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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 find all divisors of a number
Find all prime factors
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
Odd

2. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
P(event NOT occurring) = 1 - P(event occurring)
Odd
347
14 liters

3. Sq. rt(3)
The amount after deductions
1.7
347
D or E

4. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Number is a multiple of 3 and 2
principle (interest rate - in decimal form) (time - in years)
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.
p/100 = is/of

5. Odd and Even rule.
Any multiplication involving an even number creates an even product.
x(sq. rt 3) - x - 2x
180(n-2)
x - x - x(sq. rt 2)

6. Permutations: Order Matters
n! / (n - r)!
Find all prime factors
The amount after deductions
p/100 = is/of

7. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
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)!
Odd numbers only have ___________

8. In general - medium questions require how many steps to solve?
Find simple interest then look for the answer that is a little bigger
2 steps
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 9

9. 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
Even
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(sum of bases)(height) / 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.

10. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
y2 - y1 / x2 - x1
Last two digits are multiple of 4 or the number can be divided by 2 twice.
gcd(m,n)*lcm(m,n) = mn

11. Prime Factorization to find Greatest Common Factor
Any multiplication involving an even number creates an even product.
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
n! / (n - r)!

12. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
Number is a multiple of 3 and 2
1/16
p/100 = is/of

13. The average of consecutive numbers
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 A) / (total B)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Sum of digits is multiple of 3

14. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
(# of favorable outcomes) / (# of possible outcomes)
s Sq. rt (x^r)
The probability of event occurring is...

15. 2n - 2n+2 - 2n+4
Even
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
at least 3 steps
(n-1)!

16. Average Rate: Average speed
principle (interest rate - in decimal form) (time - in years)
P(event NOT occurring) = 1 - P(event occurring)
Purchase price
(total distance) / (total time)

17. Percent increase = ?
347
Balancing
(amount of change) / (original amount)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

18. In general - difficult questions require how many steps to solve?
4/3 TT r ^3
at least 3 steps
P(event NOT occurring) = 1 - P(event occurring)
14 liters

19. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
P(E) + P(F) - P(E and F)
1/16
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Even

20. 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?
(amount of change) / (original amount)
0.15n + 0.08(5) = 0.1(n+5)
83.3%
The amount after deductions

21. Net
Sum of digits is multiple of 9
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
The amount after deductions

22. 3rd Rule of Probability: Conditional 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.
Group 1 + Group 2 + Neither - Both = Total
Divide 4999 by 15 => 333 integers

23. 4th rule of Probability
gcd(m,n)*lcm(m,n) = mn
Odd numbers only have ___________
180(n-2)
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)

24. 1/6 = what %
x(sq. rt 3) - x - 2x
180(n-2)
16.6%
(n-1)!

25. 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?
Gross Profit = Selling Price - Cost
Odd
market value
14 liters

26. Combined Events: E and F
s Sq. rt (x^r)
P(E)P(F)
-b +- sq. rt(b^2 - 4ac) / 2a
P(E) + P(F) - P(E and F)

27. Gross
16.6%
The total amount before any deductions
2 steps
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.

28. Average Rate: Average A per B
1.7
Figure out the probability for each individual event. Multiply the individual probabilities together.
(total A) / (total B)
______ |m-n|

29. 1/8 = what %
Even
12.5%
Exterior angle d is equal to the sum of the two remote interior angles a and b
s Sq. rt (x^r)

30. 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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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 number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

31. How to check whether number is multiple of 9
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)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Sum of digits is multiple of 9

32. 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.
A = P(1 + r) ^n
(amount of change) / (original amount)
Minor arc = 2(inscribed angle)

33. Three triangle length patterns
14 liters
Organize into a grid.
3-4-5 - 5-12-13 - 9-12-15
Odd numbers only have ___________

34. 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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
1st Rule of Probability: Basic Rule is what?
Immediately try factoring/simplifying when possible
P(event NOT occurring) = 1 - P(event occurring)

35. How to check for a prime number.

36. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
Balancing
1
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

37. Multiples of 3
12^3
1st Rule of Probability: Basic Rule is what?
(n-1)!
3 - 6 - 9 - 12

38. Sq. rt(2)
s Sq. rt (x^r)
market value
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)
1.4

39. 2nd Rule of Probability: P(E) = 1 - P(not E)
Number is a multiple of 3 and 2
3-4-5 - 5-12-13 - 9-12-15
(amount of change) / (original amount)
The probability of an event occurring plus the probability of the event not occurring = 1

40. 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
Balancing
Immediately UNFACTOR or vice versa
4/3 TT r ^3
If the outcome of one event affects the outcome of the other event.

41. To determine multiple-event probability where each individual event must occur in a certain way.
$11 - 025
gcd(m,n)*lcm(m,n) = mn
0.15n + 0.08(5) = 0.1(n+5)
Figure out the probability for each individual event. Multiply the individual probabilities together.

42. What to do with equations that have fractions
gcd(m,n)*lcm(m,n) = mn
(sum of bases)(height) / 2
Immediately try factoring/simplifying when possible
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.

43. 2n+1 - 2n+3 - 2n+5
Immediately try factoring/simplifying when possible
Odd
$11 - 025
1.7

44. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
P(event NOT occurring) = 1 - P(event occurring)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
sum = (average)(number of terms)
A = P(1 + r) ^n

45. How to check whether a number is a multiple of 6
| A union B| = |A| + |B| - |A intersect B|
Number is a multiple of 3 and 2
(amount of change) / (original amount)
(total A) / (total B)

46. 5/6 = what %
D or E
at least 3 steps
Exterior angle d is equal to the sum of the two remote interior angles a and b
83.3%

47. Formula for area of a Trapezoid
(sum of bases)(height) / 2
(amount of change) / (original amount)
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

48. Quadratic formula
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.
Odd
180(n-2)
-b +- sq. rt(b^2 - 4ac) / 2a

49. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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
Purchase price

50. 0! = ?
Immediately try factoring/simplifying when possible
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
1