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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. Volume of a sphere
(x-n(n)y-n)
$11 - 025
Number is a multiple of 3 and 2
4/3 TT r ^3

2. What does the Sum of the angles in a Regular Polygon formula look like?
P(event NOT occurring) = 1 - P(event occurring)
180(n-2)
Minor arc = 2(inscribed angle)
| A union B| = |A| + |B| - |A intersect B|

3. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
1/16
D or E
2 steps
-b +- sq. rt(b^2 - 4ac) / 2a

4. Net
P(E) + P(F) - P(E and F)
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
Immediately try factoring/simplifying when possible
The amount after deductions

5. Permutations: Order Matters
3-4-5 - 5-12-13 - 9-12-15
Find all prime factors
12^3
n! / (n - r)!

6. Percent Formula
p/100 = is/of
Sum of digits is multiple of 3 - last two digits multiple of 4.
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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

7. Properties of 0
P(E)P(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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
______ |m-n|

8. Work problem rule
gcd(m,n)*lcm(m,n) = mn
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
n! / (n - r)!

9. Dependent events: When are two events said to be dependent events?
347
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The total amount before any deductions
If the outcome of one event affects the outcome of the other event.

10. Combined Events: E or F
Gross Profit = Selling Price - Cost
-b +- sq. rt(b^2 - 4ac) / 2a
Figure out the probability for each individual event. Multiply the individual probabilities together.
P(E) + P(F) - P(E and F)

11. Percent increase = ?
1.4
3 - 6 - 9 - 12
(amount of change) / (original amount)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

12. How do you multiply roots together.
Odd numbers only have ___________
s Sq. rt (x^r)
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

13. How to find the slope.
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
180(n-2)
y2 - y1 / x2 - x1
x(sq. rt 3) - x - 2x

14. Odd Factors
Figure out the probability for each individual event. Multiply the individual probabilities together.
Odd numbers only have ___________
(total A) / (total B)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

15. Simple probability
always try to factor
(# of favorable outcomes) / (# of possible outcomes)
If the outcome of one event affects the outcome of the other event.
sum = (average)(number of terms)

16. How to check for a prime number.

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17. 45-45-90 triangle basic lengths of sides
P(E)P(F)
x - x - x(sq. rt 2)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Organize into a grid.

18. 1/8 = what %
347
12.5%
Odd numbers only have ___________
22

19. 2nd Rule of Probability: P(E) = 1 - P(not E)
x - x - x(sq. rt 2)
The probability of an event occurring plus the probability of the event not occurring = 1
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.
16.6%

20. Multiples of 3
P(E) + P(F) - P(E and F)
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.
3 - 6 - 9 - 12
If the outcome of one event affects the outcome of the other event.

21. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
4/3 TT r ^3
principle (interest rate - in decimal form) (time - in years)
x - x - x(sq. rt 2)
always try to factor

22. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
n! / (n - r)!
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
12.5%
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

23. Gross Profit formula
Gross Profit = Selling Price - Cost
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
83.3%
Sum of digits is multiple of 3 - last two digits multiple of 4.

24. In general - difficult questions require how many steps to solve?
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
Find all prime factors
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.

25. 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)
s Sq. rt (x^r)
180(n-2)
Sum of digits is multiple of 3

26. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
(amount of change) / (original amount)
always try to factor
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)

27. (1/4)^2
1/16
14 liters
Even
sum = (average)(number of terms)

28. 2n+1 - 2n+3 - 2n+5
A = P(1 + r) ^n
The total amount before any deductions
Number is a multiple of 3 and 2
Odd

29. Set Problems formula
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(x-n(n)y-n)
347
$11 - 025

30. Compound interest rule
4/3 TT r ^3
1.4
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

31. Average Rate: Average speed
n! / (n - r)!
$11 - 025
(total distance) / (total time)
3 - 6 - 9 - 12

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.
12^3
Sum of digits is multiple of 9
1 - P(E)

33. How to check whether a number is a multiple of 4.
D or E
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(n-1)!
347

34. Sum of consecutive numbers
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Organize into a grid.
sum = (average)(number of terms)

35. How to check whether a number is a multiple of 6
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Number is a multiple of 3 and 2
Last two digits are multiple of 4 or the number can be divided by 2 twice.
A = P(1 + r) ^n

36. Three triangle length patterns
Even
3-4-5 - 5-12-13 - 9-12-15
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.
4/3 TT r ^3

37. 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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Organize into a grid.
14 liters
2 steps

38. gcd(m,n)*lcm(m,n)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Immediately UNFACTOR or vice versa
gcd(m,n)*lcm(m,n) = mn
P(event NOT occurring) = 1 - P(event occurring)

39. The average of consecutive numbers
Find simple interest then look for the answer that is a little bigger
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Exterior angle d is equal to the sum of the two remote interior angles a and b
sum = (average)(number of terms)

40. Inscribed Angle - Minor Arc
1st Rule of Probability: Basic Rule is what?
principle (interest rate - in decimal form) (time - in years)
Minor arc = 2(inscribed angle)
The total amount before any deductions

41. To determine the number of integers less than 5000 that are evenly divisible by 15...?
x - x - x(sq. rt 2)
Immediately try factoring/simplifying when possible
Divide 4999 by 15 => 333 integers
(total A) / (total B)

42. 0! = ?
$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.
1
14 liters

43. How to find all divisors of a number
14 liters
If the outcome of one event affects the outcome of the other event.
Even
Find all prime factors

44. gcd(m,n)
1
1st Rule of Probability: Basic Rule is what?
Odd numbers only have ___________
______ |m-n|

45. Probability and Geometry.
P(event NOT occurring) = 1 - P(event occurring)
Exterior angle d is equal to the sum of the two remote interior angles 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
P(E)P(F)

46. Price sold for by retailer (after markup)
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.
If the outcome of one event affects the outcome of the other event.
1 - P(E)

47. When you see an equation in factored form in a question?
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 total amount before any deductions
Immediately UNFACTOR or vice versa
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

48. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Number is a multiple of 3 and 2
$11 - 025
(total A) / (total B)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

49. 30-60-90 triangle basic lengths of sides
Even
Divide 4999 by 15 => 333 integers
x(sq. rt 3) - x - 2x
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.

50. Price purchased for by wholesaler
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.
Purchase price
Odd
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.