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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. 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
y2 - y1 / x2 - x1
Organize into a grid.
Sum of digits is multiple of 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.

2. In general - medium questions require how many steps to solve?
2 steps
Odd numbers only have ___________
16.6%
12.5%

3. (1/4)^2
1/16
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.
______ |m-n|
16.6%

4. 3^3 x 4^3 = ?
12^3
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.
-b +- sq. rt(b^2 - 4ac) / 2a
gcd(m,n)*lcm(m,n) = mn

5. How to check whether a number is a multiple of 4.
n! / (n - r)!
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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
______ |m-n|

6. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
p/100 = is/of
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(E) + P(F) - P(E and F)

7. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Organize into a grid.
If the outcome of one event affects the outcome of the other event.
$11 - 025
Immediately try factoring/simplifying when possible

8. Trial Problems: look at the probability of NOT OCCURRING
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
22
P(event NOT occurring) = 1 - P(event occurring)
at least 3 steps

9. Three triangle length patterns
1
The total amount before any deductions
3-4-5 - 5-12-13 - 9-12-15
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.

10. 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.
$11 - 025
(amount of change) / (original amount)
1.4
Organize into a grid.

11. Triangle abc with d on the outside with a line. What does d = ?
x(sq. rt 3) - x - 2x
Exterior angle d is equal to the sum of the two remote interior angles a and b
(n-1)!
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. Indistinguishable events how to find the number of permutations

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13. Multiplication principle
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
0.15n + 0.08(5) = 0.1(n+5)
(x-n(n)y-n)
s Sq. rt (x^r)

14. x^r/s = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
s Sq. rt (x^r)
Divide 4999 by 15 => 333 integers
P(event NOT occurring) = 1 - P(event occurring)

15. What does the Sum of the angles in a Regular Polygon formula look like?
P(E)P(F)
at least 3 steps
(amount of change) / (original amount)
180(n-2)

16. Sum of consecutive numbers
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(amount of change) / (original amount)
sum = (average)(number of terms)
Find simple interest then look for the answer that is a little bigger

17. Average Rate: Average A per B
n! / (n - r)!
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.
Minor arc = 2(inscribed angle)
(total A) / (total B)

18. Gross Profit formula
Gross Profit = Selling Price - Cost
The probability of an event occurring plus the probability of the event not occurring = 1
Principal (1 + interest/number times compounded)^(t)(n)
s Sq. rt (x^r)

19. Sq. rt(3)
12.5%
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1.7
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

20. The number of outcomes that result in A divided by the total number of possible outcomes.
1.4
3-4-5 - 5-12-13 - 9-12-15
Any multiplication involving an even number creates an even product.
The probability of event occurring is...

21. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Immediately try factoring/simplifying when possible
347
(total distance) / (total time)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

22. How to check for a prime number.

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23. 3rd Rule of Probability: Conditional Probability
A = P(1 + r) ^n
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.
market value
1 - P(E)

24. 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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Immediately try factoring/simplifying when possible

25. 5/6 = what %
Principal (1 + interest/number times compounded)^(t)(n)
at least 3 steps
Last two digits are multiple of 4 or the number can be divided by 2 twice.
83.3%

26. 45-45-90 triangle basic lengths of sides
Organize into a grid.
x - x - x(sq. rt 2)
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
Balancing

27. 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?
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.
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.
Organize into a grid.
14 liters

28. 1/8 = what %
Find simple interest then look for the answer that is a little bigger
12.5%
y2 - y1 / x2 - x1
Exterior angle d is equal to the sum of the two remote interior angles a and b

29. Percent increase = ?
(amount of change) / (original amount)
(x-n(n)y-n)
s Sq. rt (x^r)
D or E

30. Volume of a sphere
Group 1 + Group 2 + Neither - Both = Total
4/3 TT r ^3
3-4-5 - 5-12-13 - 9-12-15
180(n-2)

31. How to check whether a number is a multiple of 3.
22
Sum of digits is multiple of 3
x(sq. rt 3) - x - 2x
n! / (n - r)!

32. How to check whether number is multiple of 9
The probability of event occurring is...
Exterior angle d is equal to the sum of the two remote interior angles a and b
Sum of digits is multiple of 9
3 - 6 - 9 - 12

33. Net
(# of favorable outcomes) / (# of possible outcomes)
1
The amount after deductions
(n-1)!

34. To determine multiple-event probability where each individual event must occur in a certain way.
2 steps
(total distance) / (total time)
1.7
Figure out the probability for each individual event. Multiply the individual probabilities together.

35. 1/6 = what %
The probability of event occurring is...
16.6%
D or E
347

36. Combined Events: Not E = P(not E) = ?
1 - P(E)
x(sq. rt 3) - x - 2x
-b +- sq. rt(b^2 - 4ac) / 2a
1/16

37. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
(total A) / (total 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.
market value
principle (interest rate - in decimal form) (time - in years)

38. Combined Events: E or F
(total A) / (total B)
P(E) + P(F) - P(E and F)
D or E
2 steps

39. Formula for area of a Trapezoid
(sum of bases)(height) / 2
x(sq. rt 3) - x - 2x
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
market value

40. The average of consecutive numbers
Find all prime factors
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
4/3 TT r ^3
The probability of event occurring is...

41. 2nd Rule of Probability: P(E) = 1 - P(not E)
3 - 6 - 9 - 12
The probability of an event occurring plus the probability of the event not occurring = 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)

42. Properties of 0
Figure out the probability for each individual event. Multiply the individual probabilities together.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(total distance) / (total time)
______ |m-n|

43. How to find all divisors of a number
p/100 = is/of
Find all prime factors
The total amount before any deductions
Divide 4999 by 15 => 333 integers

44. When you see an equation in factored form in a question?
1
Gross Profit = Selling Price - Cost
(total A) / (total B)
Immediately UNFACTOR or vice versa

45. gcd(m,n)*lcm(m,n)
0.15n + 0.08(5) = 0.1(n+5)
gcd(m,n)*lcm(m,n) = mn
y2 - y1 / x2 - x1
(total distance) / (total time)

46. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
0.15n + 0.08(5) = 0.1(n+5)
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)
at least 3 steps

47. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Purchase price
22
83.3%
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.

48. 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
347
Balancing
4/3 TT r ^3
______ |m-n|

49. 2n - 2n+2 - 2n+4
Even
A = P(1 + r) ^n
| A union B| = |A| + |B| - |A intersect B|
$11 - 025

50. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
22
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.
83.3%