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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. How to check whether number is multiple of 9
Sum of digits is multiple of 9
D or E
principle (interest rate - in decimal form) (time - in years)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

2. 3^3 x 4^3 = ?
$11 - 025
Find all prime factors
Principal (1 + interest/number times compounded)^(t)(n)
12^3

3. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(# of favorable outcomes) / (# of possible outcomes)

4. Average Rate: Average A per B
(total A) / (total B)
Divide 4999 by 15 => 333 integers
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Find simple interest then look for the answer that is a little bigger

5. Net
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
Immediately try factoring/simplifying when possible
83.3%
The amount after deductions

6. Multiples of 3
(# of favorable outcomes) / (# of possible outcomes)
1.7
| A union B| = |A| + |B| - |A intersect B|
3 - 6 - 9 - 12

7. 30-60-90 triangle basic lengths of sides
Immediately try factoring/simplifying when possible
x(sq. rt 3) - x - 2x
Figure out the probability for each individual event. Multiply the individual probabilities together.
Organize into a grid.

8. Sum of consecutive numbers
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%
sum = (average)(number of terms)
Purchase price

9. How to check whether a number is a multiple of 6
The probability of event occurring is...
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Number is a multiple of 3 and 2
gcd(m,n)*lcm(m,n) = mn

10. Combined Events: Not E = P(not E) = ?
347
1 - P(E)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Divide 4999 by 15 => 333 integers

11. Work problem rule
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Find all prime factors
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. In general - difficult questions require how many steps to solve?
1.4
at least 3 steps
Any multiplication involving an even number creates an even product.
3-4-5 - 5-12-13 - 9-12-15

13. How to find all divisors of a number
Find all prime factors
4/3 TT r ^3
$11 - 025
Any multiplication involving an even number creates an even product.

14. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
(amount of change) / (original amount)
$11 - 025
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Exterior angle d is equal to the sum of the two remote interior angles a and b

15. Percent Formula
p/100 = is/of
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
14 liters
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

16. 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.
(# of favorable outcomes) / (# of possible outcomes)
market value
Balancing

17. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
P(E)P(F)
D or E

18. Prime Factorization to find Greatest Common Factor
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(amount of change) / (original amount)
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...

19. x^r/s = ?
always try to factor
s Sq. rt (x^r)
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 9

20. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
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
12.5%
347

21. (1/4)^2
1/16
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
(total distance) / (total time)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

22. 3rd Rule of Probability: Conditional Probability
(n-1)!
p/100 = is/of
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 = P(1 + r) ^n

23. Three triangle length patterns
p/100 = is/of
3-4-5 - 5-12-13 - 9-12-15
(total A) / (total B)
1

24. Price sold for by retailer (after markup)
Group 1 + Group 2 + Neither - Both = Total
Organize into a grid.
Figure out the probability for each individual event. Multiply the individual probabilities together.
market value

25. 4th rule of Probability
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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)
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/100 = is/of

26. Odd Factors
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.
4/3 TT r ^3
Minor arc = 2(inscribed angle)
Odd numbers only have ___________

27. Sq. rt(3)
1 - P(E)
1.7
Sum of digits is multiple of 3 - last two digits multiple of 4.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

28. 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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.

29. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 3 - last two digits multiple of 4.
-b +- sq. rt(b^2 - 4ac) / 2a
sum = (average)(number of terms)

30. Permutations: Order Matters
n! / (n - r)!
Divide 4999 by 15 => 333 integers
(amount of change) / (original amount)
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.

31. 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.
Principal (1 + interest/number times compounded)^(t)(n)
1st Rule of Probability: Basic Rule is what?
1.4
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.

32. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
(total distance) / (total time)
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
12^3

33. How do you multiply roots together.
(sum of bases)(height) / 2
(amount of change) / (original amount)
D or E
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

34. Percent increase = ?
Odd
(sum of bases)(height) / 2
-b +- sq. rt(b^2 - 4ac) / 2a
(amount of change) / (original amount)

35. 1/6 = what %
| A union B| = |A| + |B| - |A intersect B|
The probability of an event occurring plus the probability of the event not occurring = 1
16.6%
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

36. Always try to factor
The probability of event occurring is...
at least 3 steps
always try to factor
180(n-2)

37. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
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)
Figure out the probability for each individual event. Multiply the individual probabilities together.
______ |m-n|

38. Indistinguishable events how to find the number of permutations

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39. Average Rate: Average speed
4/3 TT r ^3
Figure out the probability for each individual event. Multiply the individual probabilities together.
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.
(total distance) / (total time)

40. Probability and Geometry.
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.
2 steps
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
(sum of bases)(height) / 2

41. Dependent events: When are two events said to be dependent events?
always try to factor
If the outcome of one event affects the outcome of the other event.
The probability of event occurring is...
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

42. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
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
p/100 = is/of
(x-n(n)y-n)

43. When you see an equation in factored form in a question?
0.15n + 0.08(5) = 0.1(n+5)
x - x - x(sq. rt 2)
Immediately UNFACTOR or vice versa
1.7

44. Price purchased for by wholesaler
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
Exterior angle d is equal to the sum of the two remote interior angles a and b
-b +- sq. rt(b^2 - 4ac) / 2a
Purchase price

45. Combined Events: E and F
Divide 4999 by 15 => 333 integers
Figure out the probability for each individual event. Multiply the individual probabilities together.
principle (interest rate - in decimal form) (time - in years)
P(E)P(F)

46. How to check for a prime number.

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47. To determine multiple-event probability where each individual event must occur in a certain way.
Immediately try factoring/simplifying when possible
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Figure out the probability for each individual event. Multiply the individual probabilities together.
Minor arc = 2(inscribed angle)

48. 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)
P(E) + P(F) - P(E and F)
The total amount before any deductions
Even

49. gcd(m,n)
$11 - 025
Immediately try factoring/simplifying when possible
______ |m-n|
1st Rule of Probability: Basic Rule is what?

50. 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)
The probability of event occurring is...
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.
347