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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 number is multiple of 9
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
22
Sum of digits is multiple of 9

2. Set Problems formula
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(E) + P(F) - P(E and F)
(x-n(n)y-n)
347

3. 3rd Rule of Probability: Conditional Probability
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.
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.
Balancing
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

4. Indistinguishable events how to find the number of permutations

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5. 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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Number is a multiple of 3 and 2
Sum of digits is multiple of 9

6. Combined Events: Not E = P(not E) = ?
The probability of event occurring is...
Figure out the probability for each individual event. Multiply the individual probabilities together.
1 - P(E)
Exterior angle d is equal to the sum of the two remote interior angles a and b

7. Average Rate: Average A per B
-b +- sq. rt(b^2 - 4ac) / 2a
(total A) / (total B)
1.7
Sum of digits is multiple of 3

8. Odd Factors
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(amount of change) / (original amount)
(total distance) / (total time)
Odd numbers only have ___________

9. Number added or deleted
Last two digits are multiple of 4 or the number can be divided by 2 twice.
sum = (average)(number of terms)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Minor arc = 2(inscribed angle)

10. 1/8 = what %
principle (interest rate - in decimal form) (time - in years)
The probability of event occurring is...
12.5%
Gross Profit = Selling Price - Cost

11. Trial Problems: look at the probability of NOT OCCURRING
The total amount before any deductions
| A union B| = |A| + |B| - |A intersect B|
22
P(event NOT occurring) = 1 - P(event occurring)

12. Sq. rt(2)
Gross Profit = Selling Price - Cost
(total A) / (total B)
Odd
1.4

13. Odd and Even rule.
Divide 4999 by 15 => 333 integers
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.

14. Percent Formula
1/16
A = P(1 + r) ^n
3-4-5 - 5-12-13 - 9-12-15
p/100 = is/of

15. Inscribed Angle - Minor Arc
-b +- sq. rt(b^2 - 4ac) / 2a
Minor arc = 2(inscribed angle)
Sum of digits is multiple of 3
Find all prime factors

16. Multiples of 3
at least 3 steps
Principal (1 + interest/number times compounded)^(t)(n)
3 - 6 - 9 - 12
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.

17. Compound interest rule
$11 - 025
______ |m-n|
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

18. Triangle abc with d on the outside with a line. What does d = ?
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.
Organize into a grid.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Even

19. In general - difficult questions require how many steps to solve?
Exterior angle d is equal to the sum of the two remote interior angles a and b
Odd
1
at least 3 steps

20. Net
The amount after deductions
Figure out the probability for each individual event. Multiply the individual probabilities together.
gcd(m,n)*lcm(m,n) = mn
14 liters

21. How to check whether a number is a multiple of 3.
(sum of bases)(height) / 2
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 3
3-4-5 - 5-12-13 - 9-12-15

22. Always try to factor
12.5%
market value
always try to factor
1st Rule of Probability: Basic Rule is what?

23. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 3 - last two digits multiple of 4.
The total amount before any deductions
Odd

24. What does the Sum of the angles in a Regular Polygon formula look like?
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)
Odd
180(n-2)
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.

25. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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
The probability of event occurring is...
(total distance) / (total time)
D or E

26. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
gcd(m,n)*lcm(m,n) = mn
22
Group 1 + Group 2 + Neither - Both = Total
Find simple interest then look for the answer that is a little bigger

27. Average Rate: Average speed
(total distance) / (total time)
3 - 6 - 9 - 12
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
P(event NOT occurring) = 1 - P(event occurring)

28. 5/6 = what %
83.3%
16.6%
2 steps
1st Rule of Probability: Basic Rule is what?

29. When you see an equation in factored form in a question?
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.
14 liters
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Immediately UNFACTOR or vice versa

30. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
P(E) + P(F) - P(E and F)
| A union B| = |A| + |B| - |A intersect B|
gcd(m,n)*lcm(m,n) = mn

31. Gross Profit formula
A = P(1 + r) ^n
Gross Profit = Selling Price - Cost
at least 3 steps
The probability of event occurring is...

32. 2n - 2n+2 - 2n+4
Even
1.7
Gross Profit = Selling Price - Cost
3-4-5 - 5-12-13 - 9-12-15

33. gcd(m,n)
Immediately try factoring/simplifying when possible
$11 - 025
______ |m-n|
Group 1 + Group 2 + Neither - Both = Total

34. How to check whether a number is a multiple of 4.
14 liters
Balancing
347
Last two digits are multiple of 4 or the number can be divided by 2 twice.

35. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(sum of bases)(height) / 2
-b +- sq. rt(b^2 - 4ac) / 2a
s Sq. rt (x^r)

36. 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
Find simple interest then look for the answer that is a little bigger
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 amount after deductions
Divide 4999 by 15 => 333 integers

37. Price purchased for by wholesaler
P(E) + P(F) - P(E and F)
Purchase price
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The amount after deductions

38. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
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.
Odd
Exterior angle d is equal to the sum of the two remote interior angles a and b

39. Simple probability
If the outcome of one event affects the outcome of the other event.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each 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
(# of favorable outcomes) / (# of possible outcomes)

40. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
The probability of an event occurring plus the probability of the event not occurring = 1
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
347

41. Permutations: Order Matters
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
Minor arc = 2(inscribed angle)
n! / (n - r)!

42. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
Organize into a grid.
Divide 4999 by 15 => 333 integers
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.

43. Combined Events: 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.
P(E)P(F)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(total A) / (total B)

44. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
(x-n(n)y-n)
The total amount before any deductions
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.

45. Combined Events: E or F
Last two digits are multiple of 4 or the number can be divided by 2 twice.
83.3%
P(E) + P(F) - P(E and F)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

46. 3^3 x 4^3 = ?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
0.15n + 0.08(5) = 0.1(n+5)
12^3
(# of favorable outcomes) / (# of possible outcomes)

47. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
Any multiplication involving an even number creates an even product.
D or E
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

48. Formula for area of a Trapezoid
(sum of bases)(height) / 2
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(n-1)!
gcd(m,n)*lcm(m,n) = mn

49. 0! = ?
D or E
s Sq. rt (x^r)
1
1 - P(E)

50. 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.
Gross Profit = Selling Price - Cost
y2 - y1 / x2 - x1
-b +- sq. rt(b^2 - 4ac) / 2a
Organize into a grid.