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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. Work problem rule
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.
0.15n + 0.08(5) = 0.1(n+5)
s Sq. rt (x^r)
Principal (1 + interest/number times compounded)^(t)(n)

2. Volume of a sphere
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
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.
The probability of event occurring is...

3. Prime Factorization to find Greatest Common Factor
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 3
(total A) / (total B)
1/16

4. 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?
(# of favorable outcomes) / (# of possible outcomes)
(x-n(n)y-n)
14 liters
1

5. 2n+1 - 2n+3 - 2n+5
Odd
2 steps
p/100 = is/of
Figure out the probability for each individual event. Multiply the individual probabilities together.

6. In general - difficult questions require how many steps to solve?
at least 3 steps
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.
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)

7. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Balancing
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
Figure out the probability for each individual event. Multiply the individual probabilities together.

8. Inscribed Angle - Minor Arc
14 liters
Minor arc = 2(inscribed angle)
(n-1)!
347

9. Percent Formula
Sum of digits is multiple of 3 - last two digits multiple of 4.
Divide 4999 by 15 => 333 integers
16.6%
p/100 = is/of

10. How to check whether number is multiple of 9
$11 - 025
1 - P(E)
sum = (average)(number of terms)
Sum of digits is multiple of 9

11. Sum of consecutive numbers
1st Rule of Probability: Basic Rule is what?
sum = (average)(number of terms)
The probability of an event occurring plus the probability of the event not occurring = 1
P(event NOT occurring) = 1 - P(event occurring)

12. Compound interest formula
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.
(amount of change) / (original amount)
Principal (1 + interest/number times compounded)^(t)(n)
12^3

13. Odd and Even rule.
y2 - y1 / x2 - x1
Organize into a grid.
always try to factor
Any multiplication involving an even number creates an even product.

14. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
14 liters
4/3 TT r ^3
principle (interest rate - in decimal form) (time - in years)
n! / (n - r)!

15. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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
D or E
Any multiplication involving an even number creates an even product.
gcd(m,n)*lcm(m,n) = mn

16. To determine the number of integers less than 5000 that are evenly divisible by 15...?
x - x - x(sq. rt 2)
y2 - y1 / x2 - x1
Divide 4999 by 15 => 333 integers
If the outcome of one event affects the outcome of the other event.

17. 3^3 x 4^3 = ?
Even
12^3
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.

18. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
Balancing
Group 1 + Group 2 + Neither - Both = Total
Last two digits are multiple of 4 or the number can be divided by 2 twice.

19. 30-60-90 triangle basic lengths of sides
market value
12^3
x(sq. rt 3) - x - 2x
1

20. How to find all divisors of a number
1 - P(E)
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
market value
Find all prime factors

21. 4th rule of Probability
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 probability of an event occurring plus the probability of the event not occurring = 1
3-4-5 - 5-12-13 - 9-12-15
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)

22. 2n - 2n+2 - 2n+4
0.15n + 0.08(5) = 0.1(n+5)
Even
14 liters
Organize into a grid.

23. Multiples of 3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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)
3 - 6 - 9 - 12
1st Rule of Probability: Basic Rule is what?

24. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
Odd
P(event NOT occurring) = 1 - P(event occurring)
D or E

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?
12.5%
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
1st Rule of Probability: Basic Rule is what?
0.15n + 0.08(5) = 0.1(n+5)

26. When you see an equation in factored form in a question?
12.5%
Immediately UNFACTOR or vice versa
gcd(m,n)*lcm(m,n) = mn
(total distance) / (total time)

27. How to check whether a number is a multiple of 6
n! / (n - r)!
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Any multiplication involving an even number creates an even product.
Number is a multiple of 3 and 2

28. How to check whether a number is a multiple of 4.
______ |m-n|
principle (interest rate - in decimal form) (time - in years)
The total amount before any deductions
Last two digits are multiple of 4 or the number can be divided by 2 twice.

29. The average of consecutive numbers
A = P(1 + r) ^n
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.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

30. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.

31. Net
| A union B| = |A| + |B| - |A intersect B|
The amount after deductions
______ |m-n|
Minor arc = 2(inscribed angle)

32. 5/6 = what %
(x-n(n)y-n)
n! / (n - r)!
83.3%
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

33. Combined Events: E and F
1
Even
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)

34. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
(x-n(n)y-n)
Sum of digits is multiple of 3 - last two digits multiple of 4.
3-4-5 - 5-12-13 - 9-12-15

35. (1/4)^2
1/16
(sum of bases)(height) / 2
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 3 - last two digits multiple of 4.

36. 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.
(n-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

37. Indistinguishable events how to find the number of permutations

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38. Sq. rt(3)
1.7
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)
12.5%
P(E)P(F)

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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(total A) / (total B)
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

40. Sq. rt(2)
-b +- sq. rt(b^2 - 4ac) / 2a
83.3%
1 - P(E)
1.4

41. Gross
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
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.
The total amount before any deductions
The probability of event occurring is...

42. Compound interest rule
Find simple interest then look for the answer that is a little bigger
Even
P(event NOT occurring) = 1 - P(event occurring)
Balancing

43. 0! = ?
1
The probability of event occurring is...
n! / (n - r)!
Odd numbers only have ___________

44. What to do with equations that have fractions
Immediately UNFACTOR or vice versa
x(sq. rt 3) - x - 2x
-b +- sq. rt(b^2 - 4ac) / 2a
Immediately try factoring/simplifying when possible

45. Properties of 0
(total A) / (total B)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
x(sq. rt 3) - x - 2x
4/3 TT r ^3

46. 1/6 = what %
The probability of event occurring is...
market value
16.6%
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

47. The number of ways independent events can occur together.
347
gcd(m,n)*lcm(m,n) = mn
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.

48. 45-45-90 triangle basic lengths of sides
Gross Profit = Selling Price - Cost
x - x - x(sq. rt 2)
$11 - 025
Even

49. Percent increase = ?
Even
(amount of change) / (original amount)
2 steps
Figure out the probability for each individual event. Multiply the individual probabilities together.

50. Odd Factors
If the outcome of one event affects the outcome of the other event.
347
Odd numbers only have ___________
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.

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GMAT Quantitative General

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