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GMAT Quantitative General

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
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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 number 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
D or E
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.

2. How to find all divisors of a number
Balancing
347
1
Find all prime factors

3. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Exterior angle d is equal to the sum of the two remote interior angles a and b
principle (interest rate - in decimal form) (time - in years)
The total amount before any deductions
at least 3 steps

4. Inscribed Angle - Minor Arc
1
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.
Minor arc = 2(inscribed angle)
P(E) + P(F) - P(E and F)

5. Combined Events: E or F
Find all prime factors
P(E) + P(F) - P(E and F)
Figure out the probability for each individual event. Multiply the individual probabilities together.
Sum of digits is multiple of 3

6. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
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.
s Sq. rt (x^r)
347
Sum of digits is multiple of 3 - last two digits multiple of 4.

7. Multiples of 3
16.6%
Odd
3 - 6 - 9 - 12
(total distance) / (total time)

8. Indistinguishable events how to find the number of permutations

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9. Multiplication principle
1.4
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
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.

10. 5/6 = what %
83.3%
(amount of change) / (original amount)
______ |m-n|
Immediately UNFACTOR or vice versa

11. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Odd
1.7

12. Number added or deleted
A = P(1 + r) ^n
1st Rule of Probability: Basic Rule is what?
Odd
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

13. 2n - 2n+2 - 2n+4
Gross Profit = Selling Price - Cost
______ |m-n|
P(event NOT occurring) = 1 - P(event occurring)
Even

14. Percent increase = ?
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. 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.
(amount of change) / (original amount)

15. 2n+1 - 2n+3 - 2n+5
Odd
(amount of change) / (original amount)
Minor arc = 2(inscribed angle)
12.5%

16. 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?
The total amount before any deductions
Immediately try factoring/simplifying when possible
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)
0.15n + 0.08(5) = 0.1(n+5)

17. In general - medium questions require how many steps to solve?
83.3%
2 steps
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.
y2 - y1 / x2 - x1

18. Set Problems formula
(x-n(n)y-n)
P(E)P(F)
16.6%
4/3 TT r ^3

19. The number of outcomes that result in A divided by the total number of possible outcomes.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Exterior angle d is equal to the sum of the two remote interior angles a and b
The probability of event occurring is...
The total amount before any deductions

20. (1/4)^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
1/16
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
180(n-2)

21. gcd(m,n)
Minor arc = 2(inscribed angle)
Sum of digits is multiple of 3 - last two digits multiple of 4.
______ |m-n|
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

22. Prime Factorization to find Greatest Common Factor
always try to factor
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
1.7

23. Sq. rt(3)
market value
Figure out the probability for each individual event. Multiply the individual probabilities together.
22
1.7

24. Odd Factors
Odd numbers only have ___________
1st Rule of Probability: Basic Rule is what?
market value
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

25. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
Organize into a grid.
16.6%
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

26. 1. A and B < A or B 2. A or B > Individual probabilities of A - B 3. P(A and B) = P(A) x P(B) <-- 'fewer options' 4. P(A or B) = P(A) + P(B) <-- 'more options' - Probability of multiple events rules.
22
1st Rule of Probability: Basic Rule is what?
3 - 6 - 9 - 12
Sum of digits is multiple of 9

27. 1/6 = what %
Immediately try factoring/simplifying when possible
principle (interest rate - in decimal form) (time - in years)
16.6%
Sum of digits is multiple of 3

28. Three triangle length patterns
(sum of bases)(height) / 2
x(sq. rt 3) - x - 2x
3-4-5 - 5-12-13 - 9-12-15
1st Rule of Probability: Basic Rule is what?

29. Formula for area of a Trapezoid
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.
1.4
(sum of bases)(height) / 2
Immediately UNFACTOR or vice versa

30. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
Balancing
0.15n + 0.08(5) = 0.1(n+5)
$11 - 025

31. How to check for a prime number.

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32. Trial Problems: look at the probability of NOT OCCURRING
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.
P(event NOT occurring) = 1 - P(event occurring)
at least 3 steps
0.15n + 0.08(5) = 0.1(n+5)

33. Net
The amount after deductions
x(sq. rt 3) - x - 2x
1 - P(E)
3-4-5 - 5-12-13 - 9-12-15

34. 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
Even
x - x - x(sq. rt 2)
Odd numbers only have ___________
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.

35. Sum of consecutive numbers
(total distance) / (total time)
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.
sum = (average)(number of terms)

36. How to find the slope.
P(event NOT occurring) = 1 - P(event occurring)
16.6%
y2 - y1 / x2 - x1
$11 - 025

37. 4th rule of Probability
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.
x - x - x(sq. rt 2)
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)

38. Simple probability
180(n-2)
1st Rule of Probability: Basic Rule is what?
Principal (1 + interest/number times compounded)^(t)(n)
(# of favorable outcomes) / (# of possible outcomes)

39. The number of ways independent events can occur together.
(amount of change) / (original amount)
(total A) / (total B)
x(sq. rt 3) - x - 2x
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

40. 1/8 = what %
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)
180(n-2)
12.5%
Divide 4999 by 15 => 333 integers

41. 3^3 x 4^3 = ?
2 steps
12^3
Odd
83.3%

42. In general - difficult questions require how many steps to solve?
at least 3 steps
0.15n + 0.08(5) = 0.1(n+5)
gcd(m,n)*lcm(m,n) = mn
1 - P(E)

43. Probability and Geometry.
22
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
$11 - 025

44. Combined Events: Not E = P(not E) = ?
always try to factor
16.6%
1 - P(E)
1.4

45. 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
Minor arc = 2(inscribed angle)
Balancing
at least 3 steps
x - x - x(sq. rt 2)

46. Price sold for by retailer (after markup)
market value
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.
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. Average Rate: Average A per B
at least 3 steps
(total A) / (total B)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
x - x - x(sq. rt 2)

48. How many liters of a solution that is 10% alcohol by volume must be added to 2 liters of a solution that is 50% alcohol by volume to create a solution that is 15% alcohol by volume?
14 liters
The total amount before any deductions
principle (interest rate - in decimal form) (time - in years)
______ |m-n|

49. Odd and Even rule.
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
gcd(m,n)*lcm(m,n) = mn
P(E)P(F)
Any multiplication involving an even number creates an even product.

50. How to check whether a number is a multiple of 4.
-b +- sq. rt(b^2 - 4ac) / 2a
1.7
D or E
Last two digits are multiple of 4 or the number can be divided by 2 twice.

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GMAT Quantitative General

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