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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. 2n+1 - 2n+3 - 2n+5
Odd
$11 - 025
Immediately try factoring/simplifying when possible
Purchase price

2. Gross
Balancing
______ |m-n|
1 - P(E)
The total amount before any deductions

3. The number of outcomes that result in A divided by the total number of possible outcomes.
Number is a multiple of 3 and 2
Find simple interest then look for the answer that is a little bigger
The probability of event occurring is...
Sum of digits is multiple of 3 - last two digits multiple of 4.

4. 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?
0.15n + 0.08(5) = 0.1(n+5)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(total distance) / (total time)
14 liters

5. Formula for area of a Trapezoid
D or E
(sum of bases)(height) / 2
p/100 = is/of
83.3%

6. 30-60-90 triangle basic lengths of sides
4/3 TT r ^3
Number is a multiple of 3 and 2
The amount after deductions
x(sq. rt 3) - x - 2x

7. Average Rate: Average speed
______ |m-n|
(total distance) / (total time)
p/100 = is/of
market value

8. Volume of a sphere
1st Rule of Probability: Basic Rule is what?
4/3 TT r ^3
P(event NOT occurring) = 1 - P(event occurring)
Immediately try factoring/simplifying when possible

9. In general - difficult questions require how many steps to solve?
P(event NOT occurring) = 1 - P(event occurring)
at least 3 steps
Exterior angle d is equal to the sum of the two remote interior angles a and b
Principal (1 + interest/number times compounded)^(t)(n)

10. Properties of 0
180(n-2)
principle (interest rate - in decimal form) (time - in years)
P(E) + P(F) - P(E and F)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

11. How to find all divisors of a number
Purchase price
(# of favorable outcomes) / (# of possible outcomes)
(total A) / (total B)
Find all prime factors

12. Number added or deleted
1.4
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Sum of digits is multiple of 3
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

13. 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
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.
Organize into a grid.
x - x - x(sq. rt 2)
market value

14. 4th rule of Probability
y2 - y1 / x2 - x1
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)
(sum of bases)(height) / 2
Exterior angle d is equal to the sum of the two remote interior angles a and b

15. Percent Formula
If the outcome of one event affects the outcome of the other event.
p/100 = is/of
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.
14 liters

16. How to check for a prime number.

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17. 0! = ?
(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
1
______ |m-n|

18. Sq. rt(2)
Sum of digits is multiple of 3
0.15n + 0.08(5) = 0.1(n+5)
Purchase price
1.4

19. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
s Sq. rt (x^r)
(sum of bases)(height) / 2
principle (interest rate - in decimal form) (time - in years)
y2 - y1 / x2 - x1

20. Combined Events: Not E = P(not E) = ?
1 - P(E)
1st Rule of Probability: Basic Rule is what?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
83.3%

21. Three triangle length patterns
Odd
3-4-5 - 5-12-13 - 9-12-15
y2 - y1 / x2 - x1
sum = (average)(number of terms)

22. Intersecting Sets
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
______ |m-n|
| A union B| = |A| + |B| - |A intersect B|
Figure out the probability for each individual event. Multiply the individual probabilities together.

23. 3^3 x 4^3 = ?
1.4
Divide 4999 by 15 => 333 integers
3-4-5 - 5-12-13 - 9-12-15
12^3

24. Quadratic formula
(total distance) / (total time)
Balancing
Figure out the probability for each individual event. Multiply the individual probabilities together.
-b +- sq. rt(b^2 - 4ac) / 2a

25. 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
1
A = P(1 + r) ^n
| A union B| = |A| + |B| - |A intersect B|

26. The average of consecutive numbers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The amount after deductions
1
0.15n + 0.08(5) = 0.1(n+5)

27. How to find the slope.
1 - P(E)
(sum of bases)(height) / 2
Balancing
y2 - y1 / x2 - x1

28. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
-b +- sq. rt(b^2 - 4ac) / 2a
$11 - 025
(n-1)!
Sum of digits is multiple of 9

29. Price purchased for by wholesaler
(# of favorable outcomes) / (# of possible outcomes)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Purchase price
83.3%

30. Prime Factorization to find Greatest Common Factor
Find simple interest then look for the answer that is a little bigger
at least 3 steps
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
2 steps

31. Always try to factor
y2 - y1 / x2 - x1
Gross Profit = Selling Price - Cost
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.

32. Triangle abc with d on the outside with a line. What does d = ?
16.6%
Exterior angle d is equal to the sum of the two remote interior angles a and b
180(n-2)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

33. How to check whether a number is a multiple of 12.
(sum of bases)(height) / 2
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
p/100 = is/of
Sum of digits is multiple of 3 - last two digits multiple of 4.

34. Net
22
The amount after deductions
market value
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. Sum of consecutive numbers
Group 1 + Group 2 + Neither - Both = Total
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.
-b +- sq. rt(b^2 - 4ac) / 2a
sum = (average)(number of terms)

36. gcd(m,n)
Sum of digits is multiple of 3
-b +- sq. rt(b^2 - 4ac) / 2a
______ |m-n|
The amount after deductions

37. Sq. rt(3)
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.
Organize into a grid.
gcd(m,n)*lcm(m,n) = mn
1.7

38. Dependent events: When are two events said to be dependent events?
Any multiplication involving an even number creates an even product.
If the outcome of one event affects the outcome of the other event.
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.
Find all prime factors

39. How to check whether number is multiple of 9
14 liters
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 9
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.

40. Average Rate: Average A per B
12.5%
Gross Profit = Selling Price - Cost
Balancing
(total A) / (total B)

41. Multiples of 3
The amount after deductions
3 - 6 - 9 - 12
14 liters
Organize into a grid.

42. Odd Factors
Odd numbers only have ___________
x - x - x(sq. rt 2)
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.
4/3 TT r ^3

43. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
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)
P(E)P(F)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

44. Formula for Mixed Group problems (involving Both/Neither)
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.
Group 1 + Group 2 + Neither - Both = Total
Find simple interest then look for the answer that is a little bigger
(sum of bases)(height) / 2

45. In general - medium questions require how many steps to solve?
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.
x(sq. rt 3) - x - 2x
2 steps
(amount of change) / (original amount)

46. Combined Events: E and F
Immediately UNFACTOR or vice versa
The probability of an event occurring plus the probability of the event not occurring = 1
(# of favorable outcomes) / (# of possible outcomes)
P(E)P(F)

47. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Immediately UNFACTOR or vice versa
D or E
n! / (n - r)!
A = P(1 + r) ^n

48. x^r/s = ?
s Sq. rt (x^r)
______ |m-n|
(total A) / (total B)
market value

49. 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
(total A) / (total B)
n! / (n - r)!
22

50. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
1/16
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Group 1 + Group 2 + Neither - Both = Total