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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. Price sold for by retailer (after markup)
sum = (average)(number of terms)
14 liters
Purchase price
market value

2. How to find the slope.
Exterior angle d is equal to the sum of the two remote interior angles a and b
y2 - y1 / x2 - x1
1
P(E)P(F)

3. Always try to factor
always try to factor
If the outcome of one event affects the outcome of the other event.
Odd
1/16

4. How to check whether a number is a multiple of 3.
83.3%
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Sum of digits is multiple of 3
s Sq. rt (x^r)

5. Properties of 0
(n-1)!
(sum of bases)(height) / 2
______ |m-n|
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

6. How to check whether number is multiple of 9
83.3%
Sum of digits is multiple of 9
A = P(1 + r) ^n
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.

7. Average Rate: Average speed
(total distance) / (total time)
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.
Find simple interest then look for the answer that is a little bigger
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.

8. When you see an equation in factored form in a question?
s Sq. rt (x^r)
Sum of digits is multiple of 3
3-4-5 - 5-12-13 - 9-12-15
Immediately UNFACTOR or vice versa

9. Percent increase = ?
3-4-5 - 5-12-13 - 9-12-15
Immediately try factoring/simplifying when possible
y2 - y1 / x2 - x1
(amount of change) / (original amount)

10. Quadratic formula
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)
y2 - y1 / x2 - x1
principle (interest rate - in decimal form) (time - in years)
-b +- sq. rt(b^2 - 4ac) / 2a

11. Average Rate: Average A per B
(total A) / (total B)
4/3 TT r ^3
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Immediately UNFACTOR or vice versa

12. Triangle abc with d on the outside with a line. What does d = ?
14 liters
Minor arc = 2(inscribed angle)
n! / (n - r)!
Exterior angle d is equal to the sum of the two remote interior angles a and b

13. x^r/s = ?
Find all prime factors
Odd
s Sq. rt (x^r)
| A union B| = |A| + |B| - |A intersect B|

14. Probability and Geometry.
12.5%
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
Organize into a grid.
A = P(1 + r) ^n

15. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Any multiplication involving an even number creates an even product.
(amount of change) / (original amount)
P(E) + P(F) - P(E and F)
22

16. 3^3 x 4^3 = ?
(amount of change) / (original amount)
12^3
22
The total amount before any deductions

17. 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
180(n-2)
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.
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)

18. Multiples of 3
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
83.3%
P(event NOT occurring) = 1 - P(event occurring)
3 - 6 - 9 - 12

19. How do you multiply roots together.
Find simple interest then look for the answer that is a little bigger
(amount of change) / (original amount)
Number is a multiple of 3 and 2
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

20. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
y2 - y1 / x2 - x1
Figure out the probability for each individual event. Multiply the individual probabilities together.
1
$11 - 025

21. What to do with equations that have fractions
n! / (n - r)!
Immediately try factoring/simplifying when possible
Immediately UNFACTOR or vice versa
1.4

22. Dependent events: When are two events said to be dependent events?
Exterior angle d is equal to the sum of the two remote interior angles a and b
Odd
If the outcome of one event affects the outcome of the other event.
x(sq. rt 3) - x - 2x

23. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
1 - P(E)
Divide 4999 by 15 => 333 integers
(x-n(n)y-n)
principle (interest rate - in decimal form) (time - in years)

24. Formula for area of a Trapezoid
1 - P(E)
A = P(1 + r) ^n
Organize into a grid.
(sum of bases)(height) / 2

25. Prime Factorization to find Greatest Common Factor
1.7
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
Purchase price
Any multiplication involving an even number creates an even product.

26. 5/6 = what %
Principal (1 + interest/number times compounded)^(t)(n)
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.
Group 1 + Group 2 + Neither - Both = Total

27. Set Problems formula
(x-n(n)y-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
Exterior angle d is equal to the sum of the two remote interior angles a and b
3-4-5 - 5-12-13 - 9-12-15

28. gcd(m,n)*lcm(m,n)
1/16
sum = (average)(number of terms)
Minor arc = 2(inscribed angle)
gcd(m,n)*lcm(m,n) = mn

29. Inscribed Angle - Minor Arc
D or E
14 liters
Sum of digits is multiple of 3
Minor arc = 2(inscribed angle)

30. How to check whether a number is a multiple of 12.
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.
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 3 - last two digits multiple of 4.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

31. How to check whether a number is a multiple of 4.
| A union B| = |A| + |B| - |A intersect B|
180(n-2)
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)

32. The number of ways independent events can occur together.
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)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Minor arc = 2(inscribed angle)
0.15n + 0.08(5) = 0.1(n+5)

33. 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.
gcd(m,n)*lcm(m,n) = mn
Purchase price
Odd

34. 45-45-90 triangle basic lengths of sides
1 - P(E)
Organize into a grid.
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.
x - x - x(sq. rt 2)

35. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Purchase price
Immediately try factoring/simplifying when possible

36. Combined Events: Not E = P(not E) = ?
1/16
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
22
1 - P(E)

37. To determine the number of integers less than 5000 that are evenly divisible by 15...?
P(E)P(F)
Divide 4999 by 15 => 333 integers
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Immediately UNFACTOR or vice versa

38. 1/8 = what %
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.
12.5%
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
1 - P(E)

39. How to check for a prime number.

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40. Intersecting Sets
Group 1 + Group 2 + Neither - Both = Total
P(event NOT occurring) = 1 - P(event occurring)
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
| A union B| = |A| + |B| - |A intersect B|

41. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
at least 3 steps
180(n-2)
The amount after deductions

42. Net
Even
The probability of event occurring is...
The amount after deductions
(# of favorable outcomes) / (# of possible outcomes)

43. 2n - 2n+2 - 2n+4
22
Even
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Odd

44. Multiplication principle
83.3%
(amount of change) / (original amount)
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

45. Percent Formula
p/100 = is/of
n! / (n - r)!
The amount after deductions
12^3

46. Formula for Mixed Group problems (involving Both/Neither)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Even
(total distance) / (total time)
Group 1 + Group 2 + Neither - Both = Total

47. Three triangle length patterns
1.7
3-4-5 - 5-12-13 - 9-12-15
Immediately try factoring/simplifying when possible
Number is a multiple of 3 and 2

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
(total A) / (total B)
Balancing
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/100 = is/of

49. The average of consecutive numbers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
16.6%
Organize into a grid.
1

50. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 3
1/16
D or E