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GMAT Quantitative General

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
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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. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
D or E
22
P(E)P(F)

2. How to check whether a number is a multiple of 12.
Odd numbers only have ___________
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.
-b +- sq. rt(b^2 - 4ac) / 2a
Sum of digits is multiple of 3 - last two digits multiple of 4.

3. 2n - 2n+2 - 2n+4
(x-n(n)y-n)
Even
P(E)P(F)
2 steps

4. The average of consecutive numbers
Any multiplication involving an even number creates an even product.
0.15n + 0.08(5) = 0.1(n+5)
16.6%
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

5. Sum of consecutive numbers
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)
sum = (average)(number of terms)
(total A) / (total B)
180(n-2)

6. Percent increase = ?
(total distance) / (total time)
principle (interest rate - in decimal form) (time - in years)
P(event NOT occurring) = 1 - P(event occurring)
(amount of change) / (original amount)

7. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
Immediately UNFACTOR or vice versa
The probability of an event occurring plus the probability of the event not occurring = 1
x(sq. rt 3) - x - 2x

8. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
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
Odd
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.

9. What to do with equations that have fractions
-b +- sq. rt(b^2 - 4ac) / 2a
1 - P(E)
at least 3 steps
Immediately try factoring/simplifying when possible

10. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
14 liters
gcd(m,n)*lcm(m,n) = mn
Odd

11. Multiples 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)
3 - 6 - 9 - 12
Balancing
at least 3 steps

12. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
3 - 6 - 9 - 12
P(E) + P(F) - P(E and F)
Even

13. 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
22
1st Rule of Probability: Basic Rule is what?
gcd(m,n)*lcm(m,n) = mn
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.

14. Set Problems formula
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(x-n(n)y-n)
Number is a multiple of 3 and 2

15. Multiplication principle
always try to factor
1st Rule of Probability: Basic Rule is what?
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
$11 - 025

16. How to check for a prime number.

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17. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Group 1 + Group 2 + Neither - Both = Total
D or E
A = P(1 + r) ^n
Find all prime factors

18. Intersecting Sets
The total amount before any deductions
Sum of digits is multiple of 9
| A union B| = |A| + |B| - |A intersect B|
Odd numbers only have ___________

19. gcd(m,n)*lcm(m,n)
at least 3 steps
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.
market value
gcd(m,n)*lcm(m,n) = mn

20. Combined Events: E and F
x - x - x(sq. rt 2)
Sum of digits is multiple of 3 - last two digits multiple of 4.
P(E)P(F)
Number is a multiple of 3 and 2

21. Formula for Mixed Group problems (involving Both/Neither)
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 amount after deductions
Group 1 + Group 2 + Neither - Both = Total
(amount of change) / (original amount)

22. Combined Events: E or 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
Purchase price
P(E) + P(F) - P(E and F)
2 steps

23. 5/6 = what %
Find all prime factors
D or E
83.3%
sum = (average)(number of terms)

24. Average Rate: Average A per B
(total A) / (total B)
(total distance) / (total time)
Find all prime factors
3 - 6 - 9 - 12

25. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
P(E) + P(F) - P(E and F)
market value
347

26. 1/8 = what %
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.
Principal (1 + interest/number times compounded)^(t)(n)
12.5%

27. 2nd Rule of Probability: P(E) = 1 - P(not E)
(total distance) / (total time)
The probability of an event occurring plus the probability of the event not occurring = 1
Immediately UNFACTOR or vice versa
Exterior angle d is equal to the sum of the two remote interior angles a and b

28. Permutations: Order Matters
(total distance) / (total time)
n! / (n - r)!
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.
3-4-5 - 5-12-13 - 9-12-15

29. Odd and Even rule.
Any multiplication involving an even number creates an even product.
Odd numbers only have ___________
(total distance) / (total time)
(sum of bases)(height) / 2

30. Number added or deleted
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
Odd
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 = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

31. Volume of a sphere
always try to factor
Sum of digits is multiple of 3
4/3 TT r ^3
P(E)P(F)

32. 0! = ?
1
Organize into a grid.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Any multiplication involving an even number creates an even product.

33. Price purchased for by wholesaler
Purchase price
180(n-2)
gcd(m,n)*lcm(m,n) = mn
Principal (1 + interest/number times compounded)^(t)(n)

34. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
Divide 4999 by 15 => 333 integers
s Sq. rt (x^r)
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)

35. Average Rate: Average speed
at least 3 steps
Immediately try factoring/simplifying when possible
(total distance) / (total time)
2 steps

36. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Divide 4999 by 15 => 333 integers
347
Number is a multiple of 3 and 2
Purchase price

37. Prime Factorization to find Greatest Common Factor
The total amount before any deductions
4/3 TT r ^3
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
y2 - y1 / x2 - x1

38. How to find the slope.
Odd numbers only have ___________
y2 - y1 / x2 - x1
Odd
The probability of event occurring is...

39. Quadratic formula
Any multiplication involving an even number creates an even product.
Number is a multiple of 3 and 2
Last two digits are multiple of 4 or the number can be divided by 2 twice.
-b +- sq. rt(b^2 - 4ac) / 2a

40. Gross
The total amount before any deductions
| A union B| = |A| + |B| - |A intersect B|
(sum of bases)(height) / 2
The amount after deductions

41. Sq. rt(2)
Odd numbers only have ___________
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.
1.4
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. 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.
180(n-2)
1st Rule of Probability: Basic Rule is what?
22
Any multiplication involving an even number creates an even product.

43. Compound interest formula
(amount of change) / (original amount)
p/100 = is/of
(sum of bases)(height) / 2
Principal (1 + interest/number times compounded)^(t)(n)

44. 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.
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
(total distance) / (total time)
Balancing

45. Formula for area of a Trapezoid
Principal (1 + interest/number times compounded)^(t)(n)
(sum of bases)(height) / 2
Exterior angle d is equal to the sum of the two remote interior angles a and b
Divide 4999 by 15 => 333 integers

46. 3^3 x 4^3 = ?
Find simple interest then look for the answer that is a little bigger
Sum of digits is multiple of 9
12^3
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)

47. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Purchase price
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
at least 3 steps
Exterior angle d is equal to the sum of the two remote interior angles a and b

48. In general - difficult questions require how many steps to solve?
(# of favorable outcomes) / (# of possible outcomes)
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
at least 3 steps

49. x^r/s = ?
always try to factor
s Sq. rt (x^r)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Odd numbers only have ___________

50. 2n+1 - 2n+3 - 2n+5
y2 - y1 / x2 - x1
Odd
Principal (1 + interest/number times compounded)^(t)(n)
D or E

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GMAT Quantitative General

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