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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 for a prime number.

2. How to check whether a number is a multiple of 3.
Any multiplication involving an even number creates an even product.
Divide 4999 by 15 => 333 integers
Sum of digits is multiple of 3
The total amount before any deductions

3. Gross
x - x - x(sq. rt 2)
The total amount before any deductions
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
1/16

4. 4th rule of Probability
A = P(1 + r) ^n
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)
(total A) / (total B)
Purchase price

5. Permutations: Order Matters
Last two digits are multiple of 4 or the number can be divided by 2 twice.
n! / (n - 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
16.6%

6. Percent increase = ?
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
Purchase price
1.7
(amount of change) / (original amount)

7. 2n+1 - 2n+3 - 2n+5
Exterior angle d is equal to the sum of the two remote interior angles a and b
Sum of digits is multiple of 3
Odd
Immediately UNFACTOR or vice versa

8. Average Rate: Average speed
Immediately try factoring/simplifying when possible
Find all prime factors
Find simple interest then look for the answer that is a little bigger
(total distance) / (total time)

9. Compound interest rule
(sum of bases)(height) / 2
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
y2 - y1 / x2 - x1
Find simple interest then look for the answer that is a little bigger

10. Volume of a sphere
4/3 TT r ^3
180(n-2)
y2 - y1 / x2 - x1
The probability of an event occurring plus the probability of the event not occurring = 1

11. 5/6 = what %
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
83.3%
Number is a multiple of 3 and 2
gcd(m,n)*lcm(m,n) = mn

12. How to check whether a number is a multiple of 4.
Immediately UNFACTOR or vice versa
(total A) / (total B)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

13. 30-60-90 triangle basic lengths of sides
P(E)P(F)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Immediately try factoring/simplifying when possible
x(sq. rt 3) - x - 2x

14. Price sold for by retailer (after markup)
Group 1 + Group 2 + Neither - Both = Total
market value
4/3 TT r ^3
3-4-5 - 5-12-13 - 9-12-15

15. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
(amount of change) / (original amount)
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
A = P(1 + r) ^n

16. Three triangle length patterns
principle (interest rate - in decimal form) (time - in years)
Any multiplication involving an even number creates an even product.
sum = (average)(number of terms)
3-4-5 - 5-12-13 - 9-12-15

17. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Immediately try factoring/simplifying when possible
P(E) + P(F) - P(E and F)
D or E
The total amount before any deductions

18. Sq. rt(3)
(n-1)!
16.6%
1.7
at least 3 steps

19. Combined Events: E and F
P(E)P(F)
P(event NOT occurring) = 1 - P(event occurring)
Principal (1 + interest/number times compounded)^(t)(n)
347

20. Work problem rule
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.
Organize into a grid.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

21. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
1.4
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)
12^3

22. How to find the slope.
y2 - y1 / x2 - x1
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.
Divide 4999 by 15 => 333 integers
1st Rule of Probability: Basic Rule is what?

23. Quadratic formula
Exterior angle d is equal to the sum of the two remote interior angles a and b
12^3
-b +- sq. rt(b^2 - 4ac) / 2a
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

24. Multiples of 3
1st Rule of Probability: Basic Rule is what?
3 - 6 - 9 - 12
Sum of digits is multiple of 9
principle (interest rate - in decimal form) (time - in years)

25. How to find all divisors of a number
(amount of change) / (original amount)
market value
Find all prime factors
12^3

26. The average of consecutive numbers
12^3
(total A) / (total B)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The probability of event occurring is...

27. How to check whether a number is a multiple of 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.
gcd(m,n)*lcm(m,n) = mn
Number is a multiple of 3 and 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

28. To determine the number of integers less than 5000 that are evenly divisible by 15...?
x(sq. rt 3) - x - 2x
(x-n(n)y-n)
Find simple interest then look for the answer that is a little bigger
Divide 4999 by 15 => 333 integers

29. Properties of 0
2 steps
sum = (average)(number of terms)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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.

30. x^r/s = ?
14 liters
12.5%
-b +- sq. rt(b^2 - 4ac) / 2a
s Sq. rt (x^r)

31. 3^3 x 4^3 = ?
A = P(1 + r) ^n
12^3
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The probability of event occurring is...

32. Compound interest formula
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Principal (1 + interest/number times compounded)^(t)(n)
3 - 6 - 9 - 12
-b +- sq. rt(b^2 - 4ac) / 2a

33. 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. 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
Balancing
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/100 = is/of

34. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
1 - P(E)
Divide 4999 by 15 => 333 integers
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
4/3 TT r ^3

35. 45-45-90 triangle basic lengths of sides
Number is a multiple of 3 and 2
Minor arc = 2(inscribed angle)
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 - x - x(sq. rt 2)

36. Combined Events: E or F
Any multiplication involving an even number creates an even product.
1.7
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.
P(E) + P(F) - P(E and F)

37. In general - medium questions require how many steps to solve?
1.7
2 steps
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
______ |m-n|

38. 2nd Rule of Probability: P(E) = 1 - P(not E)
sum = (average)(number of terms)
Gross Profit = Selling Price - Cost
The probability of an event occurring plus the probability of the event not occurring = 1
83.3%

39. Sq. rt(2)
1.4
Any multiplication involving an even number creates an even product.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Sum of digits is multiple of 9

40. 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
Sum of digits is multiple of 3 - last two digits multiple of 4.
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.
Immediately try factoring/simplifying when possible

41. Multiplication principle
(# of favorable outcomes) / (# of possible outcomes)
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
1.7
2 steps

42. Set Problems formula
(x-n(n)y-n)
A = P(1 + r) ^n
p/100 = is/of
Sum of digits is multiple of 3

43. When you see an equation in factored form in a question?
1.4
Immediately UNFACTOR or vice versa
Exterior angle d is equal to the sum of the two remote interior angles a and b
Last two digits are multiple of 4 or the number can be divided by 2 twice.

44. How to check whether number is multiple of 9
Immediately try factoring/simplifying when possible
347
Sum of digits is multiple of 9
22

45. Triangle abc with d on the outside with a line. What does d = ?
Odd numbers only have ___________
principle (interest rate - in decimal form) (time - in years)
Organize into a grid.
Exterior angle d is equal to the sum of the two remote interior angles a and b

46. Probability and Geometry.
Find simple interest then look for the answer that is a little bigger
The probability of an event occurring plus the probability of the event not occurring = 1
Divide 4999 by 15 => 333 integers
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

47. Percent Formula
(# of favorable outcomes) / (# of possible outcomes)
12^3
p/100 = is/of
22

48. 3rd Rule of Probability: Conditional Probability
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 A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
1
gcd(m,n)*lcm(m,n) = mn

49. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
P(E) + P(F) - P(E and F)
Any multiplication involving an even number creates an even product.
12^3

50. Average Rate: Average A per B
3-4-5 - 5-12-13 - 9-12-15
Gross Profit = Selling Price - Cost
(total A) / (total B)
180(n-2)