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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. 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
-b +- sq. rt(b^2 - 4ac) / 2a
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
Gross Profit = Selling Price - Cost

2. How to check whether a number is a multiple of 3.
16.6%
(amount of change) / (original amount)
______ |m-n|
Sum of digits is multiple of 3

3. The number of outcomes that result in A divided by the total number of possible outcomes.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1st Rule of Probability: Basic Rule is what?
The probability of event occurring is...
Find all prime factors

4. Sq. rt(2)
Sum of digits is multiple of 3 - last two digits multiple of 4.
1.4
3 - 6 - 9 - 12
Purchase price

5. Combined Events: Not E = P(not E) = ?
Odd
1 - P(E)
p/100 = is/of
Purchase price

6. 30-60-90 triangle basic lengths of sides
(amount of change) / (original amount)
x(sq. rt 3) - x - 2x
x - x - x(sq. rt 2)
at least 3 steps

7. 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.
Minor arc = 2(inscribed angle)
$11 - 025
(x-n(n)y-n)

8. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
s Sq. rt (x^r)
22
3 - 6 - 9 - 12
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.

9. 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
Odd numbers only have ___________
Any multiplication involving an even number creates an even product.
| A union B| = |A| + |B| - |A intersect B|

10. 3^3 x 4^3 = ?
(n-1)!
P(E)P(F)
12^3
The total amount before any deductions

11. 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.
2 steps
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

12. x^r/s = ?
s Sq. rt (x^r)
______ |m-n|
x(sq. rt 3) - x - 2x
Figure out the probability for each individual event. Multiply the individual probabilities together.

13. Sum of consecutive numbers
sum = (average)(number of terms)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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
If the outcome of one event affects the outcome of the other event.

14. Inscribed Angle - Minor Arc
22
If the outcome of one event affects the outcome of the other event.
(x-n(n)y-n)
Minor arc = 2(inscribed angle)

15. When you see an equation in factored form in a question?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Immediately UNFACTOR or vice versa
y2 - y1 / x2 - x1
(amount of change) / (original amount)

16. How to check whether number is multiple of 9
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 9
Sum of digits is multiple of 3 - last two digits multiple of 4.
1st Rule of Probability: Basic Rule is what?

17. Number added or deleted
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.
(sum of bases)(height) / 2
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

18. What does the Sum of the angles in a Regular Polygon formula look like?
Divide 4999 by 15 => 333 integers
180(n-2)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
If the outcome of one event affects the outcome of the other event.

19. (1/4)^2
1.7
1/16
p/100 = is/of
Balancing

20. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
1st Rule of Probability: Basic Rule is what?
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.
Sum of digits is multiple of 3 - last two digits multiple of 4.

21. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
The amount after deductions
347
Divide 4999 by 15 => 333 integers

22. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Number is a multiple of 3 and 2
______ |m-n|
Find all prime factors
principle (interest rate - in decimal form) (time - in years)

23. Odd Factors
Odd numbers only have ___________
2 steps
| A union B| = |A| + |B| - |A intersect B|
12.5%

24. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
n! / (n - r)!
Find all prime factors
D or E
principle (interest rate - in decimal form) (time - in years)

25. Average Rate: Average speed
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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(total distance) / (total time)
P(E)P(F)

26. 1/8 = what %
12.5%
0.15n + 0.08(5) = 0.1(n+5)
P(event NOT occurring) = 1 - P(event occurring)
Odd

27. Set Problems formula
4/3 TT r ^3
The amount after deductions
(x-n(n)y-n)
12^3

28. Work problem rule
Odd numbers only have ___________
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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)
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.

29. Probability and Geometry.
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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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
P(event NOT occurring) = 1 - P(event occurring)

30. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Group 1 + Group 2 + Neither - Both = Total
The probability of an event occurring plus the probability of the event not occurring = 1

31. 1/6 = what %
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Group 1 + Group 2 + Neither - Both = Total
12.5%
16.6%

32. The average of consecutive numbers
principle (interest rate - in decimal form) (time - in years)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
16.6%
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

33. Always try to factor
1.4
Sum of digits is multiple of 9
y2 - y1 / x2 - x1
always try to factor

34. How do you multiply roots together.
| A union B| = |A| + |B| - |A intersect B|
x(sq. rt 3) - x - 2x
22
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

35. 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
A = P(1 + r) ^n
Balancing
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(sum of bases)(height) / 2

36. 2n - 2n+2 - 2n+4
Find all prime factors
(total A) / (total B)
Purchase price
Even

37. Sq. rt(3)
1.7
180(n-2)
A = P(1 + r) ^n
$11 - 025

38. Price purchased for by wholesaler
22
Purchase price
Any multiplication involving an even number creates an even product.
12.5%

39. Odd and Even rule.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
x - x - x(sq. rt 2)
| A union B| = |A| + |B| - |A intersect B|
Any multiplication involving an even number creates an even product.

40. 2nd Rule of Probability: P(E) = 1 - P(not E)
Balancing
The probability of an event occurring plus the probability of the event not occurring = 1
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Number is a multiple of 3 and 2

41. The number of ways independent events can occur together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
$11 - 025
1/16
s Sq. rt (x^r)

42. Properties of 0
1/16
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Organize into a grid.
Sum of digits is multiple of 9

43. To determine the number of integers less than 5000 that are evenly divisible by 15...?
n! / (n - r)!
3-4-5 - 5-12-13 - 9-12-15
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.

44. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
The probability of an event occurring plus the probability of the event not occurring = 1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
$11 - 025
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)

45. 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.
Organize into a grid.
3 - 6 - 9 - 12
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Find all prime factors

46. How to check for a prime number.

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47. Price sold for by retailer (after markup)
22
Last two digits are multiple of 4 or the number can be divided by 2 twice.
180(n-2)
market value

48. How to check whether a number is a multiple of 4.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Gross Profit = Selling Price - Cost
180(n-2)

49. How to find the slope.
14 liters
(amount of change) / (original amount)
Minor arc = 2(inscribed angle)
y2 - y1 / x2 - x1

50. Multiples of 3
3 - 6 - 9 - 12
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
16.6%
180(n-2)