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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. In general - difficult questions require how many steps to solve?
If the outcome of one event affects the outcome of the other event.
at least 3 steps
4/3 TT r ^3
s Sq. rt (x^r)

2. 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
If the outcome of one event affects the outcome of the other event.
3 - 6 - 9 - 12
always try to factor
Balancing

3. Compound interest formula
P(event NOT occurring) = 1 - P(event occurring)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Principal (1 + interest/number times compounded)^(t)(n)
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

4. Formula for Mixed Group problems (involving Both/Neither)
(total distance) / (total time)
Group 1 + Group 2 + Neither - Both = Total
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.
Figure out the probability for each individual event. Multiply the individual probabilities together.

5. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Principal (1 + interest/number times compounded)^(t)(n)
The amount after deductions
D or E
Number is a multiple of 3 and 2

6. Simple probability
The amount after deductions
(# of favorable outcomes) / (# of possible outcomes)
1/16
Principal (1 + interest/number times compounded)^(t)(n)

7. To determine the number of integers less than 5000 that are evenly divisible by 15...?
market value
Divide 4999 by 15 => 333 integers
Number is a multiple of 3 and 2
1.7

8. Probability and Geometry.
12.5%
3 - 6 - 9 - 12
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
Odd numbers only have ___________

9. Three triangle length patterns
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
D or E
Find all prime factors
3-4-5 - 5-12-13 - 9-12-15

10. Average Rate: Average A per B
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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)
Minor arc = 2(inscribed angle)

11. When you see an equation in factored form in a question?
1/16
Immediately UNFACTOR or vice versa
x - x - x(sq. rt 2)
P(E) + P(F) - P(E and F)

12. Set Problems formula
(x-n(n)y-n)
Gross Profit = Selling Price - Cost
(total A) / (total B)
Sum of digits is multiple of 3

13. Quadratic formula
(amount of change) / (original amount)
P(E) + P(F) - P(E and F)
Find all prime factors
-b +- sq. rt(b^2 - 4ac) / 2a

14. Inscribed Angle - Minor Arc
Sum of digits is multiple of 3 - last two digits multiple of 4.
P(E)P(F)
Minor arc = 2(inscribed angle)
1.7

15. Odd Factors
Odd numbers only have ___________
1 - P(E)
83.3%
P(E) + P(F) - P(E and F)

16. Sq. rt(3)
1.7
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.
Immediately UNFACTOR or vice versa
Organize into a grid.

17. Trial Problems: look at the probability of NOT OCCURRING
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(event NOT occurring) = 1 - P(event occurring)
3 - 6 - 9 - 12
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. Sum of consecutive numbers
at least 3 steps
sum = (average)(number of terms)
Group 1 + Group 2 + Neither - Both = Total
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

19. Dependent events: When are two events said to be dependent events?
Sum of digits is multiple of 3
If the outcome of one event affects the outcome of the other event.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Number is a multiple of 3 and 2

20. How to check whether a number is a multiple of 3.
The probability of an event occurring plus the probability of the event not occurring = 1
4/3 TT r ^3
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 3

21. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
180(n-2)
Odd numbers only have ___________
principle (interest rate - in decimal form) (time - in years)
(# of favorable outcomes) / (# of possible outcomes)

22. 2n - 2n+2 - 2n+4
4/3 TT r ^3
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
Even
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)

23. How to check for a prime number.

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24. The number of outcomes that result in A divided by the total number of possible outcomes.
1/16
The probability of event occurring is...
1.7
Immediately try factoring/simplifying when possible

25. Percent Formula
p/100 = is/of
Group 1 + Group 2 + Neither - Both = Total
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
0.15n + 0.08(5) = 0.1(n+5)

26. What does the Sum of the angles in a Regular Polygon formula look like?
1/16
gcd(m,n)*lcm(m,n) = mn
principle (interest rate - in decimal form) (time - in years)
180(n-2)

27. 1/8 = what %
Divide 4999 by 15 => 333 integers
12.5%
n! / (n - r)!
(x-n(n)y-n)

28. Net
The amount after deductions
14 liters
at least 3 steps
p/100 = is/of

29. Compound interest rule
Find simple interest then look for the answer that is a little bigger
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
The amount after deductions
gcd(m,n)*lcm(m,n) = mn

30. 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
$11 - 025
at least 3 steps
22

31. Gross
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.
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.
If the outcome of one event affects the outcome of the other event.
The total amount before any deductions

32. gcd(m,n)
Find simple interest then look for the answer that is a little bigger
______ |m-n|
Organize into a grid.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

33. 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)
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
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.
Any multiplication involving an even number creates an even product.

34. In general - medium questions require how many steps to solve?
1st Rule of Probability: Basic Rule is what?
2 steps
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

35. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
sum = (average)(number of terms)
1st Rule of Probability: Basic Rule is what?
Odd

36. Gross Profit formula
Figure out the probability for each individual event. Multiply the individual probabilities together.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
3 - 6 - 9 - 12
Gross Profit = Selling Price - Cost

37. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
(total distance) / (total time)
1.4
22
Gross Profit = Selling Price - Cost

38. Multiples of 3
-b +- sq. rt(b^2 - 4ac) / 2a
3 - 6 - 9 - 12
If the outcome of one event affects the outcome of the other event.
Minor arc = 2(inscribed angle)

39. Work problem rule
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
at least 3 steps
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.
If the outcome of one event affects the outcome of the other event.

40. 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.
The probability of event occurring is...
Find all prime factors
Minor arc = 2(inscribed angle)

41. 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
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
market value
16.6%

42. 3^3 x 4^3 = ?
x(sq. rt 3) - x - 2x
12^3
16.6%
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.

43. 5/6 = what %
83.3%
12.5%
Even
Purchase price

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?
-b +- sq. rt(b^2 - 4ac) / 2a
0.15n + 0.08(5) = 0.1(n+5)
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
3-4-5 - 5-12-13 - 9-12-15

45. 1/6 = what %
16.6%
$11 - 025
| A union B| = |A| + |B| - |A intersect B|
1/16

46. Combined Events: Not E = P(not E) = ?
1 - P(E)
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.
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
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)

47. Average Rate: Average speed
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 distance) / (total time)
14 liters
-b +- sq. rt(b^2 - 4ac) / 2a

48. How to find all divisors of a number
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 all prime factors
(sum of bases)(height) / 2
1 - P(E)

49. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
x(sq. rt 3) - x - 2x
$11 - 025
(# of favorable outcomes) / (# of possible outcomes)
Balancing

50. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
(x-n(n)y-n)
Immediately try factoring/simplifying when possible
(amount of change) / (original amount)