

36. x^r/s = ?
s Sq. rt (x^r)
Minor arc = 2(inscribed angle)
(amount of change) / (original amount)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

37. Formula for Mixed Group problems (involving Both/Neither)
A = P(1 + r) ^n
Even
Group 1 + Group 2 + Neither - Both = Total
(sum of bases)(height) / 2

38. 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
x - x - x(sq. rt 2)
Balancing
3 - 6 - 9 - 12
P(event NOT occurring) = 1 - P(event occurring)

39. In general - medium questions require how many steps to solve?
1/16
Figure out the probability for each individual event. Multiply the individual probabilities together.
2 steps
Group 1 + Group 2 + Neither - Both = Total

40. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
principle (interest rate - in decimal form) (time - in years)
gcd(m,n)*lcm(m,n) = mn
$11 - 025
0.15n + 0.08(5) = 0.1(n+5)

41. Combined Events: Not E = P(not E) = ?
1 - P(E)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
market value
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.

42. Formula for area of a Trapezoid
180(n-2)
1.4
(sum of bases)(height) / 2
4/3 TT r ^3

43. Properties of 0
Figure out the probability for each individual event. Multiply the individual probabilities together.
y2 - y1 / x2 - x1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1.7

44. Prime Factorization to find Greatest Common Factor
The total amount before any deductions
Sum of digits is multiple of 3
Gross Profit = Selling Price - Cost
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

45. Probability and Geometry.
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
always try to factor
(total distance) / (total time)
p/100 = is/of

46. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
1st Rule of Probability: Basic Rule is what?
Even
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

47. The average of consecutive numbers
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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Sum of digits is multiple of 3
s Sq. rt (x^r)

48. 4th rule of Probability
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)
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
s Sq. rt (x^r)
P(E) + P(F) - P(E and F)

49. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
3-4-5 - 5-12-13 - 9-12-15
Immediately try factoring/simplifying when possible

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