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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. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
A = P(1 + r) ^n
22
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

2. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
0.15n + 0.08(5) = 0.1(n+5)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Find all prime factors

3. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
(n-1)!
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)
$11 - 025

4. 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)
y2 - y1 / x2 - x1
P(E) + P(F) - P(E and F)
A = P(1 + r) ^n

5. 0! = ?
1
The amount after deductions
Minor arc = 2(inscribed angle)
-b +- sq. rt(b^2 - 4ac) / 2a

6. Sq. rt(3)
Gross Profit = Selling Price - Cost
1.7
The probability of an event occurring plus the probability of the event not occurring = 1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

7. Average Rate: Average speed
market value
1
12.5%
(total distance) / (total time)

8. Simple probability
always try to factor
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.
Immediately UNFACTOR or vice versa
(# of favorable outcomes) / (# of possible outcomes)

9. Combined Events: E and F
n! / (n - r)!
(# of favorable outcomes) / (# of possible outcomes)
P(E)P(F)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

10. The number of outcomes that result in A divided by the total number of possible outcomes.
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
The probability of event occurring is...
Sum of digits is multiple of 3
n! / (n - r)!

11. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
P(E)P(F)
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
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

12. 5/6 = what %
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.
Gross Profit = Selling Price - Cost
The total amount before any deductions

13. Percent Formula
p/100 = is/of
Minor arc = 2(inscribed angle)
1
Principal (1 + interest/number times compounded)^(t)(n)

14. Net
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The amount after deductions
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.

15. 4th rule of Probability
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
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)
(n-1)!
(# of favorable outcomes) / (# of possible outcomes)

16. (1/4)^2
1/16
Odd numbers only have ___________
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
x - x - x(sq. rt 2)

17. gcd(m,n)
Sum of digits is multiple of 9
1
The total amount before any deductions
______ |m-n|

18. Formula for Mixed Group problems (involving Both/Neither)
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.
180(n-2)
Group 1 + Group 2 + Neither - Both = Total

19. Compound interest rule
n! / (n - r)!
Find simple interest then look for the answer that is a little bigger
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1

20. 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.
-b +- sq. rt(b^2 - 4ac) / 2a
______ |m-n|
1st Rule of Probability: Basic Rule is what?
Purchase price

21. How to check whether a number is a multiple of 6
The probability of an event occurring plus the probability of the event not occurring = 1
Number is a multiple of 3 and 2
12^3
(sum of bases)(height) / 2

22. Probability and Geometry.
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
x(sq. rt 3) - x - 2x
(sum of bases)(height) / 2

23. 2nd Rule of Probability: P(E) = 1 - P(not E)
Odd numbers only have ___________
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
22
The probability of an event occurring plus the probability of the event not occurring = 1

24. Percent increase = ?
Sum of digits is multiple of 3
0.15n + 0.08(5) = 0.1(n+5)
(amount of change) / (original amount)
(sum of bases)(height) / 2

25. Permutations: Order Matters
p/100 = is/of
4/3 TT r ^3
y2 - y1 / x2 - x1
n! / (n - r)!

26. In general - difficult questions require how many steps to solve?
The amount after deductions
Principal (1 + interest/number times compounded)^(t)(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.
at least 3 steps

27. What to do with equations that have fractions
Divide 4999 by 15 => 333 integers
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 9
(amount of change) / (original amount)

28. How to check for a prime number.

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29. In general - medium questions require how many steps to solve?
Sum of digits is multiple of 9
The total amount before any deductions
2 steps
347

30. 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
(x-n(n)y-n)
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.
(total distance) / (total time)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

31. Price purchased for by wholesaler
Purchase price
16.6%
If the outcome of one event affects the outcome of the other event.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

32. Odd and Even rule.
principle (interest rate - in decimal form) (time - in years)
Any multiplication involving an even number creates an even product.
P(E)P(F)
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)

33. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Figure out the probability for each individual event. Multiply the individual probabilities together.
-b +- sq. rt(b^2 - 4ac) / 2a
The amount after deductions

34. How to check whether number is multiple of 9
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Sum of digits is multiple of 9
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.
(amount of change) / (original amount)

35. Sum of consecutive numbers
sum = (average)(number of terms)
347
12.5%
Even

36. How to find the slope.
y2 - y1 / x2 - x1
If the outcome of one event affects the outcome of the other event.
principle (interest rate - in decimal form) (time - in years)
Principal (1 + interest/number times compounded)^(t)(n)

37. Number added or deleted
______ |m-n|
1.4
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)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

38. 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
Sum of digits is multiple of 3
Figure out the probability for each individual event. Multiply the individual probabilities together.
12^3
Balancing

39. Indistinguishable events how to find the number of permutations

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40. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
y2 - y1 / x2 - x1
-b +- sq. rt(b^2 - 4ac) / 2a
Immediately try factoring/simplifying when possible

41. 2n - 2n+2 - 2n+4
Gross Profit = Selling Price - Cost
Find simple interest then look for the answer that is a little bigger
Even
Principal (1 + interest/number times compounded)^(t)(n)

42. Compound interest formula
Group 1 + Group 2 + Neither - Both = Total
Principal (1 + interest/number times compounded)^(t)(n)
$11 - 025
Immediately try factoring/simplifying when possible

43. Price sold for by retailer (after markup)
P(event NOT occurring) = 1 - P(event occurring)
P(E) + P(F) - P(E and F)
market value
1/16

44. Formula for area of a Trapezoid
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
-b +- sq. rt(b^2 - 4ac) / 2a
The total amount before any deductions
(sum of bases)(height) / 2

45. 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
P(event NOT occurring) = 1 - P(event occurring)
Immediately UNFACTOR or vice versa
Group 1 + Group 2 + Neither - Both = Total

46. 3rd Rule of Probability: Conditional Probability
The amount after deductions
Divide 4999 by 15 => 333 integers
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.
If the outcome of one event affects the outcome of the other event.

47. Work problem rule
P(E) + P(F) - P(E and F)
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.
Find simple interest then look for the answer that is a little bigger
p/100 = is/of

48. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
14 liters
The total amount before any deductions
1.4

49. Set Problems formula
(x-n(n)y-n)
Balancing
(total A) / (total B)
Immediately try factoring/simplifying when possible

50. Gross Profit formula
Gross Profit = Selling Price - Cost
1
Sum of digits is multiple of 3 - last two digits multiple of 4.
A = P(1 + r) ^n