Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

GMAT > Algebra > Flashcards

Algebra Flashcards

1
Q

(x+y)^2 - (x-y)^2

A

4xy

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

(x+y+z)^2

A

x^2 + y^2 + z^2 + 2(xy + xz + yz)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

x^3 + y^3

A

(x+y)(x^2 + y^2 - xy)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

x^3 - y^3

A

(x-y)(x^2 +y^2 +xy)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

T or F. a^n - b^n is always divisible by a- b

A

T

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

a^n - b^n is divisible by a+b if

A

n is even

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

a^n + b^n is divisible by a+b if

A

n is odd

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

How do you express negative exponents ?

A

reciprocal of the inside base and turn negative to positive exponent

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

T or F. if 0^x = 0 = 0^y , x is equal to y

A

False. 0^4 = 0 = 0^3 but 4 ≠ 3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

How do you express exponential growth formula?

A

y(t) = y(0).k^t

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

T or F. In GMAT, you should always subtract or divide two inequalities

A

F. You should never

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

If 0< G < 1 then how does G^n compare to G (if n is odd/even positive integer)

A

G^n is less than original G

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

If 0< G < 1 then how does G^n compare to G (if n is odd/even negative integer)

A

G^n is larger than original G

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

If -1< G < 0 then how does G^n compare to G (if n is odd/even positive integer)

A

G^n is larger than original G

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

If -1< G < 0 then how does G^n compare to G (if n is odd/even negative integer)

A

G^n is larger than original G (if n is even)

G^n is smaller than original G (if n is odd)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

T or F. If both sides are known to be negative, you can’t flip the inequalities sign when you square

A

False. You can flip the sign.

Ex: -4 < - 3 then 16 > 9

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

T or F. If both sides are known to be positive, you don’t flip the inequalities sign when you square

A

True.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

T or F. If one side is positive and one side is negative, the inequality sign stays when you square

A

False.

it may or may not

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

T or F. If the signs are unclear, then you cannot square

A

True.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

If x < y, then how does 1/x compare to 1/y when x and y are both positive or both negative?

A

1/x > 1/y (flip the sign)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

If x < y, then how does 1/x compare to 1/y when x is negative and y is positive?

A

1/x < 1/y

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

T or F. If you don’t know the sign of x or y, you can still take the reciprocals.

A

False.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

if |x| > a then:

A

x > a or x < -a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

if |x| < a then:

A

-a < x < a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

If |A| = |B| then

A 
A = B or 
A = - B
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

What is the equation expression for directional proportionality?

A

y(1)/ x(1) = y(2)/ x(2)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

What is the equation expression for inverse proportionality?

A

y(1) . x(1) = y(2) . x(2)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

When 0< G < 1, G^n < G if

A

n is positive integer

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

When 0< G < 1, G^n > G if

A

n is negative integer

30
Q

When -1 < G < 0, G^n < G if

A

n is odd negative integer

31
Q

When -1< G< 0, G^n > G if

A

n is positive integer or

n is negative even integer

32
Q

square root of 2

A

about 1.4

33
Q

square root of 3

A

about 1.7

34
Q

square root of 5

A

around 2.25

35
Q

square root of 121

A

11

36
Q

square root of 144

A

12

37
Q

13^2

A

169

38
Q

square root of 196

A

14

39
Q

square root of 225

A

15

40
Q

square root of 256

A

16

41
Q

square root of 625

A

25

42
Q

G^n < G when

A

0< G < 1

-1 < G < 0 if n is negative odd

43
Q

G^n > G when

A

n is negative for 0< G < 1
n is negative even for -1< G < 0
n is positive for -1< G < 0

44
Q

T or F. Any positive proper fraction raised to a power between 0 and 1 will result in a number larger than the original fraction.

A

T (problem #3 p. 125 Manhattan)

45
Q

T or F. Any positive proper fraction raised to a power greater than 1 will result in a number larger than the original fraction.

A

F.

46
Q

How do you translate “The retailer has less than twice as many radios as clocks in inventory” in math expression?

A

r < 2c

47
Q

How do we know a quadratic function has a solution or not?

A

if the discriminant (b^2 - 4ac) < 0, = 0 or > 0

48
Q

If the discriminant is greater than zero, then how many solutions are there?

A

two

49
Q

If the discriminant is equal to zero, then how many solutions are there?

A

one solution

50
Q

If the discriminant is less than zero, then how many solutions are there?

A

no solution

51
Q

The answer (A) in data sufficiency is?

A

Statement (1) alone is sufficient, but statement (2) is not

52
Q

The answer (B) in data sufficiency is?

A

Statement (2) alone is sufficient, but statement (1) is not

53
Q

The answer (C) in data sufficiency is?

A

Both statement together are sufficient, but neither statement alone is sufficient

54
Q

The answer (D) in data sufficiency is?

A

EACH statement ALONE is sufficient

55
Q

The answer (E) in data sufficiency is?

A

Statement (1) and (2) TOGETHER are NOT sufficient.

56
Q

The trick to translate fractional exponent of a number to a root

A

denominator OUT

numerator IN

57
Q

The trick to translate a root to fraction exponent

A

in NUMERATOR

out DENOMINATOR

58
Q

Can absolute value result in negative number?

A

NO. its results are always greater than 0

59
Q

x^0 = ?

A

1

60
Q

0^x = ?

A

0

61
Q

proper fraction

A

a fraction between 0 and 1

62
Q

How do you express proper fraction with decimals with exponents?

Ex: (0.6)^2 (0.5)^4 (0.1)^5

A

The decimals move to the left in accordance with the value of exponent after exponent non-zero digits.

Ex: (0.6)^2= 0.36

(0. 5)^2 = 0.0625
(0. 1)^5 = 0.00001

63
Q

what is the value of 0^0 ?

A

undefined

64
Q

T or F. There is no solution for the even root of a negative number

A

T

65
Q

What does x^2 - x < 0 imply?

A

x^2 < x, so 0 < x < 1

66
Q

square root of 324

A

18

67
Q

square root of 289

A

17

68
Q

19^2

A

361

69
Q

What is the vertex (x,y) of equation:

a(x-h)^2 + k = 0

A

(h,k)

70
Q

T or F. Any two points the same distance from the origin along perpendicular lines will have the opposite coordinates from one another - if one point is (a,b), the other will be (b,a)

A

True.

71
Q

T or F. In x-y plane, the quadrants is upper shaded area if the inequality is equal to or greater (>=)

A

True.

72
Q

T or F. In x-y plane, the quadrants is below shaded area if the inequality is equal to or less (=

A

True.

GMAT (9 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions