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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. Sq. rt(3)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
n! / (n - r)!
Divide 4999 by 15 => 333 integers
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.
D or E
$11 - 025
at least 3 steps

3. Gross Profit formula
Odd
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Gross Profit = Selling Price - Cost
Find simple interest then look for the answer that is a little bigger

4. (1/4)^2
The probability of event occurring is...
principle (interest rate - in decimal form) (time - in years)
market value
1/16

5. Volume of a sphere
1.4
4/3 TT r ^3
1
Balancing

6. 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
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.
Gross Profit = Selling Price - Cost
Principal (1 + interest/number times compounded)^(t)(n)

7. x^r/s = ?
s Sq. rt (x^r)
x(sq. rt 3) - x - 2x
sum = (average)(number of terms)
(amount of change) / (original amount)

8. What does the Sum of the angles in a Regular Polygon formula look like?
Immediately UNFACTOR or vice versa
Even
180(n-2)
The amount after deductions

9. How to check whether a number is a multiple of 4.
1/16
Purchase price
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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

10. Net
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.
Find simple interest then look for the answer that is a little bigger
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.
The amount after deductions

11. To determine multiple-event probability where each individual event must occur in a certain way.
1/16
Gross Profit = Selling Price - Cost
Figure out the probability for each individual event. Multiply the individual probabilities together.
3 - 6 - 9 - 12

12. 45-45-90 triangle basic lengths of sides
Principal (1 + interest/number times compounded)^(t)(n)
n! / (n - r)!
gcd(m,n)*lcm(m,n) = mn
x - x - x(sq. rt 2)

13. Always try to factor
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Sum of digits is multiple of 3
always try to factor
sum = (average)(number of terms)

14. In general - difficult questions require how many steps to solve?
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.
1
at least 3 steps
The total amount before any deductions

15. Formula for area of a Trapezoid
1.4
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.
(sum of bases)(height) / 2
1/16

16. Set Problems formula
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(sum of bases)(height) / 2
p/100 = is/of
(x-n(n)y-n)

17. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
1 - P(E)
A = P(1 + r) ^n
market value
1

18. gcd(m,n)
x(sq. rt 3) - x - 2x
______ |m-n|
y2 - y1 / x2 - x1
Divide 4999 by 15 => 333 integers

19. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 3
(total A) / (total B)
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.

20. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
A = P(1 + r) ^n
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
16.6%
D or E

21. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Find simple interest then look for the answer that is a little bigger
Gross Profit = Selling Price - Cost
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

22. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
Immediately try factoring/simplifying when possible
180(n-2)
Odd numbers only have ___________

23. How to check whether a number is a multiple of 12.
347
(total A) / (total B)
Sum of digits is multiple of 3 - last two digits multiple of 4.
at least 3 steps

24. How to check whether number is multiple of 9
Sum of digits is multiple of 9
180(n-2)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Organize into a grid.

25. 1/8 = what %
If the outcome of one event affects the outcome of the other event.
(x-n(n)y-n)
y2 - y1 / x2 - x1
12.5%

26. 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
Minor arc = 2(inscribed angle)
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
1/16

27. Formula for Mixed Group problems (involving Both/Neither)
The amount after deductions
market value
Group 1 + Group 2 + Neither - Both = Total
always try to factor

28. Gross
p/100 = is/of
The total amount before any deductions
Number is a multiple of 3 and 2
Minor arc = 2(inscribed angle)

29. Combined Events: Not E = P(not E) = ?
12^3
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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 - P(E)

30. How do you multiply roots together.
3 - 6 - 9 - 12
2 steps
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
at least 3 steps

31. 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
always try to factor
Odd numbers only have ___________
(n-1)!

32. When you see an equation in factored form in a question?
3-4-5 - 5-12-13 - 9-12-15
Immediately UNFACTOR or vice versa
12.5%
Any multiplication involving an even number creates an even product.

33. 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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
x - x - x(sq. rt 2)
Find all prime factors
1st Rule of Probability: Basic Rule is what?

34. Multiples of 3
16.6%
3 - 6 - 9 - 12
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
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

35. 2n+1 - 2n+3 - 2n+5
(# of favorable outcomes) / (# of possible outcomes)
Odd
Sum of digits is multiple of 3 - last two digits multiple of 4.
Sum of digits is multiple of 9

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.
principle (interest rate - in decimal form) (time - in years)
83.3%
Organize into a grid.
1.4

37. 4th rule of Probability
1
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.
0.15n + 0.08(5) = 0.1(n+5)
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)

38. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
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
22

39. What to do with equations that have fractions
Odd
(amount of change) / (original amount)
Immediately try factoring/simplifying when possible
0.15n + 0.08(5) = 0.1(n+5)

40. Indistinguishable events how to find the number of permutations

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41. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
p/100 = is/of
12^3
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.

42. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
16.6%
D or E
s Sq. rt (x^r)

43. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
x - x - x(sq. rt 2)
$11 - 025
16.6%
P(E) + P(F) - P(E and F)

44. Permutations: Order Matters
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)
n! / (n - r)!
Immediately try factoring/simplifying when possible

45. Triangle abc with d on the outside with a line. What does d = ?
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.
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
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.

46. Percent Formula
(# of favorable outcomes) / (# of possible outcomes)
p/100 = is/of
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.
The total amount before any deductions

47. Work problem rule
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)
principle (interest rate - in decimal form) (time - in years)
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-n(n)y-n)

48. The number of ways independent events can occur together.
22
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
P(event NOT occurring) = 1 - P(event occurring)
Number is a multiple of 3 and 2

49. 0! = ?
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
1
347
(total A) / (total B)

50. How to find all divisors of a number
1st Rule of Probability: Basic Rule is what?
180(n-2)
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.
Find all prime factors