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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. 2n+1 - 2n+3 - 2n+5
Any multiplication involving an even number creates an even product.
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
1.7

2. 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.
A = P(1 + r) ^n
Figure out the probability for each individual event. Multiply the individual probabilities together.
(x-n(n)y-n)

3. Average Rate: Average A per B
Immediately UNFACTOR or vice versa
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.
12^3
(total A) / (total B)

4. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(n-1)!
$11 - 025
3 - 6 - 9 - 12

5. 1/8 = what %
12.5%
y2 - y1 / x2 - x1
x(sq. rt 3) - x - 2x
(total distance) / (total time)

6. Properties of 0
16.6%
1st Rule of Probability: Basic Rule is what?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
4/3 TT r ^3

7. Gross
The total amount before any deductions
y2 - y1 / x2 - x1
1/16
Group 1 + Group 2 + Neither - Both = Total

8. 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?
y2 - y1 / x2 - x1
Exterior angle d is equal to the sum of the two remote interior angles a and b
14 liters
22

9. Multiplication principle
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 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 total amount before any deductions
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

10. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
P(E)P(F)
2 steps
347
Balancing

11. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
(amount of change) / (original amount)
Find simple interest then look for the answer that is a little bigger
Find all prime factors

12. Trial Problems: look at the probability of NOT OCCURRING
P(E) + P(F) - P(E and F)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Immediately UNFACTOR or vice versa
P(event NOT occurring) = 1 - P(event occurring)

13. Gross Profit formula
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
P(E) + P(F) - P(E and F)
Gross Profit = Selling Price - Cost
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

14. 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
Last two digits are multiple of 4 or the number can be divided by 2 twice.
always try to factor
Balancing
Figure out the probability for each individual event. Multiply the individual probabilities together.

15. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
If the outcome of one event affects the outcome of the other event.
Balancing
Organize into a grid.

16. Formula for area of a Trapezoid
(sum of bases)(height) / 2
Immediately try factoring/simplifying when possible
s Sq. rt (x^r)
Exterior angle d is equal to the sum of the two remote interior angles a and b

17. 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.
Figure out the probability for each individual event. Multiply the individual probabilities together.
A = P(1 + r) ^n
22

18. Combined Events: E or F
$11 - 025
12.5%
0.15n + 0.08(5) = 0.1(n+5)
P(E) + P(F) - P(E and F)

19. Work problem rule
(x-n(n)y-n)
Minor arc = 2(inscribed angle)
83.3%
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.

20. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
principle (interest rate - in decimal form) (time - in years)
Find all prime factors
(amount of change) / (original amount)
A = P(1 + r) ^n

21. 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.
always try to factor
1/16
0.15n + 0.08(5) = 0.1(n+5)
Organize into a grid.

22. Triangle abc with d on the outside with a line. What does d = ?
$11 - 025
Exterior angle d is equal to the sum of the two remote interior angles a and b
p/100 = is/of
at least 3 steps

23. Sq. rt(2)
1.4
The amount after deductions
Principal (1 + interest/number times compounded)^(t)(n)
P(E)P(F)

24. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Immediately try factoring/simplifying when possible
gcd(m,n)*lcm(m,n) = mn
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Exterior angle d is equal to the sum of the two remote interior angles a and b

25. To determine multiple-event probability where each individual event must occur in a certain way.
(x-n(n)y-n)
A = P(1 + r) ^n
Figure out the probability for each individual event. Multiply the individual probabilities together.
(# of favorable outcomes) / (# of possible outcomes)

26. How to check whether a number is a multiple of 3.
y2 - y1 / x2 - x1
Sum of digits is multiple of 3
Even
Any multiplication involving an even number creates an even product.

27. How do you multiply roots together.
Divide 4999 by 15 => 333 integers
D or E
14 liters
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

28. When you see an equation in factored form in a question?
347
y2 - y1 / x2 - x1
Immediately UNFACTOR or vice versa
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

29. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
P(event NOT occurring) = 1 - P(event occurring)
Any multiplication involving an even number creates an even product.
Purchase price

30. 2n - 2n+2 - 2n+4
Purchase price
p/100 = is/of
Even
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.

31. Net
Principal (1 + interest/number times compounded)^(t)(n)
The amount after deductions
Balancing
1

32. Indistinguishable events how to find the number of permutations

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33. Prime Factorization to find Greatest Common Factor
Odd
-b +- sq. rt(b^2 - 4ac) / 2a
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
Divide 4999 by 15 => 333 integers

34. Permutations: Order Matters
(sum of bases)(height) / 2
4/3 TT r ^3
(# of favorable outcomes) / (# of possible outcomes)
n! / (n - r)!

35. 30-60-90 triangle basic lengths of sides
(total A) / (total B)
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.
x(sq. rt 3) - x - 2x
180(n-2)

36. In general - medium questions require how many steps to solve?
Purchase price
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
2 steps
P(E) + P(F) - P(E and F)

37. Price purchased for by wholesaler
Purchase price
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.
| A union B| = |A| + |B| - |A intersect B|
Exterior angle d is equal to the sum of the two remote interior angles a and b

38. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
(amount of change) / (original amount)
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.
1.4

39. 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
3-4-5 - 5-12-13 - 9-12-15
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
0.15n + 0.08(5) = 0.1(n+5)

40. Combined Events: Not E = P(not E) = ?
P(E) + P(F) - P(E and F)
1 - P(E)
If the outcome of one event affects the outcome of the other event.
1/16

41. (1/4)^2
Figure out the probability for each individual event. Multiply the individual probabilities together.
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
1/16
16.6%

42. Sq. rt(3)
Number is a multiple of 3 and 2
______ |m-n|
1.7
P(E) + P(F) - P(E and F)

43. 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?
1st Rule of Probability: Basic Rule is what?
0.15n + 0.08(5) = 0.1(n+5)
(n-1)!
1 - P(E)

44. gcd(m,n)*lcm(m,n)
Divide 4999 by 15 => 333 integers
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 9
(# of favorable outcomes) / (# of possible outcomes)

45. 1. A and B < A or B 2. A or B > Individual probabilities of A - B 3. P(A and B) = P(A) x P(B) <-- 'fewer options' 4. P(A or B) = P(A) + P(B) <-- 'more options' - Probability of multiple events rules.
Balancing
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.
1st Rule of Probability: Basic Rule is what?
n! / (n - r)!

46. Inscribed Angle - Minor Arc
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
14 liters
-b +- sq. rt(b^2 - 4ac) / 2a
Minor arc = 2(inscribed angle)

47. Price sold for by retailer (after markup)
347
market value
______ |m-n|
The amount after deductions

48. 1/6 = what %
Any multiplication involving an even number creates an even product.
Immediately try factoring/simplifying when possible
16.6%
______ |m-n|

49. Three triangle length patterns
1.4
Balancing
3-4-5 - 5-12-13 - 9-12-15
22

50. Set Problems formula
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(E) + P(F) - P(E and F)
Sum of digits is multiple of 3
(x-n(n)y-n)