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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. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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
180(n-2)
D or E
Any multiplication involving an even number creates an even product.

2. gcd(m,n)
Odd
s Sq. rt (x^r)
______ |m-n|
Sum of digits is multiple of 3

3. gcd(m,n)*lcm(m,n)
P(E) + P(F) - P(E and F)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
y2 - y1 / x2 - x1
gcd(m,n)*lcm(m,n) = mn

4. Sq. rt(2)
1.4
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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Sum of digits is multiple of 9

5. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
gcd(m,n)*lcm(m,n) = mn
The total amount before any deductions
x(sq. rt 3) - x - 2x

6. 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
1.4
Purchase price
Balancing
The probability of an event occurring plus the probability of the event not occurring = 1

7. Average Rate: Average A per B
$11 - 025
(total A) / (total B)
Immediately UNFACTOR or vice versa
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

8. Intersecting Sets
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
2 steps
$11 - 025
| A union B| = |A| + |B| - |A intersect B|

9. Trial Problems: look at the probability of NOT OCCURRING
347
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(event NOT occurring) = 1 - P(event occurring)
(# of favorable outcomes) / (# of possible outcomes)

10. How to check for a prime number.

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11. Simple probability
at least 3 steps
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Sum of digits is multiple of 9
(# of favorable outcomes) / (# of possible outcomes)

12. 30-60-90 triangle basic lengths of sides
always try to factor
Find all prime factors
4/3 TT r ^3
x(sq. rt 3) - x - 2x

13. Set Problems formula
(x-n(n)y-n)
Balancing
Find all prime factors
Minor arc = 2(inscribed angle)

14. Odd and Even rule.
P(event NOT occurring) = 1 - P(event occurring)
Any multiplication involving an even number creates an even product.
p/100 = is/of
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)

15. x^r/s = ?
s Sq. rt (x^r)
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
(# of favorable outcomes) / (# of possible outcomes)
sum = (average)(number of terms)

16. Combined Events: E or F
Number is a multiple of 3 and 2
P(E) + P(F) - P(E and F)
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)
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.

17. Quadratic formula
347
Find all prime factors
-b +- sq. rt(b^2 - 4ac) / 2a
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.

18. Average Rate: Average speed
Organize into a grid.
(x-n(n)y-n)
1 - P(E)
(total distance) / (total time)

19. The average of consecutive numbers
(amount of change) / (original amount)
n! / (n - r)!
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.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

20. How to check whether a number is a multiple of 6
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
______ |m-n|
Number is a multiple of 3 and 2

21. 0! = ?
-b +- sq. rt(b^2 - 4ac) / 2a
1
Minor arc = 2(inscribed angle)
s Sq. rt (x^r)

22. 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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Minor arc = 2(inscribed angle)
12^3

23. In general - medium questions require how many steps to solve?
2 steps
(n-1)!
180(n-2)
Odd numbers only have ___________

24. 1/6 = what %
16.6%
s Sq. rt (x^r)
(total distance) / (total time)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

25. Compound interest formula
Odd
D or E
Gross Profit = Selling Price - Cost
Principal (1 + interest/number times compounded)^(t)(n)

26. Volume of a sphere
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.
4/3 TT r ^3
P(E) + P(F) - P(E and F)
If the outcome of one event affects the outcome of the other event.

27. 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
P(E) + P(F) - P(E and F)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
n! / (n - r)!

28. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
14 liters
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1.7

29. 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.
1st Rule of Probability: Basic Rule is what?
Immediately UNFACTOR or vice versa
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.
180(n-2)

30. Formula for area of a Trapezoid
p/100 = is/of
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
Number is a multiple of 3 and 2
(sum of bases)(height) / 2

31. Combined Events: Not E = P(not E) = ?
1 - P(E)
Figure out the probability for each individual event. Multiply the individual probabilities together.
4/3 TT r ^3
1

32. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Organize into a grid.
22
12^3
3-4-5 - 5-12-13 - 9-12-15

33. Compound interest rule
347
market value
Sum of digits is multiple of 3
Find simple interest then look for the answer that is a little bigger

34. Net
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 amount after deductions
0.15n + 0.08(5) = 0.1(n+5)
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.

35. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
16.6%
principle (interest rate - in decimal form) (time - in years)
Odd numbers only have ___________
(x-n(n)y-n)

36. How to check whether a number is a multiple of 4.
Minor arc = 2(inscribed angle)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1/16
The probability of an event occurring plus the probability of the event not occurring = 1

37. To determine multiple-event probability where each individual event must occur in a certain way.
3-4-5 - 5-12-13 - 9-12-15
-b +- sq. rt(b^2 - 4ac) / 2a
Figure out the probability for each individual event. Multiply the individual probabilities together.
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)

38. Permutations: Order Matters
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
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.
n! / (n - r)!

39. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
Minor arc = 2(inscribed angle)
Immediately try factoring/simplifying when possible
| A union B| = |A| + |B| - |A intersect B|

40. Prime Factorization to find Greatest Common Factor
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
1st Rule of Probability: Basic Rule is what?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
2 steps

41. In general - difficult questions require how many steps to solve?
2 steps
at least 3 steps
(amount of change) / (original amount)
Odd

42. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
1.4
(x-n(n)y-n)
1/16

43. Gross
A = P(1 + r) ^n
1 - P(E)
1.4
The total amount before any deductions

44. 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?
Figure out the probability for each individual event. Multiply the individual probabilities together.
x - x - x(sq. rt 2)
p/100 = is/of
0.15n + 0.08(5) = 0.1(n+5)

45. The number of outcomes that result in A divided by the total number of possible outcomes.
(x-n(n)y-n)
The probability of event occurring is...
Immediately try factoring/simplifying when possible
P(event NOT occurring) = 1 - P(event occurring)

46. How to check whether a number is a multiple of 12.
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.
12.5%
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.
Sum of digits is multiple of 3 - last two digits multiple of 4.

47. Dependent events: When are two events said to be dependent events?
n! / (n - r)!
If the outcome of one event affects the outcome of the other event.
Organize into a grid.
14 liters

48. How to find the slope.
| 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
y2 - y1 / x2 - x1
at least 3 steps

49. Always try to factor
always try to factor
(x-n(n)y-n)
1
Find simple interest then look for the answer that is a little bigger

50. Formula for Mixed Group problems (involving Both/Neither)
| A union B| = |A| + |B| - |A intersect B|
Group 1 + Group 2 + Neither - Both = Total
Gross Profit = Selling Price - Cost
principle (interest rate - in decimal form) (time - in years)