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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. How to check whether a number is a multiple of 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.
Minor arc = 2(inscribed angle)
Sum of digits is multiple of 3
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.

2. Inscribed Angle - Minor Arc
y2 - y1 / x2 - x1
Minor arc = 2(inscribed angle)
3 - 6 - 9 - 12
Gross Profit = Selling Price - Cost

3. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
sum = (average)(number of terms)
16.6%
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. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
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 simple interest then look for the answer that is a little bigger
P(event NOT occurring) = 1 - P(event occurring)

5. Permutations: Order Matters
Odd
Sum of digits is multiple of 3
n! / (n - r)!
s Sq. rt (x^r)

6. Triangle abc with d on the outside with a line. What does d = ?
x - x - x(sq. rt 2)
(total distance) / (total time)
Exterior angle d is equal to the sum of the two remote interior angles a and b
22

7. Price purchased for by wholesaler
Purchase price
12.5%
A = P(1 + r) ^n
x - x - x(sq. rt 2)

8. Prime Factorization to find Greatest Common Factor
P(E)P(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
n! / (n - r)!
16.6%

9. Indistinguishable events how to find the number of permutations

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10. Average Rate: Average A per B
s Sq. rt (x^r)
Balancing
| A union B| = |A| + |B| - |A intersect B|
(total A) / (total B)

11. 5/6 = what %
83.3%
1.7
Group 1 + Group 2 + Neither - Both = Total
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)

12. 0! = ?
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 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
-b +- sq. rt(b^2 - 4ac) / 2a

13. 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?
3 - 6 - 9 - 12
180(n-2)
0.15n + 0.08(5) = 0.1(n+5)
Any multiplication involving an even number creates an even product.

14. What does the Sum of the angles in a Regular Polygon formula look like?
(total A) / (total B)
market value
180(n-2)
16.6%

15. Three triangle length patterns
______ |m-n|
3-4-5 - 5-12-13 - 9-12-15
Even
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

16. Odd Factors
Number is a multiple of 3 and 2
Odd
D or E
Odd numbers only have ___________

17. Quadratic formula
Group 1 + Group 2 + Neither - Both = Total
Divide 4999 by 15 => 333 integers
22
-b +- sq. rt(b^2 - 4ac) / 2a

18. Odd and Even rule.
Any multiplication involving an even number creates an even product.
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)
1.4

19. Combined Events: E and F
22
If the outcome of one event affects the outcome of the other event.
P(E)P(F)
-b +- sq. rt(b^2 - 4ac) / 2a

20. How to check for a prime number.

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21. Combined Events: E or F
P(E) + P(F) - P(E and F)
Find simple interest then look for the answer that is a little bigger
3-4-5 - 5-12-13 - 9-12-15
Sum of digits is multiple of 3

22. 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.
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.
p/100 = is/of
x - x - x(sq. rt 2)

23. Multiplication principle
Sum of digits is multiple of 3
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
x - x - x(sq. rt 2)
______ |m-n|

24. 2n - 2n+2 - 2n+4
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Even
Sum of digits is multiple of 3 - last two digits multiple of 4.
The probability of event occurring is...

25. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
x(sq. rt 3) - x - 2x
P(E)P(F)
22
(total A) / (total B)

26. To determine multiple-event probability where each individual event must occur in a certain way.
P(E) + P(F) - P(E and F)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Figure out the probability for each individual event. Multiply the individual probabilities together.
2 steps

27. The number of outcomes that result in A divided by the total number of possible outcomes.
principle (interest rate - in decimal form) (time - in years)
A = P(1 + r) ^n
The probability of event occurring is...
p/100 = is/of

28. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
The probability of event occurring is...
12^3

29. When you see an equation in factored form in a question?
x(sq. rt 3) - x - 2x
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.
Sum of digits is multiple of 9
Immediately UNFACTOR or vice versa

30. Gross Profit formula
The total amount before any deductions
3 - 6 - 9 - 12
Gross Profit = Selling Price - Cost
A = P(1 + r) ^n

31. (1/4)^2
1st Rule of Probability: Basic Rule is what?
1/16
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.
Figure out the probability for each individual event. Multiply the individual probabilities together.

32. Sq. rt(3)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1 - P(E)
1.7
(total distance) / (total time)

33. 30-60-90 triangle basic lengths of sides
gcd(m,n)*lcm(m,n) = mn
x(sq. rt 3) - x - 2x
Purchase price
x - x - x(sq. rt 2)

34. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Any multiplication involving an even number creates an even product.
1 - P(E)
$11 - 025
Sum of digits is multiple of 3 - last two digits multiple of 4.

35. The number of ways independent events can occur together.
always try to factor
Figure out the probability for each individual event. Multiply the individual probabilities together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1.4

36. How to check whether number is multiple of 9
3-4-5 - 5-12-13 - 9-12-15
y2 - y1 / x2 - x1
Sum of digits is multiple of 9
-b +- sq. rt(b^2 - 4ac) / 2a

37. Sq. rt(2)
Minor arc = 2(inscribed angle)
(total A) / (total B)
always try to factor
1.4

38. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
If the outcome of one event affects the outcome of the other event.
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
Sum of digits is multiple of 9
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

39. 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 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
(amount of change) / (original amount)
Sum of digits is multiple of 9
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.

40. Formula for Mixed Group problems (involving Both/Neither)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Group 1 + Group 2 + Neither - Both = Total
$11 - 025
Immediately try factoring/simplifying when possible

41. In general - medium questions require how many steps to solve?
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)
2 steps
(n-1)!
s Sq. rt (x^r)

42. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
x(sq. rt 3) - x - 2x
Organize into a grid.
A = P(1 + r) ^n
| A union B| = |A| + |B| - |A intersect B|

43. Set Problems formula
(x-n(n)y-n)
Balancing
1.7
1

44. Multiples of 3
Sum of digits is multiple of 9
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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
3 - 6 - 9 - 12

45. Gross
The total amount before any deductions
Divide 4999 by 15 => 333 integers
16.6%
Principal (1 + interest/number times compounded)^(t)(n)

46. 45-45-90 triangle basic lengths of sides
at least 3 steps
principle (interest rate - in decimal form) (time - in years)
P(E)P(F)
x - x - x(sq. rt 2)

47. Sum of consecutive numbers
principle (interest rate - in decimal form) (time - in years)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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
sum = (average)(number of terms)

48. Price sold for by retailer (after markup)
market value
(n-1)!
(total A) / (total B)
always try to factor

49. 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
Find all prime factors
1.4
x - x - x(sq. rt 2)

50. How to check whether a number is a multiple of 12.
12^3
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
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 3 - last two digits multiple of 4.