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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. 0! = ?
s Sq. rt (x^r)
1
Any multiplication involving an even number creates an even product.
1.7

2. Volume of a sphere
3-4-5 - 5-12-13 - 9-12-15
y2 - y1 / x2 - x1
Any multiplication involving an even number creates an even product.
4/3 TT r ^3

3. How to check whether a number is a multiple of 4.
s Sq. rt (x^r)
n! / (n - r)!
| A union B| = |A| + |B| - |A intersect B|
Last two digits are multiple of 4 or the number can be divided by 2 twice.

4. Compound interest formula
Sum of digits is multiple of 3 - last two digits multiple of 4.
Gross Profit = Selling Price - Cost
Odd numbers only have ___________
Principal (1 + interest/number times compounded)^(t)(n)

5. Probability and Geometry.
P(E) + P(F) - P(E and F)
1
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 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

6. 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
83.3%
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.
Number is a multiple of 3 and 2
(total A) / (total B)

7. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
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
Even
A = P(1 + r) ^n
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

8. Compound interest rule
1.4
Group 1 + Group 2 + Neither - Both = Total
Find simple interest then look for the answer that is a little bigger
Sum of digits is multiple of 3 - last two digits multiple of 4.

9. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Sum of digits is multiple of 3
(n-1)!
The probability of an event occurring plus the probability of the event not occurring = 1

10. How to find the slope.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
y2 - y1 / x2 - x1
x(sq. rt 3) - x - 2x

11. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
(amount of change) / (original amount)
at least 3 steps
Purchase price

12. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
4/3 TT r ^3
The amount after deductions
1.7

13. Formula for area of a Trapezoid
x(sq. rt 3) - x - 2x
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 of bases)(height) / 2
n! / (n - r)!

14. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Balancing
Odd numbers only have ___________
Immediately UNFACTOR or vice versa

15. To determine multiple-event probability where each individual event must occur in a certain way.
1
$11 - 025
Gross Profit = Selling Price - Cost
Figure out the probability for each individual event. Multiply the individual probabilities together.

16. 30-60-90 triangle basic lengths of sides
(total A) / (total B)
x(sq. rt 3) - x - 2x
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
83.3%

17. How to check for a prime number.

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18. 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?
0.15n + 0.08(5) = 0.1(n+5)
22
x(sq. rt 3) - x - 2x
y2 - y1 / x2 - x1

19. How to check whether a number is a multiple of 3.
3-4-5 - 5-12-13 - 9-12-15
Sum of digits is multiple of 3
(amount of change) / (original amount)
The probability of event occurring is...

20. Number added or deleted
3-4-5 - 5-12-13 - 9-12-15
gcd(m,n)*lcm(m,n) = mn
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.

21. Price purchased for by wholesaler
n! / (n - r)!
Purchase price
P(event NOT occurring) = 1 - P(event occurring)
0.15n + 0.08(5) = 0.1(n+5)

22. In general - medium questions require how many steps to solve?
1 - P(E)
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 of bases)(height) / 2
2 steps

23. Combined Events: Not E = P(not E) = ?
-b +- sq. rt(b^2 - 4ac) / 2a
1 - P(E)
Organize into a grid.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

24. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
22
Sum of digits is multiple of 9
Group 1 + Group 2 + Neither - Both = Total

25. Percent Formula
2 steps
Immediately try factoring/simplifying when possible
p/100 = is/of
Odd

26. The number of ways independent events can occur together.
Balancing
(# of favorable outcomes) / (# of possible outcomes)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(total A) / (total B)

27. 5/6 = what %
0.15n + 0.08(5) = 0.1(n+5)
Exterior angle d is equal to the sum of the two remote interior angles a and b
83.3%
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

28. Average Rate: Average speed
sum = (average)(number of terms)
(# of favorable outcomes) / (# of possible outcomes)
(total distance) / (total time)
x(sq. rt 3) - x - 2x

29. 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?
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
Immediately try factoring/simplifying when possible
always try to factor
14 liters

30. 1/6 = what %
s Sq. rt (x^r)
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.
14 liters
16.6%

31. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.
sum = (average)(number of terms)
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

32. In general - difficult questions require how many steps to solve?
s Sq. rt (x^r)
Minor arc = 2(inscribed angle)
3-4-5 - 5-12-13 - 9-12-15
at least 3 steps

33. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.
83.3%

34. The number of outcomes that result in A divided by the total number of possible outcomes.
1
The probability of event occurring is...
y2 - y1 / x2 - x1
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.

35. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
sum = (average)(number of terms)
Sum of digits is multiple of 3
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.
22

36. 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.
Odd
P(E)P(F)
0.15n + 0.08(5) = 0.1(n+5)

37. 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.
(amount of change) / (original amount)
s Sq. rt (x^r)
Find all prime factors

38. 3^3 x 4^3 = ?
Find simple interest then look for the answer that is a little bigger
Organize into a grid.
12^3
y2 - y1 / x2 - x1

39. Permutations: Order Matters
Purchase price
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
x - x - x(sq. rt 2)
n! / (n - r)!

40. Set Problems formula
| A union B| = |A| + |B| - |A intersect B|
(x-n(n)y-n)
(amount of change) / (original amount)
Find all prime factors

41. 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.
3 - 6 - 9 - 12
16.6%
Purchase price

42. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
(sum of bases)(height) / 2
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1

43. Sum of consecutive numbers
sum = (average)(number of terms)
Find all prime factors
(n-1)!
22

44. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
D or E
x(sq. rt 3) - x - 2x
0.15n + 0.08(5) = 0.1(n+5)

45. Gross Profit formula
Find all prime factors
A = P(1 + r) ^n
Gross Profit = Selling Price - Cost
1/16

46. Sq. rt(2)
gcd(m,n)*lcm(m,n) = mn
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
12^3
1.4

47. Gross
The total amount before any deductions
1st Rule of Probability: Basic Rule is what?
Balancing
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

48. gcd(m,n)
Even
______ |m-n|
Sum of digits is multiple of 3
(n-1)!

49. Price sold for by retailer (after markup)
1 - P(E)
market value
(x-n(n)y-n)
Odd numbers only have ___________

50. Net
Sum of digits is multiple of 3
The amount after deductions
(total distance) / (total time)
(amount of change) / (original amount)